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The Chemistry of Extrasolar Planetary Systems

Item Type text; Electronic Dissertation

Authors Bond, Jade

Publisher The University of Arizona.

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Link to Item http://hdl.handle.net/10150/194946

http://hdl.handle.net/10150/194946

THE CHEMISTRY OF EXTRASOLAR PLANETARY SYSTEMS

by

Jade Chantelle Bond

A Dissertation Submitted to the Faculty of the

DEPARTMENT OF PLANETARY SCIENCES

In Partial Fulfillment of the RequirementsFor the Degree of

DOCTOR OF PHILOSOPHY

In the Graduate College

THE UNIVERSITY OF ARIZONA

2 0 0 8

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THE UNIVERSITY OF ARIZONAGRADUATE COLLEGE

As members of the Final Examination Committee, we certify that we have read the dis-sertation prepared by Jade Chantelle Bond entitled The Chemistry of Extrasolar PlanetarySystems and recommend that it be accepted as fulfilling the dissertation requirement forthe Degree of Doctor of Philosophy.

Date: 31 October 2008Dante S. Lauretta

Date: 31 October 2008Michael J. Drake

Date: 31 October 2008David P. O’Brien

Date: 31 October 2008Michael R. Meyer

Date: 31 October 2008Adam P. Showman

Final approval and acceptance of this dissertation is contingent upon the candidate’ssubmission of the final copies of the dissertation to the Graduate College.

I hereby certify that I have read this dissertation prepared under my direction andrecommend that it be accepted as fulfilling the dissertation requirement.

Date: 31 October 2008Dissertation Director: Dante S. Lauretta

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STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of requirements for an advanceddegree at The University of Arizona and is deposited in the University Library to be madeavailable to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission, pro-vided that accurate acknowledgment of source is made. Requests for permission for ex-tended quotation from or reproduction of this manuscript in whole or in part may begranted by the head of the major department or the Dean of the Graduate College whenin his or her judgment the proposed use of the material is in the interests of scholarship.In all other instances, however, permission must be obtained from the author.

SIGNED: Jade Chantelle Bond

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ACKNOWLEDGMENTS

Science, like most other activities in life, is a collaborative effort and as such there aremany people who deserve thanks for their assistance with producing my dissertation. Firstand foremost, I’d like to thank my Ph.D. advisor, Dr. Dante Lauretta, for his invaluablesupport and guidance throughout my time with him. There is simply no way that this workcould have been completed without his assistance, both professionally and personally,along with the support of his wife, Kate. For that, I am beyond grateful.

David O’Brien deserves a massive thank you for the incredible support and assis-tance he has provided through out my entire PhD. From first helping me to move in toHawthorne House to now providing me with countless simulations, his support has beenamazing and I am so incredibly grateful for it.

Chris Tinney has truly been an outstanding collaborator, supporter and friend through-out the development of my scientific career. His assistance and guidance have been amaz-ing and I am so grateful he took a chance on me. Similarly, Jay Melosh has always beenwilling to listen and help in any problems I may have had throughout my entire PhDstudy. His advice and assistance are greatly appreciated. I am very pleased to be able tocall both of them friends.

I’d also like to thank my entire PhD Committee for their support, ideas, feedback,assistance and tolerating a defence on Halloween! I found their guidance and ideas to beuseful in developing this work. A thank you also goes to the entire Nine Circles researchgroup (especially Glinda!) for all of their ideas and assistance and the Anglo-AustralianPlanet Search (AAPS) group for being so generous with their data.

Thank you to Michael Meyer, Cathi Duncan and the LAPLACE group for their finan-cial support, including sending me to conferences in all the cool places!

On a special note, I must thank Kathryn Gardner-Vandy, Kelly Kolb, Sarah Horst andKristin Block for putting up with me, girls nights out, giving me a break and generallybeing wonderful friends, Eve Berger for going above and beyond, Mike and Jenny Blandand Matt Pasek for simply understanding and helping me to stay sane, David Choi andColin Dundas for eating Tim Tams and gossiping, the Chamberlain Clan for their Aussiefixes, Bob Marcialis for reading numerous drafts while sending me both sane and insaneand Pete Lanagan for being . . . well, Pete.

Thank you also to the artists of the comics featured through out this dissertation andtheir syndications for allowing me to reprint them in this work.

Thank you, Hagen, for being so supportive and not grumbling too much at all of theearly morning phone calls.

Last, but certainly not least, a huge thank you goes to my Mum who always got it,even when no-one else around me did.

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DEDICATION

For Lillian and Frank Bond.

“Now, Voyager, sail thou forth, to seek and find.”

-Walt Whitman, Leaves of Grass 1900

Figure 1: CALVIN AND HOBBES (C) 1986 Watterson. Dist. By UNIVERSAL PRESSSYNDICATE. Reprinted with permission. All rights reserved. Originally published3/17/1986.

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TABLE OF CONTENTS

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

CHAPTER 1 INTRODUCTION & BACKGROUND . . . . . . . . . . . . . . . 181.1 History of Extrasolar Planets . . . . . . . . . . . . . . . . . . . . . . . . 181.2 Planetary System Chemical Properties . . . . . . . . . . . . . . . . . . . 191.3 Terrestrial Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.4 Summary of Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

CHAPTER 2 R- AND S-PROCESS ELEMENTAL ABUNDANCES IN STARSWITH PLANETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2.1 Target Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.2 Spectroscopic Analysis . . . . . . . . . . . . . . . . . . . . . . . 28

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.4 Host Star Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.4.1 Enrichment over Solar . . . . . . . . . . . . . . . . . . . . . . . 322.4.2 Enrichment over Non-Host Stars . . . . . . . . . . . . . . . . . . 33

2.5 Elemental Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.5.1 Lighter Element Trends . . . . . . . . . . . . . . . . . . . . . . 382.5.2 Heavy Element Trends . . . . . . . . . . . . . . . . . . . . . . . 402.5.3 Correlation with Planetary Parameters . . . . . . . . . . . . . . . 422.5.4 Correlation with Stellar Parameters . . . . . . . . . . . . . . . . 42

2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

CHAPTER 3 SOLAR SYSTEM SIMULATIONS . . . . . . . . . . . . . . . . . 473.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.2.1 Dynamical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.2 Chemical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.3 Combining Dynamics and Chemistry . . . . . . . . . . . . . . . 59

TABLE OF CONTENTS – Continued

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3.2.4 Stellar Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . 593.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.3.1 Abundance Trends . . . . . . . . . . . . . . . . . . . . . . . . . 623.3.2 Variations with Time . . . . . . . . . . . . . . . . . . . . . . . . 763.3.3 Late Veneer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.3.4 Hydrous Species . . . . . . . . . . . . . . . . . . . . . . . . . . 803.3.5 Volatile Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.3.6 Solar Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

CHAPTER 4 EXTRASOLAR PLANETARY SYSTEM SIMULATIONS . . . . 944.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.2 System Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.3.1 Extrasolar Planetary Systems . . . . . . . . . . . . . . . . . . . . 1064.3.2 Dynamical Simulations . . . . . . . . . . . . . . . . . . . . . . . 1104.3.3 Chemical Simulations . . . . . . . . . . . . . . . . . . . . . . . 1154.3.4 Combining Dynamics and Chemistry . . . . . . . . . . . . . . . 1194.3.5 Stellar Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1224.4.1 Dynamical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1224.4.2 Chemical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1324.4.3 Stellar Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . 155

4.5 Implications and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 1634.5.1 Frequency of Terrestrial Planets . . . . . . . . . . . . . . . . . . 1634.5.2 Planetary Types . . . . . . . . . . . . . . . . . . . . . . . . . . . 1634.5.3 Timing of Formation . . . . . . . . . . . . . . . . . . . . . . . . 1644.5.4 Detection of Terrestrial Planets . . . . . . . . . . . . . . . . . . . 1654.5.5 Hydrous Species . . . . . . . . . . . . . . . . . . . . . . . . . . 1674.5.6 Planetary Interiors and Processes . . . . . . . . . . . . . . . . . . 1714.5.7 Planet Habitability . . . . . . . . . . . . . . . . . . . . . . . . . 1754.5.8 Biologically Important Elements . . . . . . . . . . . . . . . . . . 1774.5.9 Mass Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 1784.5.10 Stellar Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . 181

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

CHAPTER 5 SUMMARY & CONCLUSIONS . . . . . . . . . . . . . . . . . . 184

APPENDIX A STELLAR PHOTOSPHERIC ABUNDANCES . . . . . . . . . . 186

TABLE OF CONTENTS – Continued

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APPENDIX B SOLAR SYSTEM TERRESTRIAL PLANET ABUNDANCES . . 198

APPENDIX C MIDPLANE TEMPERATURE AND PRESSURE PROFILES . . 246

APPENDIX D HSC CHEMISTRY GAS ABUNDANCES . . . . . . . . . . . . . 256

APPENDIX E EXTRASOLAR TERRESTRIAL PLANET ABUDNANCES . . . 266

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

9

LIST OF FIGURES

1 Calvin and Hobbes, 3/17/1986 . . . . . . . . . . . . . . . . . . . . . . . 5

1.1 Piled Higher and Deeper, 2/26/2006 . . . . . . . . . . . . . . . . . . . . 24

2.1 (X/H) vs. (Fe/H) for all elements studied. . . . . . . . . . . . . . . . . . 362.2 (X/Fe) vs. (Fe/H) for all elements studied. . . . . . . . . . . . . . . . . . 372.3 (heavy/light) vs. (Fe/H) . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.4 Orbital properties of extrasolar planetary systems vs. abundance of the

heavy elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.5 Ginger Meggs, 2/13/2008 . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.1 Schematic of the results of the simulations of O’Brien et al. (2006). . . . 513.2 Radial pressure and temperature profiles for the nominal Soalr nebula . . 603.3 Normalized abundances for the CJS1 and EJS1 simulations. . . . . . . . 663.4 Al/Si v. Mg/Si for all Solar System simulated planets. . . . . . . . . . . . 703.5 Ca/Si v. Mg/Si for all Solar System simulated planets. . . . . . . . . . . . 713.6 Oxidation state plot for CJS1 and EJS1 simulated planetary abundances. . 743.7 Distribution of mass and its composition. . . . . . . . . . . . . . . . . . 773.8 Variation in composition with time for the final planets produced by the

CJS1 and EJS1 simulations. . . . . . . . . . . . . . . . . . . . . . . . . 783.9 Normalized abundances for the CJS1 and EJS1 simulations after material

loss in impact events has been incorporated . . . . . . . . . . . . . . . . 863.10 Pearls Before Swine, 4/2/2007 . . . . . . . . . . . . . . . . . . . . . . . 93

4.1 Mg/Si vs. C/O for known planetary host stars. . . . . . . . . . . . . . . . 984.2 Mg/Si vs. C/O for host and non-host stars. . . . . . . . . . . . . . . . . . 1024.3 C/O and Mg/Si distributions for host and non-host stars . . . . . . . . . . 1034.4 C/O and Mg/Si distributions for previously published values and this study 1054.5 Schematic of the Extrasolar Planetary Systems studied. . . . . . . . . . . 1064.6 Mg/Si vs. C/O for planetary host stars studied. . . . . . . . . . . . . . . . 1104.7 Schematic of the results of the dynamical simulations for 55Cancri and

Gl777. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1244.8 Schematic of the results of the dynamical simulations for HD4203 and

HD4208. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254.9 Schematic of the results of the dynamical simulations for HD19994 and

HD72659. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

LIST OF FIGURES – Continued

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4.10 Schematic of the results of the dynamical simulations for HD108874 andHD142415. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.11 Schematic of the results of the dynamical simulations for HD177830. . . 1284.12 HSC Chemistry output for HD72659 . . . . . . . . . . . . . . . . . . . . 1354.13 HSC Chemistry output for HD177830 . . . . . . . . . . . . . . . . . . . 1364.14 HSC Chemistry output for Gl777 . . . . . . . . . . . . . . . . . . . . . . 1374.15 HSC Chemistry output for HD4208 . . . . . . . . . . . . . . . . . . . . 1384.16 HSC Chemistry output for 55Cnc . . . . . . . . . . . . . . . . . . . . . . 1394.17 HSC Chemistry output for HD142415 . . . . . . . . . . . . . . . . . . . 1404.18 HSC Chemistry output for HD19994 . . . . . . . . . . . . . . . . . . . . 1414.19 HSC Chemistry output for HD108874 . . . . . . . . . . . . . . . . . . . 1424.20 HSC Chemistry output for HD4203 . . . . . . . . . . . . . . . . . . . . 1434.21 Schematic of the planetary abundances for Gl777. . . . . . . . . . . . . . 1474.22 Al/Si v. Mg/Si for planets of Gl777. . . . . . . . . . . . . . . . . . . . . 1484.23 Schematic of the planetary abundances for HD72659. . . . . . . . . . . . 1494.24 Schematic of the planetary abundances for HD4208. . . . . . . . . . . . . 1504.25 Al/Si v. Mg/Si for the planets of HD4208 and HD72659. . . . . . . . . . 1514.26 Schematic of the planetary abundances for HD177830. . . . . . . . . . . 1524.27 Schematic of the planetary abundances for 55Cnc. . . . . . . . . . . . . . 1564.28 Schematic of the planetary abundances for HD142415. . . . . . . . . . . 1574.29 Schematic of the planetary abundances for HD19994. . . . . . . . . . . . 1584.30 Schematic of the planetary abundances for HD108874. . . . . . . . . . . 1594.31 Schematic of the planetary abundances for HD42083. . . . . . . . . . . . 1604.32 HSC Chemistry output for HD72659 . . . . . . . . . . . . . . . . . . . . 1694.33 HSC Chemistry output for HD4203 . . . . . . . . . . . . . . . . . . . . 1704.34 Schematic of extrasolar terrestrial planet interiors. . . . . . . . . . . . . . 1744.35 Schematic of terrestrial planet interiors for Gl777. . . . . . . . . . . . . . 1764.36 Solid mass distribution for the Solar-like systems. . . . . . . . . . . . . . 1804.37 Pooch Cafe, 8/12/2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

5.1 Calvin and Hobbs, 2/11/1993 . . . . . . . . . . . . . . . . . . . . . . . . 185

B.1 Normalized planetary abundances for CJS1 simulation. . . . . . . . . . . 200B.2 Normalized planetary abundances for CJS2 simulation. . . . . . . . . . . 201B.3 Normalized planetary abundances for CJS3 and CJS4 simulations. . . . . 202B.4 Normalized planetary abundances for EJS1 simulation. . . . . . . . . . . 203B.5 Normalized planetary abundances for EJS2 simulation. . . . . . . . . . . 204B.6 Normalized planetary abundances for EJS3 simulation. . . . . . . . . . . 205B.7 Normalized planetary abundances for EJS4 simulation. . . . . . . . . . . 206B.8 Normalized planetary abundances for CJS1 simulation with volatile loss. . 225


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B.9 Normalized planetary abundances for CJS2 simulation with volatile loss. . 226B.10 Normalized planetary abundances for CJS3 and CJS4 simulations with

volatile loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227B.11 Normalized planetary abundances for EJS1 simulation with volatile loss. . 228B.12 Normalized planetary abundances for EJS2 simulation with volatile loss. . 229B.13 Normalized planetary abundances for EJS3 simulation with volatile loss. . 230B.14 Normalized planetary abundances for EJS4 simulation with volatile loss. . 231

C.1 Midplane pressure and temperature profile for 55Cnc. . . . . . . . . . . . 247C.2 Midplane pressure and temperature profile for Gl777. . . . . . . . . . . . 248C.3 Midplane pressure and temperature profile for HD4203. . . . . . . . . . . 249C.4 Midplane pressure and temperature profile for HD4208. . . . . . . . . . . 250C.5 Midplane pressure and temperature profile for HD19994. . . . . . . . . . 251C.6 Midplane pressure and temperature profile for HD72659. . . . . . . . . . 252C.7 Midplane pressure and temperature profile for HD108874. . . . . . . . . 253C.8 Midplane pressure and temperature profile for HD177830. . . . . . . . . 254C.9 Midplane pressure and temperature profile for HD142415. . . . . . . . . 255

D.1 Gaseous species output from HSC Chemistry for HD72659 . . . . . . . . 257D.2 Gaseous species output from HSC Chemistry for HD177830 . . . . . . . 258D.3 Gaseous species output from HSC Chemistry for Gl777 . . . . . . . . . . 259D.4 Gaseous species output from HSC Chemistry for HD4208 . . . . . . . . 260D.5 Gaseous species output from HSC Chemistry for 55Cnc . . . . . . . . . . 261D.6 Gaseous species output from HSC Chemistry for HD142415 . . . . . . . 262D.7 Gaseous species output from HSC Chemistry for HD19994 . . . . . . . . 263D.8 Gaseous species output from HSC Chemistry for HD108874 . . . . . . . 264D.9 Gaseous species output from HSC Chemistry for HD4203 . . . . . . . . 265

E.1 Schematic of planetary composition for Gl777 for disk conditions at2.5×105 years and 5×105 years. . . . . . . . . . . . . . . . . . . . . . . 267

E.2 Schematic of planetary composition for Gl777 for disk conditions at1×106 years and 1.5×106 years. . . . . . . . . . . . . . . . . . . . . . . 268

E.3 Schematic of planetary composition for Gl777 for disk conditions at2×106 years and 2.5×106 years. . . . . . . . . . . . . . . . . . . . . . . 269

E.4 Schematic of planetary composition for Gl777 for disk conditions at3×106 years. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

E.5 Schematic of planetary composition for HD4208 for disk conditions at2.5×105 years and 5×105 years. . . . . . . . . . . . . . . . . . . . . . . 271

E.6 Schematic of planetary composition for HD4208 for disk conditions at1×106 years and 1.5×106 years. . . . . . . . . . . . . . . . . . . . . . . 272


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E.8 Schematic of planetary composition for HD4208 for disk conditions at3×106 years. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274









E.17 Schematic of planetary composition for HD55Cnc for disk conditions at2.5×105 years and 5×105 years. . . . . . . . . . . . . . . . . . . . . . . 283

E.18 Schematic of planetary composition for HD55Cnc for disk conditions at1×106 years and 1.5×106 years. . . . . . . . . . . . . . . . . . . . . . . 284

E.19 Schematic of planetary composition for HD55Cnc for disk conditions at2×106 years and 2.5×106 years. . . . . . . . . . . . . . . . . . . . . . . 285

E.20 Schematic of planetary composition for HD55Cnc for disk conditions at3×106 years. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286







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14

LIST OF TABLES

2.1 Spectral line list used for chemical abundance analysis. . . . . . . . . . . 302.2 Mean difference in abundance from previously published values. . . . . . 322.3 Statistical analysis of abundance distributions. . . . . . . . . . . . . . . . 34

3.1 Properties of Solar System simulations. . . . . . . . . . . . . . . . . . . 523.2 Chemical species included in calculations of HSC Chemistry. . . . . . . . 553.3 HSC Chemistry input values for Solar System Simulations . . . . . . . . 563.4 T50%condensation for the Solar System. . . . . . . . . . . . . . . . . . . . . 573.5 Percentage of each element assumed to be lost in impact events. . . . . . 853.6 Mean change in solar photospheric abundances produced by pollution via

accretion of solid material. . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.1 Statistical analysis of the host and non-host star distributions of Mg/Siand C/O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.2 Orbital parameters of known extrasolar planets . . . . . . . . . . . . . . 1074.3 Target star elemental abundances in logarithmic units. . . . . . . . . . . . 1084.4 Target star elemental abundances normalized to 106Si atoms. . . . . . . . 1094.5 Statistical analysis of the embryo and planetesimal and embryo only sim-

ulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144.6 HSC Chemistry input values for extrasolar planetary systems studied. . . 1174.7 Extrasolar host star accretion rates . . . . . . . . . . . . . . . . . . . . . 1204.8 Stellar convective zone masses . . . . . . . . . . . . . . . . . . . . . . . 1214.9 Properties of simulated extrasolar terrestrial planets. . . . . . . . . . . . . 1294.10 Degree of radial mixing for extrasolar planetary system simulations. . . . 1304.11 Formation time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314.12 T50% condensation for extrasolar planetary systems studied. . . . . . . . . . 1344.13 Change in host star photospheric abundances. . . . . . . . . . . . . . . . 162

A.1 Stellar abundances of all AAPS target stars. . . . . . . . . . . . . . . . . 187A.2 Stellar abundances for AAPS target stars normalized to 106 Si atoms. . . 192

B.1 Predicted bulk planetary abundances for the terrestrial planets of theO’Brien et al. (2006) simulations. . . . . . . . . . . . . . . . . . . . . . 207

B.2 Ensemble-averaged bulk predicted planetary abundances. . . . . . . . . . 221B.3 Difference in abundance between t = 2.5×105yr and t = 3×106yr. . . . . 223B.4 Bulk Planetary Abundances with Volatile Loss. . . . . . . . . . . . . . . 232

LIST OF TABLES – Continued

15

E.1 Bulk Planetary Abundances for Gl777. . . . . . . . . . . . . . . . . . . . 299E.2 Bulk Planetary Abundances for HD4208. . . . . . . . . . . . . . . . . . 306E.3 Bulk Planetary Abundances for HD72659. . . . . . . . . . . . . . . . . . 313E.4 Bulk Planetary Abundances for HD177830. . . . . . . . . . . . . . . . . 320E.5 Bulk Planetary Abundances for 55Cnc. . . . . . . . . . . . . . . . . . . . 327E.6 Bulk Planetary Abundances for HD142415. . . . . . . . . . . . . . . . . 331E.7 Bulk Planetary Abundances for HD19994. . . . . . . . . . . . . . . . . . 338E.8 Bulk Planetary Abundances for HD108874. . . . . . . . . . . . . . . . . 345E.9 Bulk Planetary Abundances for HD4203. . . . . . . . . . . . . . . . . . 349

16

ABSTRACT

This work examines the chemical nature of extrasolar planetary systems, considering both

the host star and any potential terrestrial planets located within the system. Extrasolar

planetary host stars are found to be enriched over non-host stars in several r- and s-process

elements. These enrichments, however, are in keeping with general galactic chemical

evolution trends. This implies that host stars have not experienced any unusual chemical

processing or pollution and that the observed enrichments are primordial in nature.

When combined with detailed chemical models, the dynamical models of O’Brien

et al. (2006) are found to produce terrestrial planets with bulk elemental abundances in

excellent agreement with observed planetary values. This clearly indicates that the com-

bination of dynamical and chemical modeling applied here is successfully reproducing

the terrestrial planets of the Solar System to the first order. Furthermore, these planets are

found to form with a considerable amount of water, negating the need for large amounts

of exogenous delivery. Little dependence on the orbital properties of Jupiter and Sat-

urn is observed for the main rock-forming elements due to the largely homogenous disk

composition calculated.

The same modeling approach is applied to known extrasolar planetary systems. Ter-

restrial planets were found to be ubiquitous, forming in all simulations. Generally, small

(< 1M⊕) terrestrial planets are produced close to their host star with little radial mixing

occurring. Planetary compositions are found to be diverse, ranging from Earth-like to re-

fractory dominated and C-dominated, containing significant amounts of carbide material.

Based on these simulations, stars with Solar elemental ratios are the best place to focus

future Earth-like planet searches as these systems are found to produce the most Earth-

like terrestrial planets which are located within the habitable zones of their systems and

17

containing a significant amount of water. C-rich planets, although unusual, are expected

to exist in ∼20% of known extrasolar planetary systems based on their host star photo-

spheric compositions. These planets are unlike any body we have previously observed

and provide an exciting avenue for future observation and simulation.

18

CHAPTER 1

INTRODUCTION & BACKGROUND

1.1 History of Extrasolar Planets

Extrasolar planets (planets orbiting stars other than our own Sun) are a relatively new

branch of the astronomical and planetary sciences. After the discovery of (the now de-

moted) Pluto in 1930 (see Tombaugh (1946) for a review), planet finding activities ap-

peared to have reached an end for the foreseeable future. Between 1930 and 1992, several

brown dwarfs were discovered orbiting other solar-type stars (Henry and Kirkpatrick,

1990). Commonly referred to as “failed stars”, brown dwarfs are low-mass celestial ob-

jects (M≥10MJUP) that formed by stellar processes but did not obtain the critical mass

required to sustain nuclear burning within their core. As such, they were widely believed

to be too large to be planets in the classical sense. Other claims for planetary detections

were also made during this period (Strand, 1944; Reuyl and Holmberg, 1943; van de

Kamp, 1963, 1969) but these were never independently verified or were later shown to be

false, produced by timing artifacts or instrumentation errors.

It wasn’t until 1992 that the first confirmed detection of an extrasolar planet occurred

when two bodies were found to be orbiting the millisecond pulsar PSR 1257+12 (Wol-

szczan and Frail, 1992; Backer et al., 1992). Pulsars had not previously been thought

to be likely hosts for extrasolar planets due to their formation mechanism. Pulsars are

rapidly rotating neutron stars produced during supernova events. They are exposed to ob-

servers when the outer layers of the original star are removed. The resulting reduction in

mass of the host star was believed to be significant enough that the gravitational attraction

between the host star and any orbiting planets would be reduced to the level where the

planet would no longer be gravitationally bound to the remaining neutron star, and would

19

therefore be lost.

The first detection of an extrasolar planet orbiting a solar-type star occurred two years

later in 1994 with the announcement of a planetary body orbiting 51 Paegasi (Mayor and

Queloz, 1995). This detection was later confirmed in 1995 (Marcy and Butler, 1996) and

began a virtual “planet-rush”. Over the next 18 months, we progressed from knowing of

no other planets orbiting solar-type stars to having detected nine extra-solar planetary sys-

tems by the end of 1996 (although two companions were later revised to possible brown

dwarf status because of their high mass). As of September 2008, we currently know of

294 planets orbiting a total of 252 solar-type stars (there are 30 multiple planet systems).

The vast majority of these detections have occurred via the radial velocity method (for

a summary of this method, see Schneider (1999)), although other methods such as that

of transiting photometry and microlensing are becoming increasingly important in future

planet searches as we seek to detect terrestrial-sized planetary bodies and utilize space-

based observing programs such as Kepler. Based on the detection statistics of the current

planet search programs, Marcy and Butler (1998) estimated that the Milky Way could be

“home” to up to 10 billion planets. While this rough estimate is by no means a definitive

number, it does give us some idea of the scale of the planet search that we have begun.

Upon examination, the known extrasolar planetary systems can be seen to be vastly

different to our own solar system in terms of both the bulk chemistry of the host star

and the orbital properties of the companion planets. Unravelling the causes of these two

differences have proven to be the most intriguing aspects of current extrasolar planetary

studies.

1.2 Planetary System Chemical Properties

Extrasolar planetary host stars are known to be somewhat chemically anomalous. They

have been found to be enriched in iron as compared to other average non-host field stars

(Gonzalez, 1997, 1998; Butler et al., 2000; Gonzalez and Laws, 2000; Gonzalez et al.,

20

1999; Gonzalez and Vanture, 1998; Santos et al., 2000, 2001, 2004; Gonzalez et al., 2001;

Smith et al., 2001; Reid, 2002; Fischer and Valenti, 2005; Bond et al., 2006). At present,

this observed chemical anomaly is the only externally observable correlation between

the properties of a star and the presence of a planetary companion. Furthermore, they

are potentially also enriched in other lighter, key planet building elements (Mg, Si, O),

(Gonzalez and Vanture, 1998; Gonzalez et al., 2001; Santos et al., 2000; Bodaghee et al.,

2003; Fischer and Valenti, 2005; Beirao et al., 2005; Bond et al., 2006), although not with

the same statistical significance as has been observed for iron. However, in addition to

these simple elemental enrichments, several extrasolar planetary systems are abnormal

in key cosmochemical ratios. Several systems are found to have C/O ratios at or above

unity or Mg/Si ratios almost a factor of two higher than in our Solar System. If these

ratios are primordial, established in the giant molecular cloud from which these systems

subsequently formed, then the chemistry of the planet building material and ultimately

any planets within these systems will be drastically different to that of our own Solar

System.

The exact origin of this observed elemental enrichment has been the subject of much

debate. The two main hypotheses for the observed metalicity trend are the ‘pollution’

model whereby metal rich material is added to the outer envelope of the star during

the planetary formation process and the ‘primordial’ model in which the gas cloud from

which the star formed was already enriched prior to stellar formation occurring. Propo-

nents of the primordial model cite the fact that approximately 6 M⊕ of iron would need

to be systematically added to the host star’s photosphere after the dissipation of the pro-

toplanetary disk in order to produce the observed metallicity trend (Murray et al. 2001).

However, no clear correlation between the metallicity of the host star and the orbital pa-

rameters of the remaining planetary companions can be seen. It is difficult to think of any

feasible process by which the presence of the remaining planetary companion could have

caused the accretion of another approximately Jupiter-mass planet, independent of its fi-

nal orbital parameters. Furthermore, it is even more challenging to explain why almost

21

all stars currently known to have planetary companions would have accreted significant

amounts of iron during the planetary formation process while only a small percentage of

non-host stars show a similar level of enrichment. However, neither of these arguments

clearly excludes the pollution hypothesis with proponents suggesting that an enrichment

in lighter elements, and especially in 6Li, would favor the pollution theory (Santos et al.

2001). Furthermore, enrichment is not essential for planetary formation as indicated by

the existence of a planetary hosts with iron depletions relative to the Sun (such as the

known host star HD155358 which has [Fe/H] = −0.68). As a result, no clear consensus

has emerged as to which explanation is believed to be correct and resolving this issue

and examining its implications on planetary formation and composition is one of the out-

standing questions within extrasolar planetary science.

1.3 Terrestrial Planets

The idea of terrestrial planets existing within known extrasolar planetary systems isn’t

new. In fact, Earth-sized bodies are expected to be more prevalent throughout the universe

than their more massive gas giant companions (Marcy et al., 2000). However, they remain

well beyond current detection levels. While we have been able to detect several “super

Earths” (bodies with masses between 1⊕ and 10 M⊕) (Rivera et al., 2005; Beaulieu

et al., 2006; Lovis et al., 2006; Udry et al., 2007), we are still unable to examine bodies

with masses comparable to that of the Earth. Only Kepler and possibly Darwin will be

able to determine if such bodies do exist within other systems.

Dynamical simulations have shown that several systems contain a region of orbital

space in which such bodies could potentially exist for long periods of time (e.g. Barnes

and Raymond 2004; Raymond and Barnes 2005; Asghari et al. 2004). Others have gone

one step further and simulated actual terrestrial planet formation within these systems

(e.g. Raymond et al. 2005; Mandell et al. 2007). Based on these simulations, terres-

trial planets have been found to form in a wide variety of dynamical systems, indicating

22

that they are indeed likely to exist in the majority of known extrasolar planetary systems.

Only Raymond et al. (2006) has modeled terrestrial planet formation within specific sys-

tems, finding that terrestrial planets could form in one of the systems simulated (55Can-

cri), while small bodies comparable to asteroid sized objects would be stable in another

(HD38529). Studies have also suggested that a significant portion of these planets will

reside in the habitable zone of their stellar system (Mandell et al., 2007).

However, no previous studies have considered the chemical composition of these po-

tential planets. Given the wide variety of host star compositions observed, it is likely that

terrestrial planets will display a similar variety of compositions. Of particular interest are

those systems with exceptionally high C/O values. Such systems will contain C-based

species such as SiC, TiC and graphite as the main planet forming material, therefor pro-

ducing C-rich planets unlike anything we have previously observed. These variations will

have drastic implications on a wide variety of planetary properties, including planetary

processes (such as volcanism and tectonics), our ability to detect and observe extraso-

lar terrestrial planets and their ability to host life (as we currently know it). While the

detection of a true Earth analog extrasolar terrestrial planet remains the “holy grail” of

extrasolar planetary searches, the potential diversity in planetary compositions is a fasci-

nating aspect of planetary studies.

1.4 Summary of Work

Given the anomalies observed within the extrasolar host star population, it is thus natural

to wonder about other aspects of the extrasolar planetary system. Why are extrasolar

planetary host stars enriched above other non-host field stars? Given the unusual and

often extreme orbital parameters of the known giant extrasolar planets, could terrestrial

planets still form in these systems? Would such planets be stable on geologic timescales?

If the chemistry of the host star is unusual (as compared to other non-host field stars), then

what is the chemical composition of the planets in the system like? Are all of the bodies

23

iron rich? Would we see any planets with a composition similar to that of the Earth?

Would it be chemically possible for life as we know it to develop within such a system?

This work begins to answer some of these questions, focussing specifically on the

nature of the observed elemental enrichments in known host stars, the potential for the

formation of extrasolar terrestrial planets and the chemical abundances of these planets.

In the second chapter, we determine the stellar abundances of five elements produced

by the rapid (r-) and slow (s-) processes, in addition to three lighter elements, in the known

host and non-hosts stars observed as part of the Anglo-Australian Planet Search. This is

the first study of its kind to consider elements beyond the iron peak. Such elements are

produced in specific yet vastly different formation environments and as such provide us

with information about the evolutionary history of the material that has been incorporated

into extrasolar planetary systems.

In the third chapter, we determine the detailed bulk composition of the terrestrial

planets produced in dynamical simulations for the Solar System. These predicted com-

positions are compared to the bulk compositions of the actual terrestrial planets as an

examination of the chemical validity of the dynamical simulations currently being used

to model terrestrial planet formation. This study is the first to undertake such a high

resolution and detailed chemical test of dynamical models of terrestrial planet formation.

Finally, in the fourth chapter, we expand this work out to consider extrasolar terrestrial

planets. Identical dynamical formation and chemical composition simulations are under-

taken for nine known extrasolar planetary systems, varying in both their dynamics and

chemical compositions. While other studies have considered the potential of terrestrial

planet formation in extrasolar planetary systems (e.g. Raymond et al. 2006), this is the

first time that the dynamics of formation have been simultaneously considered with the

chemistry of the associated material.

These studies will assist us in obtaining a better sense of both the dynamical and the

chemical nature of terrestrial planet formation, both within our Solar System and within

known extrasolar planetary systems.

24

Figure 1.1: “Piled Higher and Deeper” by Jorge Cham. www.phdcomics.com. Reprintedwith permission. Originally published 2/26/2006.

25

CHAPTER 2

R- AND S-PROCESS ELEMENTAL ABUNDANCES IN STARS WITH PLANETS

2.1 Introduction

Extrasolar planets are known to preferentially orbit metal-enhanced stars. Chemical

analyses of known host stars have shown that they appear to be metal enriched com-

pared to a sample of “average” F, G and K stars not known to harbor planets (Gonzalez,

1997, 1998; Gonzalez and Laws, 2000; Gonzalez et al., 1999; Gonzalez and Vanture,

1998; Santos et al., 2000, 2001, 2003; Gonzalez et al., 2001; Smith et al., 2001; Reid,

2002; Fischer and Valenti, 2005; Bond et al., 2006). In addition to this metal enrichment,

other elements have also been shown to exhibit similar trends, although not as statistically

significant or with such large host and non-host differences (Gonzalez et al. 2001; Santos

et al. 2000; Bodaghee et al. 2003; Fischer and Valenti 2005; Bond et al. 2006).

However, the vast majority of abundance studies completed so far have focussed on

elements with atomic number (Z)≤30 (i.e. those located before the iron stability peak).

These elements are produced by a variety of processes (for example alpha particle ad-

dition, the CNO cycle and stellar burning reactions) in stellar interiors during main se-

quence evolution. Elements located beyond the iron peak, however, are produced via

neutron-capture reactions, specifically the rapid (r-) and slow (s-) processes. Here rapid

and slow refers to the speed of neutron capture with respect to the β-decay rate of the

nuclei. In the r-process, neutron capture occurs before β-decay of the unstable nuclei can

occur. Alternatively, in the s-process neutron capture occurs less frequently, thus allowing

the nuclei to undergo β-decay before capturing another neutron and effectively allowing

the nuclide to remain within the valley of β stability.

Due to the different neutron fluxes required for each process (∼1023 neu-

26

trons cm−2 s−1 for the r-process vs. ∼105 neutrons cm−2 s−1 for the s-process (Clayton,

1968), the r- and s-processes occur in different stellar environments. There is some de-

bate as to exactly where the r-process occurs (see e.g. Qian 2004), but it is believed to

primarily occur in type II supernova events. The s-process is thought to produce its heav-

ier elements (such as Ba and Ce) in the interior of lower mass AGB stars and its lighter

elements (such as Sr, Y and Zr) during the He-burning stages of stellar evolution for larger

mass stars (Reddy et al., 2003). Due to these vastly different settings, the abundances of

the heavy elements produced by these processes can provide information on the history

of the material later incorporated into both the host star and planets themselves, as well

as testing models of galactic chemical evolution (e.g. Fenner et al. 2006 and Lanfranchi

et al. 2008). These elements have been part of several previous spectroscopic studies of

stars without planets (e.g. Edvardsson et al. 1993; Reddy et al. 2003; Allende Prieto et al.

2004; Bensby et al. 2005; Reddy et al. 2006), however only Ba (Huang et al., 2005) and

Eu (Gonzalez and Laws, 2007) have been specifically examined in a small number of

known extrasolar planetary host stars.

Studies of stellar abundances have become critical to our understanding of planetary

formation processes. However, in spite of significant advances in atmospheric models,

stellar interiors and atomic line data in recent years, the measurement of stellar abun-

dances is still an intricate process. In particular, choices made in the way an analysis is

carried out can result in systematic abundance differences on scales similar to the effects

we would most like to understand in the stars themselves. Additionally, in many cases

there is no consensus on the “correct” choice in these techniques.

To make headway in this field, therefore, it is essential to perform abundance studies

in a manner immune to such systematic errors, by analyzing both samples of interest, and

control samples, in an identical manner. For the abundances of exoplanetary host stars,

that means both host and non-host stars must be analyzed in an identical manner. This is

the primary goal of this current study.

Abundances of five r-and s-process elements, in addition to three other lighter ele-

27

ments, were derived for all the planet-hosting and non-planet-hosting stars in the Anglo-

Australian Planet Search (AAPS) data set with viable template spectra (28 hosts, 108

non-hosts), so that robust conclusions can be reached about the differences in their el-

emental abundances. The inclusion of these heavy elements begins to extend the spec-

troscopic studies of known host stars beyond the iron peak, thus continuing the search

for additional chemical anomalies within these systems, while also providing an indepen-

dent check of nucelosynthesis models and previously published abundances and trends

for known host stars. The lighter elements selected for study (O, Mg and Cr) are included

so as to complement the previous study of Bond et al. (2006) while also providing valu-

able information as to the cause of the metal-enrichment commonly seen in known host

stars.

The majority of this chapter appeared as Bond et al. (2008) Beyond the Iron Peak: r-

and s-Process Elemental Abundances in Stars with Planets, Astrophysical Journal, 682,

1234-1247.

2.2 Data

2.2.1 Target Stars

The F- and G-type stars, observed at the 3.9m Anglo-Australian Telescope (AAT) since

January 1998 as part of the AAPS program were selected for this present study (Butler

et al., 2001, 2002; Tinney et al., 2001, 2002, 2003, 2005, 2006; Jones et al., 2002b,a,

2006; Carter et al., 2003; McCarthy et al., 2004; Jenkins et al., 2006; Wright et al., 2007;

O’Toole et al., 2007). As at January 2007, 31 stars present within the AAPS sample were

known to be planet hosts, of which 28 had spectra useful for the purposes of this study.

Stars known to be young (age < 3 Gyr), active (logR′HK> -4.5) or with other stars within

5′′ are rejected from the AAPS search. For a more detailed description of the data and

details of the criteria applied to the AAPS target stars, the reader is referred to Butler et al.

(1996) and Tinney et al. (2005). Of the 28 host stars considered here, 26 have had some

28

common elemental abundances previously determined by other authors.

2.2.2 Spectroscopic Analysis

The method utilized in this study closely follows that outlined in Bond et al. (2006) who

studied Fe, C, Na, Al, Si, Ca, Ti and Ni. Spectra encompassing the entire visible spec-

trum from 4820 to 8420A with a signal-to-noise ratio (S/N) between 200 and 300 per

spectral pixel at resolution λ/∆λ ≈ 80000 were obtained via the University College

London Echelle Spectrograph (UCLES) using the 31.6 line/mm echelle grating as part

of the AAPS program. The raw data were reduced and processed so as to produce a

one-dimensional spectra, suitable for spectral analysis.

This study does differ slightly from Bond et al. (2006) in the method used to deter-

mine the equivalent widths of absorption lines. In Bond et al. (2006), equivalent width

estimates were obtained via direct integration over the line. In this study we follow the

method of other similar studies (eg. Santos et al. 2000; Gonzalez et al. 2001; Santos

et al. 2001) and make Gaussian line fits to the spectra using the IRAF task splot in the

package noao.onedspec (due to difficulties in automating the previous script). This

slight difference in methodology does not produce any significant difference in the final

abundances obtained.

Five heavy elements were analyzed for the first time as part of this study and they were

primarily selected based on their process of production. Y, Zr and Ba are all produced

primarily by the s-process while Eu is primarily produced by the r-process and Nd is an

almost even mix between the two based on Solar System abundances (Arlandini et al.

1999; Simmerer et al. 2004). The line list utilized in this study is shown in Table 2.1

and is derived from Gilli et al. (2006) (for Mg and Cr), Reddy et al. (2003)(for Y, Zr, Ba,

Eu and Nd) and Den Hartog et al. (2003) (for Nd). Additional Ba lines have been used

in other studies, but were neglected here as they gave consistently lower abundances by

approximately 0.60 dex. While the use of more lines in determining an abundance should

produce a more robust value, the cause of this offset could not be determined and as

29

such the single stronger line at 6496.91A was used as this line produced a Ba abundance

close to the reported solar value for a solar spectrum. Atomic parameters for each line

were obtained from the NIST Atomic Spectra Database, Version 3.0 (for O, Mg and Cr),

Pitts and Newsom (1986) and Hannaford et al. (1982) (for Y), Reddy et al. (2003) (for

Ba), Den Hartog et al. (2003) (for Nd) and the Kurucz atomic line database1 (for Zr and

Eu). All of the atomic parameters applied here have also been utilized in previous studies

and produce solar elemental abundances well within errors of those published elsewhere,

when applied to a solar spectrum, thus giving us confidence in applying them here.

Elemental abundances were obtained via standard local thermodynamic equilibrium

analysis, as has been done by previous studies (see Santos et al. 2000; Gonzalez et al.

2001; Santos et al. 2001; Bond et al. 2006). A revised version of Sneden’s (1973) MOOG

abundance code entitled width6 (Ryan 2005, personal communication) was once again

used in conjunction with a grid of Kurucz (1993) ATLAS9 atmospheres2 to obtain the final

elemental abundances. As all of the non-host, and all but 7 of the host stars, had been the

subject of an earlier study (Bond et al. 2006), previously published stellar atmospheric

parameters were used. For those stars without previously determined values, we followed

the same method as used in Bond et al. (2006) to obtain the values and refer the reader

to the paper for more details. As the OI triplet lines are known to suffer from non-LTE

effects, the corrections of Takeda (2003) for ξt=1km/s and log g=4.0 cm/s2 were applied

to obtain our final O abundances. When applied to a solar spectrum, this method produced

abundances in agreement with those of Asplund et al. (2005).

Errors were obtained via sensitivity studies. Teff , log g, [Fe/H] and microturbulence

were varied in turn by a specified amount (±100 K for Teff , ±0.3 dex for log g, ±0.3

dex for metallicity and ±0.05 dex for microturbulence) and the resulting variation in the

elemental abundance was determined. Thus the final error was obtained by summing in

quadrature the sensitivity errors, continuum placement error (typically 0.05 dex) and stan-

1http://www.pmp.uni-hannover.de/cgi-bin/ssi/test/kurucz/sekur.html2http://kurucz.harvard.edu or http://www.stsci.edu/hst/observatory/cdbs/k93models.html

30

Table 2.1: Spectral line list used for chemical abundance analysis. Atomic parameters arealso provided. See text for references.

λ Log gf χl

(A) (eV)Mg I

5711.09 -1.71 4.356318.72 -1.99 5.11

Cr I5304.18 -0.69 3.465312.87 -0.56 3.455318.81 -0.69 3.445783.09 -0.50 3.325783.89 -0.29 3.32

O I7771.94 0.37 9.157774.17 0.22 9.157775.39 0.002 9.15

Ba II6496.91 -0.41 0.60

Y II4854.87 -0.01 0.994900.12 -0.09 1.035087.43 -0.17 1.085200.42 -0.49 0.995402.78 -0.63 1.84

Zr II5112.28 -0.59 1.66

Eu II6645.13 0.20 1.38

Nd II4914.18 -0.70 0.385234.19 -0.51 0.55

31

dard deviation of each mean abundance (where the elemental abundance was determined

from more than one spectral line):

σ2final = σ2

std + σ2continuum + σ2

Teff + σ2logg + σ2

[Fe/H] + σ2micro (2.1)

2.3 Results

The stellar elemental abundances are shown in Table A.1(in the standard astronomical

logarithmic form) and Table A.2 (in the more cosmochemically useful form with abun-

dances normalized to 106 Si atoms). The notation of − for an abundance indicates that

a value could not be obtained from the spectrum due to noise. Additionally, for ease of

comparison in Section 5.1, C and Si stellar elemental abundances, along with the normal-

ized C abundances, for all target stars are presented in Tables A.1 and A.2. The C and Si

abundances were previously published in Bond et al. (2006).

Other authors have previously determined abundance values for several of the ele-

ments also studied here with many of these abundances differing from our values. Differ-

ences between the present study and that of others is not a significant issue for the primary

thrust of this paper, which is to compare host and non-host stellar abundances which have

been measured in an identical fashion. However, in the interests of completeness it is

noted that Mg abundances were determined for 29 common stars (20 hosts) by Beirao

et al. (2005), Cr in 28 stars (20 hosts) and Mg in 29 stars (20 hosts) by Gilli et al. (2006),

Cr in 25 stars (16 hosts) by Bodaghee et al. (2003), O in 8 stars (4 hosts) by Ecuvillon

et al. (2006a), O and Eu in 4 host stars, Cr and Mg in 1 host star by Gonzalez and Laws

(2007) and O in 1 host star by Santos et al. (2000). The mean differences between our

values and those previously published are shown in Table 2.2 (for those samples having

more than one common star) with the difference being defined as the abundance from this

32

Table 2.2: Mean difference in abundance between values determined in the presentstudy and previously published values. Difference is defined as Abundancethis study -Abundancepreviously published.

Study Element Difference Sample SizeBeriao et al. (2005) Mg −0.18± 0.02 29Gilli et al. (2006) Cr 0.00± 0.02 28

Mg −0.18± 0.02 29Bodaghee et al (2003) Cr 0.02± 0.01 25Ecuvillon et al (2006) O 0.11± 0.07 8

Gonzalez & Laws (2007) O −0.03± 0.04 4Eu −0.22± 0.16 4

study minus the published abundance. Generally, the results presented here can be seen to

be in agreement with those previously published for Cr and O with a significantly larger

mean difference occurring for Mg and and a large deviation occurring for Eu. The differ-

ences between our abundances and those previously published are believed to be due to

the use of a smaller number of lines in determining the abundance (for Mg), the use of

different methods (for O and Eu), the use of different atomic parameters (for Eu) and the

use of different non-LTE corrections (for O).

2.4 Host Star Enrichment

2.4.1 Enrichment over Solar

The mean and median abundances, standard deviation and the difference between the

host and non-host stars for all target stars can be seen in Table 2.3 for each element. The

quoted uncertainties are the standard error in the mean, and the median uncertainty from

the algorithm of Kendall et al. (1987)3. The mean values of this study for the known host

stars are all consistent to within the 1σ value of those listed by Beirao et al. (2005) and

Gilli et al. (2006). The data show that in general known extrasolar planetary host stars

3For a distribution with N values, the error in the median is the range in values on either side of the

median which contains (√

N)/2 values

33

differ only slightly from the mean solar abundance patterns with all of the median abun-

dances being well within 1σ of the solar abundance - as concluded by previous studies

(eg. Ecuvillon et al. 2004; Bodaghee et al. 2003). This is reassuring as the Sun is itself is

obviously a planetary host star with abundances enhanced over those of most other stars

in the solar neighborhood (based on the abundances of Asplund et al. 2005). In many

respects, therefore, the Sun is not a typical field star, based on its abundances and its mul-

tiple planetary companions. The largest enrichment over solar is seen in Nd and Zr, with

Cr showing a smaller enrichment and Mg showing minimal enrichment. Eu showed the

largest depletion relative to solar values, with Y and Ba also showing mild to moderate

depletions. Only O produced a mean abundance equal to the Solar abundance.

Similarly, the non-host stars can also be seen be depleted when compared to solar

abundances for almost all of the elements studied, with the largest depletion being −0.16

for Y and Eu. It is also worth noting that three of the five heavy elements examined show

a mean depletion relative to solar for both the host and non-host stars. Of these three, two

are produced by the s-process (Y & Ba) with the remaining element (Eu) produced by the

r-process.

2.4.2 Enrichment over Non-Host Stars

A more powerful comparison is obtained by comparing the host and non-host populations

to each other. On doing so, it can be seen that host stars are systematically enriched over

non-host stars in all elements studied. The enrichment ranges in size from 0.06 (for O) to

0.11 for (for Cr and Y) (see Table 2.3).

This difference between the host and non-host populations can also be seen in the

results of the Kolmogorov-Smirnov (K-S) statistical test. Designed to test whether two

distinct populations were drawn from the same parent sample, the K-S test determines the

distance between the cumulative probability distribution function of the two populations.

The probability of the two samples being drawn from the same parent dataset is returned.

The abundances determined here showed a significant difference between the host and

34

Table 2.3: Statistical analysis of abundance distributions. Difference is defined as hoststar abundance − non-host star abundance. Numbers in parentheses indicate the samplesize. K−S result is the % result of a Kolmogorov-Smirnov statistical test to determinethe probability of host and non-host stars having the same parent sample based on theirabundance distribution.

Non-Planetary Planetary Hosts Difference K−SHosts Result

O:Mean −0.06± 0.02 (90) +0.00± 0.03 (27) 0.06 8.8Median −0.05± 0.02 +0.00+0.04

−0.03 0.05Std. Dev. 0.15 0.17Mg:Mean −0.09± 0.01 (90) −0.02± 0.03 (28) 0.07 3.18Median −0.10+0.04

−0.01 +0.01+0.06−0.07 0.11

Std. Dev. 0.14 0.16Cr:Mean −0.03± 0.02 (90) +0.08± 0.03 (28) 0.11 0.55Median +0.00+0.04

−0.01 +0.12+0.03−0.02 0.12

Std. Dev. 0.16 0.17Y:Mean −0.16± 0.01 (90) −0.05± 0.03 (27) 0.11 0.01Median −0.15± 0.03 +0.00± 0.02 0.15Std. Dev. 0.14 0.16Zr:Mean −0.03± 0.02 (85) +0.06± 0.03 (26) 0.09 2.5Median −0.01+0.03

−0.02 +0.05+0.03−0.06 0.06

Std. Dev. 0.15 0.16Ba:Mean −0.11± 0.02 (85) −0.01± 0.04 (26) 0.10 1.8Median −0.11± 0.02 +0.05+0.04

−0.05 0.16Std. Dev. 0.18 0.19Eu:Mean −0.16± 0.02 (73) −0.10± 0.03 (26) 0.06 3.84Median −0.17+0.03

−0.04 −0.09+0.04−0.05 0.08

Std. Dev. 0.14 0.15Nd:Mean +0.00± 0.02 (84) +0.06± 0.03 (27) 0.06 2.15Median +0.01± 0.03 +0.09+0.01

−0.05 0.08Std. Dev. 0.14 0.15

35

non-host samples with probabilities of the same parent sample of stars for the two popu-

lations ranging from 0.01% for Y to 8.8% for O (see Table 2.3). This supports our claim

that host star elemental abundances are significantly different to those of non-host stars

and furthermore that host stars are enriched over non-host stars for all elements studied.

2.5 Elemental Trends

Plots of the current results are shown in Figures 2.1 and 2.2 - in Figure 2.1 [X/H] versus

[Fe/H] (as more commonly used in previous studies of planet host star abundances) is pre-

sented, while in Figure 2.2 [X/Fe] versus [Fe/H] (as usually analyzed in cosmochemical

studies) is shown. Two significant outliers can be seen - one host and one non-host sit-

ting below the general trend for O, Cr and Mg. These stars are HD142415 ([Fe/H]=0.02,

host) and HD199288 ([Fe/H]=0.04, non-host). These stars can be seen to be depleted

(compared to solar abundances) in the majority of elements studied here except for Fe,

suggesting that they have formed from Fe-rich precursor material based on the assump-

tion that it is easier to enrich one element than it is to deplete seven other elements. The

fact that HD142415 is also mildly enriched in both Ba and Y (with no Zr abundance

available) could also possibly indicate that the material had been processed through an

s-process environment, either an AGB star or the He-burning stage of a larger mass star.

Fe and Fe precursors: The [X/H] trends in Figure 2.1 are in agreement with the

understanding we currently have about the nucelosynthetic origin of the elements. All

of the elements located before the Fe peak (here O, Mg and Cr) increase linearly with

increasing [Fe/H] with Pearson product-moment correlation coefficients (r) above 0.70

for both host and non-host stars. This can be easily understood as the stellar evolutionary

processes that serve to increase the amount of Fe present in later generations of stars also

produce the pre-iron peak elements in various amounts. Thus as the stellar Fe content

increases, so too would the amount of pre-iron peak elements (neglecting any unusual

mixing or other nebula interactions).

36

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

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-0.5

0

0.5

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-0.5

0

0.5

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-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

Figure 2.1: [X/H] vs. [Fe/H] for all elements studied.Open squares represent non-hoststars and filled squares represent host stars. Typical error bars are shown in the upper leftof each panel. Numerical values are provided in Table A.1.Left Column: O, Mg and Cr.Center Column: Y, Zr and Ba. Right Column: Eu and Nd.

37

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

-0.5 0 0.5

-0.5

0

0.5

Figure 2.2: [X/Fe] vs. [Fe/H] plots for all elements studied. Open squares represent non-host stars and filled squares represent host stars. Typical error bars are shown in the upperleft of each panel. Numerical values are based on those shown in Table A.1 (in the [X/H]form). Left Column: O, Mg and Cr. Center Column: Y, Zr and Ba. Right Column: Euand Nd.

38

s-process: The r- and s-process elements, however, are less certain. All three s-process

elements (Y, Zr and Ba) still display to varying degrees the same trend of increasing abun-

dance with increasing [Fe/H] as the pre-iron peak elements. One possible explanation for

this observed trend is that the increase in s-process elemental abundances is due to the

increase in the number of seed nuclei (e.g. Fe atoms) available. Due to the nature of the

s-process, it is reliant on the sufficient availability of seed nuclei to be able to proceed.

Thus as the metallicity increases, so too does the abundance of s-process species.

r-process: Unlike the s-process elements, the r-process element (Eu) and the mixed

source element (Nd) do not display a strong correlation with increasing [Fe/H]. Obser-

vations of metal poor stars have shown that the abundances of s-process elements such

as Y and Ba decrease faster with metallicity than the abundances of r-process elements

such as Eu (Spite and Spite 1978). This has been attributed to a lack of appropriate seed

nuclei inhibiting the s-process significantly more than the r-process. We are alternatively

extending this into the metal-rich regime to conclude that the r-process is not as reliant on

the presence of elements such as Fe, thus explaining its lack of a strong dependance upon

metallicity.

From Figure 2.2, it can be seen that the overall [X/Fe] trends visible here are in good

agreement with those identified by Bodaghee et al. (2003) and Gilli et al. (2006) (which

are discussed in more detail below). They can also be seen as extensions into the high

metallicity region of those trends identified by Reddy et al. (2006).

2.5.1 Lighter Element Trends

In addition to examining the nature of the general trend of increasing elemental abun-

dances with increasing metallicity,basic determinations about the nature of the various

nucelosynthesis processes occurring within the precursors to these systems can be made

by considering the more subtle, second order trends present within the data.

O: [O/Fe] displays a weakly correlated decreasing trend with increasing [Fe/H] for

both the host stars (slope=−0.16, r=−0.22) and non-host stars (slope=−0.24, r=−0.32).

39

Previous studies have hinted at the possibility of a plateau starting at [Fe/H]∼0 (Reddy

et al., 2003, 2006). However, the overlap between the present sample and those previously

published is not large enough to allow us to undertake any meaningful comparison. It is

also worth noting that while the solar C/O ratio is 0.54 (Asplund et al., 2005), using the

[C/H] values previously published by Bond et al. (2006), the C/O values of the host stars

studied here range from 0.40 to 0.89. This variation has the potential to greatly impact

the C chemistry of the proto-stellar disc and thus also any terrestrial planets forming in

the system. This issue will be considered in more detail in Chapter 4.

Mg: [Mg/Fe] can be seen to display a weakly correlated trend of decreasing with

increasing [Fe/H] values producing r values of −0.32 (host stars) and −0.44 (non-host

stars). The distribution observed for Mg is in good agreement (for the [Fe/H] regions

in common) with those of previous studies who observed a decrease in [Mg/Fe] with

increasing [Fe/H] up to [Fe/H]∼−0.10 before both distributions plateaued (Beirao et al.

2005; Gilli et al. 2006; Reddy et al. 2006).

Also of interest is the Mg/Si ratio of our target stars as it has the potential to greatly

affect the chemical evolution of any terrestrial planets forming in the system. A high

Mg/Si ratio will result in all of the available Si forming olivine ((Fe,Mg)2SiO4) with

excess Mg still being available, while a low Mg/Si ratio will result in all of the available

Mg forming enstatite (MgSiO3) with excess Si forming SiO2. Utilizing the Si abundances

previously published in Bond et al. (2006), the host stars of this study were found to have

Mg/Si ratios ranging from 0.46 to 1.26, resulting in potentially large variations in the

nature of any terrestrial planets forming in these systems. This issue will be considered

in more detail in Chapter 4.

Fe Group (Cr): From Figure 2.2, it can be seen that (with the exception of one outlier)

[Cr/Fe] displays no significant trend, remaining largely unchanged over all of the [Fe/H]

values considered here. This is in good agreement with Reddy et al. (2003); Bensby et al.

(2005) and Gilli et al. (2006). The lack of a statistically significant trend with [Fe/H] is

confirmed by the low r value of −0.04 for hosts and 0.00 for non-hosts.

40

2.5.2 Heavy Element Trends

From Figure 2.2, it can be seen that all of the heavy elements display varying degrees of

a weakly negative to non-existent correlation with [Fe/H]. The r values produced range

from −0.22 (Y and Ba) to −0.56 (Nd) indicating that the correlation is not strong.

These trends are in agreement with Allende Prieto et al. (2004) and Bensby et al.

(2005) over the range of metallicity values in common with this study. We do differ

slightly from some previous studies in that we observed a stronger decrease in [Y/Fe]

with increasing [Fe/H] than was observed by Bensby et al. (2005) and disagree with pre-

vious studies who observed no significant trend with [Fe/H] for both [Ba/Fe] and [Nd/Fe]

(Reddy et al. 2003). We do observe trends in both of these samples and the difference is

attributed to the fact that we are examining a different metallicity region to that of Reddy

et al. (2003). Our population is largely concentrated in the region of [Fe/H]>0, while the

sample of Reddy et al. (2003) almost exclusively has values of [Fe/H]<0. However, it

is worth restating that the general trends in the neutron capture elements identified here

are the same as those previously identified for other solar-type stars. This implies that the

host stars examined in this paper follow the same trends as other field stars but with a bias

towards the high metallicity region. Additionally, the high degree of scatter observed in

these samples is also in agreement with previous studies.

Also of interest is the ratio of the heavy to light s-process elements as each are thought

to be produced in slightly different stellar settings. The abundance of the heavy s-process

element Ba to the light s-process elements Y and Zr is shown in Figure 2.3 as [heavy/light]

where:

[heavy/light] = [Ba/H]− [Y/H] + [Zr/H]

2

From Figure 2.3, it can be seen that there is no dependance on metallicity, with values

scattering around the solar value (0.0 by definition). This is in agreement with Reddy

41

Figure 2.3: [heavy/light] vs. [Fe/H] plots for the five heavy elements examined as part ofthis study. For the definition of [heavy/light], please see the text. Open squares indicatenon-host stars, filled squares indicate host stars and dashed lines indicate solar values.

42

et al. (2003). Thus we support their conclusion that the neutron exposure in AGB stars is

independent of the metallicity of the star itself, assuming (as Reddy et al. 2003 did) that

AGB stars are the primary source of both the heavy and the light s-process elements.

2.5.3 Correlation with Planetary Parameters

Figure 2.4 shows plots of [X/H] against planetary parameters (Msin i, semi-major axis

a, eccentricity and planetary period) for the 5 heavy elements considered in this study.

HD164427 was omitted as its companion is believed to be a brown dwarf, not a gas

giant. As can be seen visually and by the low r values (all ≤0.48 with most <0.15), no

statistically significant correlations exist between these abundances and any of the orbital

parameters. This agrees with previous studies of other elements (e.g. Reid, 2002; Santos

et al., 2003; Fischer and Valenti, 2005).

2.5.4 Correlation with Stellar Parameters

It is well known that the stellar atmospheric parameters (specifically Teff and log g) have

the potential to drastically alter photospherically determined stellar abundances. As such,

we examined the abundances presented here and as both samples produced r2 correlation

coefficients less than 0.5, we concluded that there is no statistically significant trends

present with either the stellar Teff or log g values.

2.6 Discussion

The host stars studied here do not significantly deviate from previously established galac-

tic chemical evolution trends. Instead, they can be regarded as being extensions of many

of those trends into metallicities above solar. This lack of deviation from previously

known trends strongly suggests that while they are more metal enriched than other stars

not known to host planets, the host stars themselves have not systematically undergone

any extraordinary chemical processing during their growth and evolution (in agreement

43

-0.6 -0.4 -0.2 0 0.2 0.4

0

4000

-0.6 -0.4 -0.2 0 0.2 0.4

0

4000

0

0.4

0.8

0

0.4

0.8

0

5

0

5

0

5

10

0

5

10

Figure 2.4: Orbital properties of extrasolar planetary systems vs. abundance of the heavyelements. The companion to HD164427 has been omitted as its mass makes it a likelybrown dwarf. Values for planetary parameters were obtained from Butler et al. (2006).Left: s-process elements Y (triangles), Zr (squares) and Ba (crosses). Right: r- and mixedprocess elements Eu (triangles) and Nd (squares). From top to bottom: Msini of theplanet, orbital semi-major axis of the planet, eccentricity of the orbit of the planet andperiod of the planet.

44

with Robinson et al. 2006). The conclusion that planetary hosts stars have essentially un-

dergone “normal” stellar evolution may indeed suggest that planetary formation is a nor-

mal result of the star formation process. Of course, this does not exclude planet formation

at lower metallicity values (as planets have been detected orbiting stars with metallici-

ties significantly below solar) nor does it guarantee planet formation at high metallicity

values.

There are two primary hypotheses that have been offered to explain the observed high

metallicity trend. The first is the “pollution” model which posits metal-rich material be-

ing added to the photosphere as a consequence of planetary formation (Laughlin, 2000;

Gonzalez et al., 2001; Murray et al., 2001). The second explanation is commonly referred

to as the primordial model and it suggests that the gas cloud from which these systems

formed was metal enriched, resulting in the star itself being enriched in the same elements

(Santos et al. 2001). Our conclusion that these host stars exhibit normal chemical evolu-

tion trends and that they are simply the metal-rich members of field star population lends

support to the primordial model. One would expect that pollution of the stellar photo-

sphere would produce deviations from the galactic evolutionary trends. To date no such

trends have been observed. Additionally, we also observe that the abundances of the more

volatile elements (such as O) increase with increasing metallicity for both the host and

non-host stars. This would not be the case in the pollution model as it is likely that only

the more refractory elements (such as Fe and Ni) would remain in the solid form as they

migrated towards the star (and thus be deposited in the stellar photosphere) while the more

volatile elements would be evaporated before they could be incorporated into the stellar

photosphere. As such, we would expect to see enrichment only in the refractory elements

and not the volatile elements if the pollution model is accurate. Furthermore, the fact that

we observe no trends with metallicity in the orbital parameters of the remaining planets

is difficult for the pollution model to explain. It is hard to imagine a situation whereby

almost all planetary host stars accreted a significant amount of material during planetary

formation without affecting the orbital parameters of the remaining planets. For these rea-

45

sons, we agree with previous studies (such as Santos et al. 2001, 2003, 2005 and Fischer

and Valenti 2005) and support the primordial model for explaining the metal enrichment

in planetary host stars.

The abundances reported here also impact on terrestrial planet formation and evo-

lution within these systems. Those with low Mg/Si ratios will have terrestrial planets

dominated by enstatite (MgSiO3) (with a small amount of Mg-rich olivine also present)

with other Si-based species also available (a composition similar to the Earth’s crust),

while those with high Mg/Si ratios will have olivine-dominated planets with other Mg-

rich species also present (a composition similar to the Earth’s mantle). Similarly, a high

C/O ratio will result in planets with greatly increased C contents due to solid C being in-

corporated into the planet itself. While the detailed consequences of these examples have

not yet been fully examined, it is conceivable that any terrestrial planets forming in these

systems could differ from currently known terrestrial planets in terms of their rheology

(thus possibly affecting the tectonics of such a planet) and the nature of volcanic activ-

ity, based on the varying silica contents of the magma. The full implications of such a

chemical composition for the evolution of the terrestrial planets themselves is the subject

of ongoing research and will be discussed in Chapter 4.

2.7 Summary

Elemental abundances for 8 elements, including 5 heavy elements produced by the r-

and s-processes, have been presented for 28 planetary host stars and 90 non-host stars

from the AAPS. Although the elemental abundances of the planetary host stars are only

slightly different from solar values, the host stars are enriched over the non-hosts stars in

all elements studied with the mean difference varying from 0.06 dex to 0.11 dex.

Additionally, the trends of the abundances (both [X/H] and [X/Fe]) with [Fe/H] were

considered and found to be largely in keeping with known galactic chemical evolution

trends. This implies that these systems have followed normal evolutionary pathways and

46

are not significantly or unusually altered. This leads us to conclude that not only are the

abundance trends we are observing primordial in origin and represent the initial compo-

sition of the gas nebula that produced the star and its planets but that planetary formation

may also be a natural companion to the evolution of stellar material.

Figure 2.5: GINGER MEGGS Dist. by Atlantic Feature Syndicate/United Feature Syndi-cate, Inc. Originally published 2/13/2008.

47

CHAPTER 3

SOLAR SYSTEM SIMULATIONS

3.1 Introduction

Before we can consider extrasolar terrestrial planets, we must first examine the terres-

trial planets of our own Solar System. Terrestrial planet formation, both in terms of the

dynamics and chemistry involved, is still not fully understood. Dynamically, basic plan-

etary formation is described through the planetesimal theory (see Chambers (2004) for

a detailed review). This theory sees planetary formation occurring through three main

steps. Initially, dust settles into the midplane and accretes to form planetesimals, the first

solid bodies of the system. This stage is followed by the collisional accretion of plan-

etesimals to produce planetary embryos. The growth of the embryos occurs initially via

runaway growth (where an increasing geometric cross-section and gravitational field al-

low for the accretion of an ever increasing number of planetesimals) before transitioning

to oligarchic growth (where neighboring embryos grow at similar rates). Finally, as num-

bers of planetesimals decrease, the interaction between embryos becomes the dominant

factor as they perturb each other onto crossing orbits, thus producing accretion via violent

collisions.

Many attempts have been made to simulate the third stage of terrestrial planet for-

mation described above (e.g. Kominami and Ida 2002, 2004; Chambers and Wetherill

1998; Chambers 2001; Raymond et al. 2004). However, these simulations have had lim-

ited success and no simulation has been able to exactly reproduce the terrestrial planets of

the Solar System in terms of their number, masses and orbital parameters. For example,

direct N-body simulations have produced systems with approximately the correct number

of planets yet with an orbital excitation greater than that observed for the Solar System

48

(Chambers and Wetherill, 1998; Chambers, 2001; Raymond et al., 2004). Similarly, sim-

ulations incorporating tidal torques (e.g. Kominami and Ida 2002, 2004) have produced

too many planets but with more favorable excitation levels.

Recent developments in modeling have occurred with the incorporation of dynamical

friction, the process whereby equipartitioning of energy between low mass planetesimals

and larger embryos results in reduced relative velocities for the embryos, thus increasing

their probability of accreting. Dynamical friction has been shown to be a viable mech-

anism to reduce the dynamical excitation levels of the final planets to better agree with

observed values within the Solar System (Levison et al., 2005). The highest resolution

simulations incorporating dynamical friction that have been completed to date are those

of O’Brien et al. (2006). These simulations represent a factor of ∼5 increase in the num-

ber of gravitationally interacting bodies compared to most other previous simulations of

this type (e.g. Chambers 2001), and because of the large number of small planetesimals in

the simulation, dynamical friction is more accurately treated than in previous simulations.

The terrestrial planets produced by these simulations are a significantly better fit to the

observed properties of the terrestrial planets of the Solar System. There are fewer planets

(averaging 3 to 3.5 planets per simulation) and the dynamical excitation of the planetary

systems is comparable to that of the actual terrestrial planets in the Solar System. Fur-

thermore, the accretion timescales of the planets simulated are in agreement to within a

factor of two with the accretion timescale for the Earth (∼10-30 Myr) as obtained from182Hf-182W dating. Previous simulations (e.g. Chambers and Wetherill 1998; Chambers

2001; Raymond et al. 2004) produced accretion timescales larger than that of the Earth by

a factor of four or more. However, more recent results from Touboul et al. (2007) imply

an increased accretion timescale for the Earth, nearing a value of 60Myr. This longer

timescale is consistent with the results of O’Brien et al. (2006). Thus it can be seen that

the O’Brien et al. (2006) simulations have provided us with the most realistic and feasible

models of terrestrial planet formation completed to date and represent a significant step

towards understanding the last stage of the planetary formation.

49

However, the vast majority of terrestrial planet formation studies completed to date

have been limited (at best) in their simultaneous chemical composition studies. Several

previous studies have estimated the amount of potentially hydrated material that may have

accreted into the terrestrial planets (e.g. Raymond et al. 2004; O’Brien et al. 2006) while

O’Brien et al. (2006) also considered the delivery of siderophile-rich late veneer mate-

rial needed to account for the siderophile element budget of the Earth’s mantle (Chou,

1978). However, detailed examination of the bulk chemical composition of the resulting

planets as a test of dynamical simulations has never been thoroughly explored. This com-

bination of the two approaches to produce a comprehensive model of both the chemistry

and dynamics of terrestrial planet formation is essential to determine how well current

numerical simulations reproduce not only the masses and dynamic state of the terrestrial

planets, but also their bulk composition. The present study represents a first step towards

such a model.

I have derived detailed bulk elemental abundances for all of the terrestrial planets

formed in the simulations of O’Brien et al. (2006). These predicted compositions are

compared to the bulk compositions of the actual terrestrial planets as an examination of

the chemical validity of the dynamical simulations currently being used to model terres-

trial planet formation. This approach allows me to not only examine the bulk elemental

composition of the final planets but to also study the compositional evolution with time.

Additionally I also investigate the delivery of hydrated material, which has important im-

plications for the development of habitable terrestrial planets, along with the composition

of the “late veneer” material accreted by the planets. Finally, the amount of material ac-

creted by the Sun as “pollution” during the terrestrial planet formation process and the

resulting changes in stellar photospheric abundances are also examined. This study is the

first to attempt to produce a comprehensive model of both the chemistry and dynamics

of terrestrial planet formation, and represents a major improvement in modeling both the

dynamical and chemical formation of terrestrial planets.

50

3.2 Simulations

3.2.1 Dynamical

The eight SyMBA sympletic N-body integrator simulations of O’Brien et al. (2006) were

utilized in this study. Each simulation consists of an equal distribution of mass between

Mars-mass embryos (0.0933M⊕, 25 per simulation) and planetesimals 1/40th the size

of the embryos (0.00233M⊕, ∼1000 per simulation). The initial distribution of bod-

ies is constrained by the disk surface density profile∑

(r)=∑

0(r/1AU)−3/2 with∑

0 = 8

gcm−2 (Chambers, 2001) and bodies initially located between 0.3 and 4.0 AU (O’Brien

et al. 2006). Four simulations were run with Jupiter and Saturn in low-eccentricity, low-

inclination orbits as predicted by the Nice Model (Gomes et al., 2005; Levison et al.,

2005; Morbidelli et al., 2005) (hereafter termed ‘Circular Jupiter and Saturn’, CJS) and

four with Jupiter and Saturn in their current, slightly eccentric orbits (hereafter termed

‘Eccentric Jupiter and Saturn’, EJS). Multiple terrestrial planets formed within 250Myr

in all simulations. The general system structure is shown in Figure 3.1 and the planetary

orbital properties are shown in Table 3.1. It should be noted that the formation of Mer-

cury analogs is not currently possible in the simulations of O’Brien et al. (2006) as all of

the embryos begin with a mass almost twice that of Mercury. Additionally, the planetes-

imals are not gravitationally interacting with each other, preventing formation of a small

‘Mercury’ via planetesimal accretion. Finally, perfect accretion is assumed throughout

the simulations, preventing giant impact events from striping off the crust and mantle of a

differentiated proto-Mercury, a scenario that widely suggested to explain Mercury’s cur-

rent high density. As the simulations, results and their implications have already been

discussed in great detail by previous publications, the reader is referred to O’Brien et al.

(2006) for further discussion.

51

0 0.5 1 1.5 2 2.5Semi-Major Axis

Final Planetary Systems

CJS1



CJS1

CJS2



CJS1

CJS2

CJS3



CJS1

CJS2

CJS3

CJS4



CJS1

CJS2

CJS3

CJS4

EJS1



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS

1.14 0.81 0.78

0.44 0.35 1.20 0.79

0.76 1.57 0.54

1.30 1.42

0.59 0.89 0.47

0.35 0.74 0.81

0.67 0.450.95 0.10

0.760.22 0.14 0.98

0.05 0.81 1.00 0.11



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS

1.14 0.81 0.78

0.44 0.35 1.20 0.79

0.76 1.57 0.54

1.30 1.42

0.59 0.89 0.47

0.35 0.74 0.81

0.67 0.450.95 0.10

0.760.22 0.14 0.98

0.05 0.81 1.00 0.11



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS

1.14 0.81 0.78

0.44 0.35 1.20 0.79

0.76 1.57 0.54

1.30 1.42

0.59 0.89 0.47

0.35 0.74 0.81

0.67 0.450.95 0.10

0.760.22 0.14 0.98

0.05 0.81 1.00 0.11



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS

1.14 0.81 0.78

0.44 0.35 1.20 0.79

0.76 1.57 0.54

1.30 1.42

0.59 0.89 0.47

0.35 0.74 0.81

0.67 0.450.95 0.10

0.760.22 0.14 0.98

0.05 0.81 1.00 0.11



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS

1.14 0.81 0.78

0.44 0.35 1.20 0.79

0.76 1.57 0.54

1.30 1.42

0.59 0.89 0.47

0.35 0.74 0.81

0.67 0.450.95 0.10

0.760.22 0.14 0.98

0.05 0.81 1.00 0.11



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS

1.14 0.81 0.78

0.44 0.35 1.20 0.79

0.76 1.57 0.54

1.30 1.42

0.59 0.89 0.47

0.35 0.74 0.81

0.67 0.450.95 0.10

0.760.22 0.14 0.98

0.05 0.81 1.00 0.11



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS

1.14 0.81 0.78

0.44 0.35 1.20 0.79

0.76 1.57 0.54

1.30 1.42

0.59 0.89 0.47

0.35 0.74 0.81

0.67 0.450.95 0.10

0.760.22 0.14 0.98

0.05 0.81 1.00 0.11



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS

1.14 0.81 0.78

0.44 0.35 1.20 0.79

0.76 1.57 0.54

1.30 1.42

0.59 0.89 0.47

0.35 0.74 0.81

0.67 0.450.95 0.10

0.760.22 0.14 0.98

0.05 0.81 1.00 0.11



CJS1

CJS2

CJS3

CJS4

EJS1

EJS2

EJS3

EJS4

SS

1.14 0.81 0.78

0.44 0.35 1.20 0.79

0.76 1.57 0.54

1.30 1.42

0.59 0.89 0.47

0.35 0.74 0.81

0.67 0.450.95 0.10

0.760.22 0.14 0.98

0.05 0.81 1.00 0.11

Figure 3.1: Schematic of the results of the simulations of O’Brien et al. (2006). Thehorizontal lines indicate the variation between aphelion and perihelion. The vertical linesindicate variation in distance from the midplane due to the inclination of the planet. Nu-merical values represent the mass of the planet in Earth masses. The Solar System (SS)is shown for comparison.

52

Table 3.1: Properties of simulated terrestrial planets produced in the Solar System sim-ulations of O’Brien et al. (2006). Numbering starts at 4 and increases with increasingdistance from the Sun. CJS denotes the results of the circular Jupiter and Saturn sim-ulations while EJS indicates the results of the eccentric Jupiter and Saturn simulations.

Planet M a e i(M⊕) (AU) (◦)

CJS1−4 1.15 0.63 0.05 4.36CJS1−5 0.81 1.21 0.06 4.85CJS1−6 0.78 1.69 0.04 2.06

CJS2−4 0.44 0.55 0.05 2.61CJS2−5 0.36 0.69 0.06 3.54CJS2−6 1.20 1.10 0.02 0.38CJS2−7 0.80 1.88 0.04 1.83

CJS3−4 0.77 0.62 0.05 1.54CJS3−5 1.57 1.14 0.06 2.11CJS3−6 0.55 2.09 0.06 2.07

CJS4−4 1.31 0.66 0.10 0.60CJS4−5 1.43 1.54 0.08 3.64

EJS1−4 0.59 0.56 0.03 1.69EJS1−5 0.89 0.84 0.03 1.24EJS1−6 0.48 1.29 0.03 1.55

EJS2−4 0.35 0.50 0.04 1.61EJS2−5 0.74 0.75 0.02 1.07EJS2−6 0.82 1.17 0.02 0.71EJS2−7 0.10 3.19 0.24 14.95

EJS3−4 0.68 0.58 0.04 2.12EJS3−5 0.45 1.52 0.04 3.20EJS3−6 0.96 0.96 0.02 2.10EJS3−7 0.11 2.08 0.13 7.83

EJS4−4 0.77 0.68 0.03 1.48EJS4−5 0.23 0.48 0.06 2.29EJS4−6 0.14 1.07 0.09 3.82EJS4−7 0.99 1.33 0.02 1.59

53

3.2.2 Chemical

The chemical composition of material within the disk is assumed to be determined by

equilibrium condensation within the primordial solar nebula. This assumption is a rea-

sonable starting point as numerous analyses of primitive chondritic material have shown

that their bulk elemental abundances are smooth functions of their equilibrium conden-

sation temperature, as determined for a solar composition gas at low pressure (Davis,

2006). Several possible explanations for this pattern have been proposed, with the most

widely accepted being that the chemistry of their parent planetesimals was established by

midplane temperature and pressure profiles (Cassen, 2001). Alternatively, the sluggish

nature of reaction kinetics within the cooler regions of the outer nebula may also be a

possible cause for the observed trend. Although the exact cause of the primitive chon-

dritic pattern is still unclear, I am able to utilize the fact that equilibrium condensation

temperature has been shown to be an excellent proxy for determining the bulk elemental

abundance of rock-forming elements within the early Solar System. Furthermore, obser-

vational evidence of these equilibrium compositions is still seen today, preserved as the

thermal stratification of the asteroid belt (Gradie and Tedesco, 1982). The mineralogy

of primitive chondritic meteorites is similar in most respects to that predicted by equi-

librium condensation (Ebel, 2006). Thus the assumption of equilibrium composition is a

valid starting point for this type of study. This assumption in turn implies that the primary

controls on embryo and planetesimal compositions are the radial midplane temperature

and pressure gradients encountered by the nebular material.

In order to determine the equilibrium composition of the solid material, I utilized

the commercial software package HSC Chemistry (v. 5.1). HSC Chemistry determines

the equilibrium chemical composition of a system by iteratively minimizing the system’s

Gibbs free energy, using the GIBBS equilibrium solver described in White et al. (1958).

This software has been successfully used in recent studies of solar nebula chemistry

(Pasek et al., 2005) and supernova stellar outflows, producing compositions that corre-

54

late with observed mineralogy in presolar interplanetary dust particles (Messenger et al.,

2005). As such, I feel confident in applying it to this current study. Several limitations

have been encountered with the program, primarily the limited number of elements and

species possible to incorporate in a simulation and its inability to handle species in solid

solutions such as pyroxene and olivine, two of the major rock-forming minerals on the

terrestrial planets. End member species can and have been considered but the non-ideal

solid solution interaction between them is not currently possible. These limitations will

not significantly affect the final conclusions of this current study but will be the subject

of future work. The list of solid and gaseous species included in the HSC Chemistry

calculations are shown in Table 3.2.

Our present simulations incorporate 14 major rock-forming elements (C, N, O, Na,

Mg, Al, Si, P, S, Ca, Ti, Cr, Fe and Ni), along with H and He, which dominate the partial

pressures of protoplanetary disks. Current solar photospheric abundances are utilized as

a proxy for the initial composition of the solar nebula. All inputs are assumed to initially

be in their gaseous, elemental forms and are then cooled and allowed to react. Solar

elemental abundances for all elements were taken from Asplund et al. (2005) and are

shown in Table 3.3. Although there has been some recent discussion about revising the

Solar C and O abundances (e.g. Socas-Navarro and Norton, 2007), I have adopted the

most recent and widely accepted values for this current study. The 50% condensation

temperature of each element in a gas with a Solar photosphere composition as obtained

from HSC Chemistry is shown in Table 3.4. It should be noted that although O is present

in high temperature condensates and silicate species, it does not obtain 50% condensation

until water ice condenses within the system, hence its low 50% condensation temperature.

Additionally, the 50% condensation temperatures from the models of Lodders (2003) are

also provided. The average difference between this study and that of Lodders (2003) is

just +11.75K (defined as Tpresent study - TLodders), with the largest difference being 83K

for P. The excellent agreement between the temperatures obtained in this study and those

of Lodders (2003) implies that the chemical models utilized in this study are accurately

55

Table 3.2: Chemical species included in the equilibrium calculations of HSC Chemistry.

Gaseous SpeciesAl CrO MgOH PN

AlH CrOH MgS POAlO CrS N PSAl2O Fe N2 SAlOH FeH NH3 S2

AlS FeO NO SNC FeOH NS SO

CH4 FeS Na SO2

CN H Na2 SiCO H2 NaH SiCCO2 HCN NaO SiHCP HCO NaOH SiNCS H2O Ni SiOCa HPO NiH SiP

CaH HS NiO SiP2

CaO H2S NiOH SiSCaOH He NiS TiCaS Mg O TiNCr MgH O2 TiO

CrH MgN P TiO2

CrN MgO PH TiS

Solid SpeciesAl2O3 FeSiO3 CaAl2Si2O8 C

CaAl12O19 Fe3P NaAlSi3O8 SiCTi2O3 Fe3C Cr2FeO4 TiC

CaTiO3 Fe Ca3(PO4)2 TiNCa2Al2SiO7 Ni FeS AlNMgAl2O4 P Fe3O4 CaSMg2SiO4 Si Mg3Si2O5(OH)4 MgSMgSiO3 Cr H2OFe2SiO4 CaMgSi2O6

56

Table 3.3: HSC Chemistry input values for Solar System Simulations. All values are inmoles. All species are assumed to initially be in their elemental and gaseous forma withno other species present within the system.

Element AbundnaceH 1.00 ×1012

He 8.51 ×1010

C 2.45 ×108

N 6.03 ×107

O 4.57 ×108

Na 1.48 ×106

Mg 3.39 ×107

Al 2.34 ×106

Si 3.24 ×107

P 2.29 ×105

S 1.38 ×107

Ca 2.04 ×106

Ti 7.94 ×104

Cr 4.37 ×105

Fe 2.82 ×107

Ni 1.70 ×106

reproducing the initial equilibrium composition of the solar disk.

In order to relate the chemical abundances to a spatial location within the original

disk, I used midplane pressure and temperature values obtained from the axisymetric α

viscosity disk model of Hersant et al. (2001). The Hersant et al. (2001) model is a two-

dimensional time-dependent turbulent accretion disk model incorporating vertical disk

structure, turbulent pressure and self-gravity. As for other standard disk models, a Kep-

lerian rotation law, hydrostatic equilibrium and energy balance between viscous heating

and cooling due to radiative losses are assumed (Hersant et al., 2001). The effects of

irradiation from the central star are neglected, as are other disk features such as inner

holes and shadow zones. To define a “nominal” disk model, Hersant et al. (2001) restrict

the initial disk mass to be 0.3M⊙ or less, in accordance with the gravitational instabil-

ity models of Shu et al. (1990). Similarly, angular momentum is assumed to have been

57

Table 3.4: T50% condensation for a gas with Solar photosphere composition and at P = 10−4

bar. Initial phase for each element is also listed. Values are provided from the models ofLodders (2003) for comparison.

Element T50% condensation (K) Initial PhaseThis Study Lodders (2003) Species Formula

Al 1639 1665 Hibonite CaAl12O19

C <150 40 Methane Clathrate CH4.7H2OCa 1527 1505 Hibonite CaAl12O19

Cr 1301 1291 Metallic Chromium CrFe 1339 1328 Metallic Iron FeMg 1339 1327 Spinel MgAl2O4

Na 941 953 Albite NaAlSi3O8

Ni 1351 1348 Metallic Nickel NiO 180 179 Hibonite CaAl12O19

P 1309 1226 Schreibersite Fe3PS 658 655 Troilite FeSSi 1329 1302 Gehlenite Ca2Al2SiO7

Ti 1580 1573 Perovskite CaTiO3

58

transferred via turbulence to the formation region of the outermost giant planet (Neptune)

in 2.5×105 years so as to allow for solid/gas decoupling and core formation to occur.

Initial disk temperature is taken to be greater than 1000K within 3AU from the Sun in

order to produce the crystalline silicate distributions observed in meteorites and comets

by Bockelee-Morvan et al. (2002). Finally, deuterium abundances produced by the model

must be in agreement with the values reported for LL3 meteorites at 3AU (the predicted

location of formation) and cometary values obtained for Halley, Hyakutake and Hale-

Bopp. Based on these restrictions, Hersant et al. (2001) find a “nominal” disk model is

produced by a stellar mass accretion rate of 5×10−6M⊙yr−1, an initial disk radius of

17 AU and an α value of 0.009. In the current study, I limit the midplane conditions

to be those produced by the “nominal” model. Previous work has successfully applied

this model to constrain the bulk composition of Jupiter (e.g. Pasek et al. 2005). Pressure

and temperature values were determined with an average radial separation of 0.03AU

throughout the study region.

The midplane temperature and the pressure, and thus also the equilibrium composition

of solids present within the disk, changes with time as the disk evolves. In order to

capture this effect in our simulations, I determined an ensemble of predicted planetary

compositions constrained by predicted disk conditions at multiple time periods. At the

earliest, I use the temperature and pressure profiles obtained for disk conditions at t =

2.5×105yr, where conditions were first determined to be suitable for solids to be present

across the entire radial region being modelled in the dynamic simulations. I end with disk

conditions at t = 3×106yr, the average lifetime for the protoplanetary gas disks (Haisch et

al., 2001). Five cases between these end points are considered (for disk conditions at t =

5×105yr, 1×106yr, 1.5×106yr, 2×106yr, 2.5×106yr). Thus I determine the planetesimal

and embryo compositions for a total of seven cases, covering the entire range of times

during which embryos and planetesimals could potentially form, either early or late in the

lifetime of the disk. Midplane P and T profiles for each set of simulations are shown in

Figure 3.2. Note that the timescale used for the evolution of the disk conditions is not

59

coupled with the timescale of the dynamical simulations. Rather, chemical compositions

are simply determined for a range of disk mid-plane conditions and no time-variation in

disk conditions over the duration of the dynamical simulation is incorporated.

3.2.3 Combining Dynamics and Chemistry

In order to combine these two different modeling approaches, I assume that each planetary

embryo and planetesimal of the dynamical models retains the chemical composition in

equilibrium with the nebula in the region that it first formed. The bulk compositions of

the final planets are simply the sum of each object they accrete. By tracing the origin

of each embryo and planetesimal incorporated into the final planets of the O’Brien et al.

(2006) dynamical simulations, and calculating the chemical composition of those bodies

based on their original locations, I constrain the bulk composition of the final terrestrial

planets. This procedure was completed for all planets using a small perl script at each of

the seven different time steps simulated within the chemical models.

3.2.4 Stellar Pollution

The extent of stellar pollution produced by terrestrial planet formation was measured

by determining the amount and composition of material accreted by the Sun during the

formation process and the resulting photospheric elemental abundance changes such an

addition would produce. Any solid material migrating to within 0.1AU from the Sun

is assumed to have accreted onto the Solar photosphere through gravitational attraction.

This material is then assumed to have been uniformly mixed throughout the solar photo-

sphere and convective zone. Granulation within the photosphere and gravitational settling

and turbulence within the convective zone are neglected from this present study, primarily

as there is still significant debate about and very little consensus on the exact nature of

these processes and their effects on specific elements. However, it is expected that each

of these processes would reduce the amount of accreted material present within the up-

per layers of the Sun, thus reducing the photospheric elemental abundance. As such, the

60

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

Figure 3.2: Radial midplane pressure and temperature profiles for the Solar nebula ob-tained from Hersant et al. (2001) for “nominal” conditions. “Nominal” refers to the con-ditions of M = 5×10−6M⊙yr−1, Rinital = 17 AU and α = 0.009. Top Panel: Pressureprofiles for each of the 7 disk conditions considered. Bottom Panel: Temperature profilesfor each of the 7 disk conditions considered. Times shown indicate evolutionary age ofthe disk, not the dynamical models.

61

resulting abundance changes determined in this study represent the maximum possible

values that I would expect to observe in the Solar spectrum. Additionally, at earlier times,

the mass of the solar convective zone would have been greater than the current value of

0.03 M⊙, again resulting in a smaller change in photospheric abundance than predicted

by this current study.

The mass of each element accreted by the Sun was determined in the same way as

described in section 3.2.3 for terrestrial planets. The resulting photospheric abundance is

given by:

[X/H] = log

fX

fX,⊙

(3.1)

where [X/H] is the resulting abundance of element X after accretion of terrestrial

planet material, fX is the mass abundance of element X in the Solar photosphere after

accretion and fX,⊙ is the initial mass abundance of element X in the Sun before accretion

(from Murray et al. 2001). fX,⊙ values were obtained by utilizing the solar abundances

of Asplund et al. (2005) and a current solar convective zone mass of 0.03M⊙ (Murray

et al., 2001). The present approach only addresses pollution by the direct accretion of

planetesimals and embryos during the current simulations, yet pollution may also occur

both before planetesimal accretion (and thus the simulation) begins and through the accre-

tion of dust produced by the impact and collisional events during the formation process.

Pollution by these processes is believed to be small, resulting in at most a factor of two

increase in the amount of material added to the solar photosphere.

62

3.3 Results

3.3.1 Abundance Trends

The bulk elemental abundances for all terrestrial planets for each set of disk conditions

examined are shown in Table B.1 (as elemental wt% of the planet). Additionally, the

Mg/Si value for each planet is also shown in Table B.1.

The average simulated terrestrial planet abundances are in reasonable agreement with

the abundances of their actual Solar System counterpart. The ensemble-averaged (i.e.

averaged over all disk conditions considered) mean elemental abundances for all of the

terrestrial planets are listed in Table B.2. The simulated abundances are all within 10 wt%

of the observed terrestrial planet values of Morgan and Anders (1980) (Venus), Kargel and

Lewis (1993)(Earth) and Lodders and Fegley (1997) (Mars) for the key planet-building

elements (Mg, Si, O, Fe) and display smaller deviations for the other elements (within

6 wt% for S, within 2 wt% for all other elements). However, it can be seen from Table

B.1 that the bulk elemental abundances of the final terrestrial planets vary significantly

with disk conditions, especially for certain elements such as O, Al and Ca. The dif-

ference in planetary composition between the chemical simulations undertaken for disk

conditions at t = 2.5×105yr and t = 3×106yr is shown in Table B.3. As expected, the

relative abundances of the most refractory elements (Al, Ca, Ti) are observed to decrease

for disk conditions at later times while the more volatile elements (O, Na, H) all increase

in abundance. The largest variation occurs in the O abundance, with simulations for disk

conditions at t = 3×106yr producing terrestrial planets with up to 30.79 wt% more O than

identical simulations for disk conditions at t = 2.5×105yr.

These compositional variations can be directly attributed to the changing conditions

of the disk itself. As the temperature and pressure at the mid-plane decrease with time, the

equilibrium composition at a specific radius also changes. Thus the assumed composition

of the planetesimals and embryos also change, in turn producing variations in the final

planetary abundances. Consequently, as time progresses and the disk cools, the planetary

63

composition can be seen to decrease in abundance of the most refractory elements (Al,

Ca) and increase in the more volatile elements (O, H) as volatile, hydrated species become

stable throughout an increasingly larger fraction of the disk.

A more accurate picture of the predicted planetary abundances is obtained by exam-

ining the abundances produced for each specific set of disk conditions simulated. Figure

3.3 shows the Si and planet-normalized bulk elemental composition for the planets pro-

duced in the CJS-1 and EJS-1 simulations for all seven disk conditions. The simulated

planets were normalized to Venus, Earth and Mars on the basis of their orbital properties,

primarily their semimajor axis. Normalized abundances were obtained for each simulated

planet via the relation:

Normalized abundance for element X =(X/Si)simulated

(X/Si)observed

(3.2)

where (X/Si)simulated are the abundances of element X and Si for the planet produced

by the present simulations while (X/Si)observed are the previously published abundances

of X and Si for Venus, Earth or Mars. Reference Solar System planetary abundances

were taken from Morgan and Anders (1980) (Venus), Kargel and Lewis (1993)(Earth)

and Lodders and Fegley (1997) (Mars).

All three suites of planetary reference values are themselves based (to some degree)

on modeling. Bulk Earth values were obtained by extrapolation of Best Bulk Silicate

Earth (Best BSE or BBSE) abundance values (as obtained from previously published

studies of mantle xenoliths, pyrolite and basaltic elemental ratios), the observed volatility

trend for volatile lithophile elements and the known physical and seismic properties of

the interior of the Earth (Kargel and Lewis, 1993). This approach, although necessary,

does introduce uncertainties especially when calculating the composition of the core as

partioning ratios are not well known for all elements. Furthermore, the use of a volatility

trend requires knowledge of the condensation temperature of the elements. While such

64

information is well known for several species (such as Fe, Mg and Si with errors on the

order of 3% of the condensation temperature), larger degrees of uncertainty remain for

more volatile elements. This uncertainty produces errors in the predicted condensation

temperatures of±14% of the condensation temperature itself and results in final elemental

abundance errors of 5-10% of the actual abundance for most elements, reducing to less

than 1% for Fe, Mg and Si. Of the elements considered in the current study, those with the

greatest overall uncertainty are O, S and C. Although not quantified by Kargel and Lewis

(1993), the uncertainty in O is derived from the fact that the O abundance was obtained

based on the valence states of cations. This approach is predicated on the assumption

of an abundance of 15% of all Fe present is in the form Fe3+. As such, any variation

within the assumed valence state distribution will induce a variation in the O abundance of

Earth. C and S abundances similarly suffer from large uncertainties (∼25% of the given

abundance) due to variations in the published BSE values, variations in the predicted

condensation temperatures and the partioning coefficients for each of these elements.

Bulk Mars abundances were taken from Lodders and Fegley (1997) and are based on

the combination of known meteorite material (H, CV and CI meteoritic material) required

to reproduce the oxygen isotopic abundances observed for the SNC meteorites. Variations

in the elemental compositions within each class of meteorite are thus the main source

of uncertainty in the current estimates. Lodders and Fegley (1997) estimate their final

abundance errors to be ±10% for all elements studied.

Finally, the marked lack of data regarding the elemental abundances of Venus re-

sulted in the necessary use of the purely theoretical bulk planetary abundances of Morgan

and Anders (1980) for this study. Morgan and Anders (1980) adopt a similar approach

to the one used here and assume that the composition of solid material initially present

within the system is controlled by equilibrium condensation. The exact predicted com-

position was obtained from the Ganapathy-Anders 7-component model (Morgan et al.,

1978). This model determines the composition of a body based on the amount of early

condensate (i.e. first solids present within the disk), metal, silicate, troilite, FeO, MnO and

65

Cr2O3 believed to be incorporated into a final planetary body. Bulk elemental abundances

are thus inferred from general cosmic proportions as compared to an “index element” for

each component. As such, general and solar elemental ratios are assumed to be homoge-

nous and remain constant for the entire planetary system. For the simulations of Morgan

and Anders (1980), the limited information available on the index elements for Venus

was supplemented by geochemical restrictions from the Earth, Moon and chondritic me-

teorites to obtain predicted bulk planet abundances. As such, large uncertainties exist in

all elements studied. As quantified uncertainty factors are not provided by Morgan and

Anders (1980), it is impossible to gauge the errors on their predicted abundances. How-

ever, they are believed to be considerable, resulting in elemental abundances for Venus

that should be taken as a guide only.

From Figure 3.3 it can be seen that although no single simulation exactly reproduced

the compositions of the terrestrial planets, the time when the adopted disk conditions pro-

duced simulated compositions that most closely resemble those of the terrestrial planets

(the ‘best fit’ time) is 5×105yr, based on the comparatively small deviations produced

in the bulk elemental abundances. For disk conditions at later times, significantly larger

enrichments can be seen in O, Na and S for all planets. Although not shown here, disk

conditions at this same time also produces the best agreement between simulated and ob-

served abundances for the other six simulations studied and as such future discussions will

focus on the compositions produced by the disk conditions at this time. This result does

not imply that the material which formed the terrestrial planets actually condensed out of

the Solar nebula exclusively at 5×105yr. Rather it is simply the time at which the disk

conditions and resultant snapshot of the chemistry of the Solar disk (as used here) best

reproduced the expected abundances. Similar plots for the other six simulations studied

are displayed in Figures B.2 - B.7.

Numerically, for simulations based upon disk conditions at 5×105yr, abundances

agree with Solar System values to within 1 wt% for all elements studied except for Mg (up

to 2 wt% deviation), Fe and O (up to 2.5 wt% deviation) and S (up to 5 wt% deviation). In

66

Al Ti Ca Mg Si O Ni Fe Cr P Na S

No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10

CJS1-4 (Venus)

CJS1-5 (Earth)

CJS1-6 (Mars)

EJS1-4 (Venus)

EJS1-5 (Earth)

EJS1-6 (Mars)

Increasing volatility Increasing volatility

Figure 3.3: Normalized abundances for CJS1 and EJS1 simulated terrestrial planets.The terrestrial planet each simulation is normalized to is shown in parentheses. Val-ues are shown for each of seven time steps considered with the following color scheme:black = 2.5×105 years, red = 5×105 years, green = 1×106 years, pink = 1.5×106 years,light blue = 2×106 years, yellow = 2.5×106 years and dark blue = 3×106 years. Left:CJS1 terrestrial planets. Right: EJS1 terrestrial planets. Reference Solar System plane-tary abundances were taken from Morgan and Anders (1980) (Venus), Kargel and Lewis(1993)(Earth) and Lodders and Fegley (1997) (Mars).

67

terms of normalized values, the predicted abundances are within a factor of 0.5 for almost

all elements studied. Enrichments can be seen in Na (up to 4× the expected value) and

S (up to 8× the expected value) and are discussed below. These abundances represent

an excellent agreement with observed Solar System values, indicating that these terres-

trial planet formation models are producing terrestrial planets with both orbital properties

and bulk elemental abundances comparable to those of the terrestrial planets of the Solar

System.

Despite the excellent agreement between the observed and predicted abundances, the

planet-normalized spider plots of Figure 3.3 display several systematic deviations from

the expected terrestrial planet abundances. Specifically, considerable deviations can be

seen in P (Venus analogs only), Na and S for all simulations. This is partly due to the

uncertainties in the expected planetary abundances for these elements as was previously

discussed. Additionally, as P, Na and S are some of the most volatile in this system, it

is believed that the observed enrichments are a result of the fact that I am currently not

considering volatile loss during the accretion process. Both the dynamical and chemical

simulations assume that in any given impact, perfect merging of the two bodies occurs

and all mass is retained. However, such violent impacts are known to both melt and eject

a considerable portion of both the target body and the impactor (such as in the moon

forming impact (Hartmann and Davis, 1975; Cameron and Ward, 1976)). This has the

potential to drastically alter the bulk elemental abundances of a planet and it is expected

that a significant fraction of the most volatile species in the system will be lost during the

accretionary process, thus reducing the observed enrichments. This effect has not been

incorporated into our simulations, resulting in volatile enriched final planetary bodies.

The results of a first order approach to include the abundance effects of volatile loss are

discussed in Section 3.3.5.

Some degree of radial compositional variation is captured by the current models. Sim-

ulated planets deemed to be Venus and Earth analogs were found to produce equivalent

normalized abundances for the major rock forming elements when normalized to the el-

68

emental abundances of Venus and Earth. Differences in the quality of the fit occur for P,

Na and S and are due to uncertainties in the abundances of Venus. The Mars analogs are

found to have a slightly better fit when normalized to the elemental abundances of Mars,

as compared to those of Venus and Earth. This difference is minor with Earth abundances

arguably producing an equivalent normalization. However, given the small normalized

radial compositional differences observed for Venus, Earth and Mars, it is not surpris-

ing that the approach adopted in this study has been unable to complectly reproduce the

expected radial variations.

In addition to matching the bulk elemental abundances, simulations such as these

should also reproduce the key geochemical ratios for the terrestrial planets. Here I have

considered the values of Mg/Si, Al/Si and Ca/Si. All three of these values differ by chemi-

cally significant amounts from the expected planetary values for all planets produced. For

simulations run with disk conditions at times of 5×105 years and beyond, the planetary

ratios are identical to the solar input ratios. This effect is produced by the fact that for disk

conditions at t = 5×105 years, all the Mg, Al, Ca and Si has condensed out over the study

region. This results in the solid species (and thus also the planets produced) possessing

the same chemical ratios as present in the initial solar nebula. For example, for Hersant

et al. (2001) disk conditions at t = 5×105 years, Mg/Si, Al/Si and Ca/Si ratios in the

solid material reach Solar values by 0.5AU, interior to the primary feeding zone for the

formation of Earth and Mars. Unfortunately, both the Mg/Si and Al/Si values are lower

than is observed for the Earth but above current Martian values (see Figure 3.4) while the

Ca/Si values are above those of both Earth and Mars (but in agreement for Venus). Thus

for the majority of disk conditions presently considered I am producing planets that have

compositional ratios in between those of Earth and Mars and are slightly enriched in Ca.

Variations in these elemental ratios from solar ratios are produced in simulations based

on disk conditions at 2.5×105 years (see Figures 3.4 and 3.5). At this time, the inner

disk (within approximately 1AU) is dominated by Al and Ca rich species such as spinel

(MgAl2O4) and gehlenite (Ca2Al2SiO7), resulting in planets with high Al/Si and Ca/Si

69

values and low Mg/Si values as can be seen in Figures 3.4 and 3.5. Thus it can be seen that

there is a temporal variation in the chemical ratios of the planets produced. This further

supports our choice of disk conditions at t = 5×105 years as producing the “best fit”

abundances as although the ratios discussed here do not precisely agree with the observed

values, the deviation is significantly smaller than for earlier disk conditions.

The fact that the current chemical ratios do not agree with observed planetary values

implies two possible solutions. The first is that the dynamical simulations are not forming

planets from material sourced from the correct region of the disk. There is a small radial

region within the disk where the values of Mg/Si, Al/Si and Ca/Si are in agreement with

those of Earth. This region occurs between temperatures of 1352 and 1305K, correspond-

ing to a radial location of 0.61 to 0.68AU for disk conditions at t = 2.5×105 years and

0.12 to 0.13AU for disk conditions at t = 3×106 years for the disk model of Hersant et al.

(2001). Thus one possible solution for the current difference may be that the dynamical

models need to form Earth from material located within this region. However, it is ex-

ceedingly difficult to imagine how such a formation process would occur as it requires

the movement of a large amount of material over a relatively long distance through the

disk. Current formation simulations do not produce this degree of radial mixing and it

is questionable whether sufficient material would be located within the region, making it

unlikely that such a scenario is feasible. On the other hand, the problem may lie in the

disk models I am currently using to obtain radial P and T profiles. Although there are

variations in disk models (see Boss (1998) for a review), I feel confident in our current

model as similar P and T profiles have been produced by other studies (Cassen, 2001) and

the current model has been successfully utilized by other chemical studies (e.g. Pasek

et al. 2005). Furthermore, planetary compositions produced at these temperatures would

not be in agreement with observed bulk planetary elemental abundances. Finally, obser-

vations have suggested that the temperature at 1AU in the disk of young stellar objects is

less than 400K (Beckwith et al., 1990), again making it unlikely that it would be possible

to produce the disk conditions required to produce the necessary Mg/Si, Al/Si and Ca/Si

70

Mars

fractionation

line

Al/Si (weight ratio)

0.0 0.2 0.4 0.6 0.8 1.0

Mg

/Si (

we

igh

t ra

tio

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Earth fractionation line

Figure 3.4: Al/Si v. Mg/Si for all simulated terrestrial planets. Black circles indicatevalues for disk conditions at t = 2.5×105 years while red circles indicate values for diskconditions at t = 5×105 years. Values at all other times are concentrated at the 5×105

years values and are not shown for clarity. Earth values are shown in green and are takenfrom Kargel and Lewis (1993) and McDonough and Sun (1995). Martian values areshown in pink and are taken from Lodders and Fegley (1997).

71

Ca/Si (weight ratio)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Mg

/Si (

wei

gh

t ra

tio

)

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Figure 3.5: Ca/Si v. Mg/Si for all simulated terrestrial planets. Black circles indicatevalues for disk conditions at t = 2.5×105 years while red circles indicate values for diskconditions at t = 5×105 years. Values at all other times are concentrated at the 5×105

years values and are not shown for clarity. Earth values are shown in green and are takenfrom Kargel and Lewis (1993) and McDonough and Sun (1995). Martian values areshown in pink and are taken from Lodders and Fegley (1997).Venus values are shown inlight blue and are taken from Morgan and Anders (1980).

72

values at 1AU.

The second possibility is that the composition of solids within the disk are controlled

by disequilibrium condensation. Disequilibrium condensation refers to the chemical

model in which once a solid has condensed, it is removed from the system and may

no longer interact with the remaining gas. Such a process may occur if condensation oc-

curs rapidly enough to for large bodies to grow quickly and thus shield the interiors from

further equilibrium reactions (Cowley, 1995). Under such conditions, secondary conden-

sates would have Mg/Si values above average (Sears, 2004), thus possibly increasing the

Mg/Si value to the required Earth value over the primary feeding zone in the O’Brien

et al. (2006) simulations. Additionally, observations of protoplanetary disks have shown

that much of the chemistry within the the disk itself is in disequilibrium (Bergin et al.,

2007), further supporting our suggestion of disequilibrium chemistry as the controlling

chemical factor. The apparent role of disequilibrium processes does not invalidate our

initial assumption of equilibrium controlled abundances. The assumption of equilibrium

is acceptable for determining bulk elemental abundances but finer details of planetary

composition will need to incorporate a greater interaction between a variety of equilib-

riums and disequilibrium processes. Furthermore, an equilibrium-based predictions for

simulations of this type need to be calculated initially to provide a baseline for future

disequilibrium studies.

The oxidation state of the planets is also of interest. As I am currently calculating pre-

dicted bulk elemental abundances and not detailed mineralogies for the simulated planets,

estimates of the bulk oxidation state of the planet are obtained by calculating the oxi-

dation state of the embryos and planetesimals before accretion occurred based on their

equilibrium compositions. The resultant oxidation states are shown in Figure 3.6. The

current simulations are producing very reduced planetary compositions for the earliest set

of disk conditions studied, containing large amounts of metallic Fe and little FeO. For disk

conditions at later times, the compositions become more oxidized, evolving through the

oxidation state of the H-type meteorites to finish closer to the redox state of the CR mete-

73

orites, primarily due to the increased amount of magnetite (Fe3O4) and fayalite (Fe2SiO4)

accreted by the planets. For midplane conditions at t = 2.5×105 years, fayalite is only

present in significant amounts beyond 1.07AU while magnetite is only present beyond

4.82AU, beyond the dynamical simulation range. For conditions at t = 3×106 years, fay-

alite is present beyond 0.2AU with magnetite now present beyond 0.95AU. Thus for later

disk conditions, the feeding zones of the terrestrial planets (and thus the planets them-

selves) are more oxidized.

In addition to the observed temporal variations, migratory processes within the disk

can also act to alter the oxidation state of the solid material. For example, the redistribu-

tion of water within the inner 5AU of the disk over time via diffusion and advection has

been found to significantly alter the oxidation state of the disk itself (Pasek et al., 2005;

Cyr et al., 1999), producing both reducing and oxidizing regions of various widths and

locations (depending on the initial conditions). As a result, the redox state of the solid

material should be drastically altered as the disk evolves. It is also worth mentioning

that the extremely reduced nature of the solid material may also be increased to some

extent by our present inability to simulate the olivine and pyroxene solid solutions. This

acts to limit the amount of Fe that can be oxidized and incorporated into silicate species,

thus producing more reduced compositions. The effect of this approach is believed to be

relatively minor.

Comparison of simulated oxidation values to those of the terrestrial planets is difficult,

either due to lack of direct information (Venus) or a varying redox state (Earth and Mars).

Earth has a reduced metallic core, slightly oxidized mantle and extremely oxidizing crust

while Mars may be composed of a relatively reduced core and highly oxidized crust.

Furthermore, it is believed that the redox state has varied through time (e.g. Galimov

2005). For example, in order for core formation to occur, a reduced mantle composition

is required. However, the mantle must have achieved its present oxidation level relatively

early in the Earths history as little temporal variation is observed in the oxidation state of

basalts younger than ∼3.5 - 3.9 billion years (Delano, 2001). Thus the generally reduced

74

L

EH

EL

K

H

CR

LL

CV

Figure 3.6: Oxidation state plot for CJS1 and EJS1 simulated planetary abundances.Squares indicate CJS1 values. Circles indicate EJS1 values. Values are shown for each ofseven time steps considered with the following color scheme: black = 2.5×105 years, red= 5×105 years, green = 1×106 years, pink = 1.5×106 years, light blue = 2×106 years,yellow = 2.5×106 years and dark blue = 3×106 years. Approximate regions for severalmeteorite groups are also shown.

75

nature of the planets produced in the current simulations is in excellent agreement with

the hypothesis of an initially reduced Earth and Mars before planetary processes altered

the redox state of their upper layers. The exact oxidation state of the primitive planets and

thus the best fit conditions implied by it are still unclear.

Although differences in the orbital and dynamical properties of the final planets are

produced by the two different types of simulations considered here (O’Brien et al., 2006),

the differences between the CJS and EJS simulations in terms of both their bulk elemen-

tal abundances and their geochemical ratios for rock forming elements are negligible.

Neglecting the small volatile rich planet formed in the asteroid belt in simulation EJS3,

comparable bulk compositional trends can be seen in both the CJS and EJS simulations.

This indicates that in the case of terrestrial planet formation within the Solar System, the

bulk composition of the final terrestrial planets formed is not highly dependent on the

orbital properties of Jupiter and Saturn. Once again, this is a result of the fact that the

majority of planet forming elements have fully condensed out of the nebula by 1253K,

corresponding to midplane radii within 0.75AU from the host star for the models of Her-

sant et al. (2001) and do not change greatly in their relative weight percentage values over

the remainder of the simulation region. As a result the majority of the solid mass within

the present simulations has solar elemental abundances. This is consistent with the idea

that the equilibrium chemical composition of the Solar nebula is not highly zoned in that

it does not contain radially narrow zones of vastly different compositions. Instead, the

vast majority of the solar disk is dominated by material composed of pyroxene (MgSiO3),

olivine (Mg2SiO4) and metals (Fe and Ni). Figure 3.7 shows the weight percentage (in

solid material) of the key planet building elements O, Fe, Mg and Si, in addition to the

mass distribution of the dynamical simulations. It can be seen that the majority of mass is

expected to have similar relative elemental abundances. The small variations observed in

the weight percent vales are caused by increases in the solid portion of disk mass gener-

ated by the condensation of FeS at 1AU and serpentine (Mg3Si2O5(OH)4) at 3.5AU. Thus

small variations in the feeding zones produced by different orbital properties of Jupiter

76

and Saturn within the CJS and EJS simulations are unlikely to produce major differences

in final bulk composition. Difference between the two types of simulation emerge when I

consider the delivery of hydrous species (Section 3.3.4).

3.3.2 Variations with Time

Figure 3.8 shows the variation with time for weight percentage values of several key

planet building elements in the planets produced by the CJS1 and EJS1 simulations. It

can be seen from Figure 3.8 that very little variation in composition (<5 wt%) occurs

during the formation process with the bodies obtaining their final compositions relatively

early during accretion and displaying only minor deviations over time. The same trend is

also observed for the six other simulations not shown. This implies that the planets within

these simulations formed homogenously (i.e. from material with similar composition

to the final planet). If formation did occur in this manner, then the presence of a 800-

1000km deep magma ocean would be required during core formation in order to produce

the siderophile abundances observed in the crust and upper mantle of the Earth (Drake,

2000).

However, it is likely that the homogenous accretion observed here is due to the ‘snap-

shot’ approach I have taken when determining the composition of solid material within

the disk. In these simulations, I have considered the composition determined by disk con-

ditions at just seven discrete times. In reality, it is quite likely that the composition of

solid material will change over time as it undergoes migration and experiences other disk

and stellar processes (such as the redistribution of water (Cyr et al., 1999)). Such changes

are not captured in our current approach. As such, more detailed chemical models incor-

porating temporal variations in the composition of solid material are required in order to

test the homogenous accretion produced here.

77

O

Fe

Si

Mg

Al

Figure 3.7: Distribution of solid mass and its relative composition within the Solar diskat 5×105 years. Top: Composition (in wt%) for the solid material within the disk for O(black), Fe, (red), Mg (green), Si (blue) and Al (yellow). Bottom: Initial distribution ofmass within the dynamical simulations of O’Brien et al. (2006).

78

Time (Myr)

0 50 100 150 200 250

wt

%

0

10

20

30

40

Time (Myr)

0 50 100 150 200 250

wt

%

0

10

20

30

40

0 50 100 150 200 250

wt

%

0

10

20

30

40

0 50 100 150 200 250

wt

%

0

10

20

30

40

0 50 100 150 200 250

wt

%

0

10

20

30

40

0 50 100 150 200 250

wt

%

0

10

20

30

40

O

Fe

Si

Mg

O

Fe

Si

Mg

O

Fe

Si

Mg

O

Fe

Si

Mg

O

Fe

Si

Mg

O

Fe

Si

Mg

CJS1-4

CJS1-5

CJS1-6

EJS1-4

EJS1-5

EJS1-6

CJS1-4

CJS1-5

CJS1-6

Figure 3.8: Temporal variation in the elemental abundances of the final terrestrial plan-ets produced by the CJS1 and EJS1 simulations. Variations in compositions are due tothe accretion of embryos and planetesimals throughout the dynamical simulations. Blackindicates the abundance of O, red indicates the abundance of Fe, blue indicates the abun-dance of Si and green indicates the abundance of Mg. Left: CJS1 simulation results.EJS1: EJS1 simulation results.

79

3.3.3 Late Veneer

An alternative hypothesis to homogenous accretion is heterogeneous accretion where the

composition of material accreted changes significantly with time. Under this hypothe-

sis, siderophile distribution within the Earth is explained via accretion of a “late veneer”

(Chou, 1978). Referring to the last ∼1% of mass accreted by the Earth, this material

would need to be siderophile-rich and highly oxidized, containing essentially no metallic

iron (Drake and Righter, 2002). Although carbonaceous chondrites are sufficiently oxi-

dized and contain limited metallic Fe, their Os isotopic abundances are not in agreement

with values required for the late veneer. On the other hand, ordinary chondrites do posses

Os isotopic ratios of the correct value but are not oxidized. As such, we currently have

no samples in the meteorite record that represent a possible source for the late veneer

material (Drake and Righter 2002).

As expected from the previously observed homogenous accretion, the late veneer of

the present simulations is similar in composition to the final planetary abundance. Here

the late veneer is taken to be the material accreted after the last impact by a projectile

with mass > Membryo. This material is not highly oxidized and is primarily composed of

olivine, pyroxene, metallic iron, troilite (FeS), diopside (CaMgSi2O6), nickel and albite

(NaAlSi3O8). This composition is similar to that of the ordinary chondrites. Furthermore,

as noted in O’Brien et al. (2006), the planets produced in the EJS simulations accrete an

average of∼10% of the final planetary mass as a late veneer, an order of magnitude above

the predicted amount. Thus it can be seen that the current simulations do not successfully

reproduce the late veneer material. However, as discussed in sections 3.3.1 and 3.3.2,

migration of material and temporal variations in the composition of solid material accreted

have the potential to drastically alter the composition of the late veneer. Such variations

are not currently captured by the current simulations.

80

3.3.4 Hydrous Species

Differences between the CJS and EJS simulations emerge when considering the delivery

of hydrous species to the final planets. In the present simulations, “hydrous species” refers

to water ice and the aqueous alteration product serpentine (specifically clinochrysotile

Mg3Si2O5(OH)4). As stated in O’Brien et al. (2006), the planets formed in the EJS sim-

ulations do not accrete significant amounts of volatile rich material from beyond 2.5AU

(with the exception of the same planet formed in the EJS3 simulations as previously men-

tioned). Thus for disk conditions before 1×106 years, these planets are found to contain

no hydrous species. For disk conditions after this time, however, all terrestrial planets pro-

duced in the EJS simulations are found to have significant water components, although

generally less than those of the CJS terrestrial planets. The appearance of water and ser-

pentine at later times is largely due to the migration of the ice line to be located within the

region from which material is being obtained for the dynamical simulations. The planets

formed via the CJS simulations, however, all contain significant amounts of serpentine

and water ice for disk conditions at t = 5×105 years. At this time, seven planets include

hydrous material (<0.008M⊕), incorporated via the accretion of one to four planetesi-

mals each containing a minor amount of serpentine. Only one planet contained a signif-

icant amount of serpentine (0.02M⊕). All eight planets accreted the hydrous material

before the late veneer and during the stage where large, violent impacts were occurring.

As such, it is expected that a significant component of this hydrous material would be

vaporized during later impact events and subsequently lost from the final planetary body

or incorporated into the planetary core. Only four planets (including two Earth analogs)

accreted serpentine (0.001 - 0.003M⊕) as part of their late veneer. Given the relatively

late delivery of this material, it is believed that the majority would be retained during later

planetary processing. As one would intuitively expect, the amount of hydrous material

accreted by a planet increases with increasing planetary semimajor axis.

Assuming that all of the hydrogen accreted as hydrous species is converted to water,

81

the current simulations are producing planets containing 0.6 to 24.8 Earth ocean masses

of water for disk conditions at 5×105 years. If I assume that Venus initially possessed

a similar amount of water to the Earth while Mars contained 0.06 - 0.27 Earth oceans

of water (Lunine et al., 2003), then it can be seen that for all of the terrestrial planets

considered, the present simulations are producing planets with sufficient water to avoid

the need to invoke other large-scale exogenous water delivery sources such as cometary

impacts. Of course, these values should be considered to be extreme upper limits on

the amount of total water present within the planet as some will undoubtedly be lost by

photodissociation, Jean’s escape and (definitely in the case of Earth) by the formation of

organic species which contain large amounts of H. Additionally, primordial accretion of

water (as predicted here) would result in H being accreted to the core of the planet via

element partioning, thus acting to decrease the amount of water available on the planetary

surface (Okuchi, 1997). Although values for the amount of water expected to be lost by

these processes are unknown, it is still likely that a significant portion of the initial water

will be retained within or on the crust.

Temporal variations in the composition of the disk are likely to increase the amount

of hydrous material accreted by the planets due to water-rich material being stable over

a drastically larger fraction of the disk. These time-dependent variations can be observed

in my current approach as simulations undertaken for conditions at 3×106 years produce

terrestrial planets containing up to 1200 Earth ocean masses of water, well above the levels

observed for simulations under disk conditions at 5×105 years. My current approach also

does not account for the possibility of water delivery via adsorption of water onto solid

grains later incorporated into planetesimals (Drake and Campins, 2006). As all of the

solid material considered in the current simulations would be bathed in H2O vapor, it

is possible that a significant amount of water could be delivered to the final planets via

adsorption that is not presently accounted for. Thus it appears likely that the terrestrial

planets form “wet” with a sizeable portion of their primordial water delivered as a natural

result the planetary formation process.

82

This conclusion does not consider the resulting D/H ratio of the accreted water, a key

constraint on any water delivery hypothesis, as isotopic abundances can not be determined

in our current approach. Primordial D/H ratios are known to vary greatly, from 2−3×10−5

for protostellar hydrogen (Lecluse and Robert, 1994) to 9×10−5 for aqueous inclusions in

meteorites (Deloule and Robert, 1995). Similar variations can be seen in solid bodies with

carbonaceous chondrites containing values close to that of the Earth (1.5×10−4) while

Mars appears to be enriched in D with D/H values around 3×10−4 (Drake and Righter,

2002). Thus it is difficult to make detailed predictions about the possible D/H ratios of the

simulated planets. However zeroth order predictions can be made if I assume that the D/H

ratio decreases linearly with increasing semimajor axis from the observed Martian value

to that of Jupiter’s atmosphere (2.6×10−5). As all of the hydrous species in the current

simulations are produced beyond 3.6AU (for disk conditions at t = 5×105 years), I can

assume that the D/H ratio will be less than 1.4×10−4. Thus it is expected that the D/H

ratios for the simulated planets will be less than the currently observed planetary values.

However, given the large degree of processing this material is expected to experience both

during and after planet formation, it is likely that the planetary D/H values will increase

as H is preferentially lost from the system.

3.3.5 Volatile Loss

Although the loss of volatile material in large impact events is believed to be significant,

detailed studies of such a loss during terrestrial planet formation have not been under-

taken. As such, I am limited to making only first-order approximations of the amount of

each element lost from the final planet due to impacts. To do this, I need to determine

both the amount of the final body that is molten and/or vaporized after each impact and

the amount of each element that would be lost from the molten phase. Using equation 9

from Tonks and Melosh (1993), the volume of melt produced by the initial shockwave of

83

an impact, Vm, is given by:

Vm = VprojρP

ρtcos1/2i

(vi

vmi

)3/2

(3.3)

where Vproj is the volume of the projectile, ρP is the density of the projectile, ρt is the

density of the target, i is the impact angle (as measured from the vertical), υi is the impact

speed and υmi is the minimum impact speed needed to produce melting.

Thus it can be seen that to first order:

Vm ∝ VprojρPv3/2i (3.4)

Since the fraction of the planet that is molten (fm) is also directly proportional to the

volume of the planet that is molten, I have:

fm ∝ VprojρPv3/2i (3.5)

Thus it is possible to determine the fraction of the final planet that is molten after each

impact by scaling the fraction given in Tonks and Melosh (1993) for a υi = 15 kms−1

impact with the Vproj , ρP and υi values determined by the O’Brien et al. (2006) models.

Note that this approach assumes constant values for ρt, i and υmi . Although these values

will undoubtedly change, I am unable to provide any limitations for them at this time. As

such, I adopt the values from Tonks and Melosh (1993).

The amount of each element assumed to be lost from the molten phase is based on the

condensation temperature of the element. The most volatile element present in solid form

84

(C, primarily present as CH4.7H2O and polyaromatic hydrocarbons in the Solar nebula)

was set to lose 100% of its mass from the melt. For all other elements, the percentage

lost was determined from the observed elemental depletions in ordinary chondrites (as

compared to CI chondrites) with respect to the 50% condensation temperature as taken

from Davis (2006). CI chondrites are widely believed to be the most primitive and un-

altered meteorites. Thus the elemental depletions relative to CI chondrites observed in

other meteorite classes are believed to be due to processing of material within the solar

protoplanetary disk and as such serves as an excellent proxy for the loss of volatile ma-

terial. The percentage of each element assumed to be lost in each impact event is shown

in Table 3.5. Note that the condensation temperature of O is taken to be the condensation

temperature of silicate, the dominant form of O throughout the majority of the disk. The

amount of each element lost was then determined after each impact event, based on the

υi value of the projectile itself. All lost volatile material was assumed to be permanently

removed from the planet.

This approach is obviously based on several broad assumptions and can only provide

order of magnitude approximations for the loss of volatile material. In addition to as-

suming details about each impact event (such as ρt, cos1/2i), this approach assumes that

the target body has completely cooled and resolidified between impacts (i.e. each impact

occurs with two cold solid bodies). A hotter body produces a larger melt fraction (Tonks

and Melosh, 1993) and is expected to result in greater loss of material from each impact

event. Furthermore, I currently only consider melting produced by the initial shockwave

as it moves through the body. Detailed hydrocode simulations need to be undertaken in

order to examine how volatile losses would vary under more realistic conditions including

differentiation (or lack thereof) of the target body, atmospheric losses, impacts into a still-

molten embryo and recapturing of re-condensed species, as well as determining the fate

of the ejected material. Furthermore, the current dynamical models assume perfect accre-

tion for each of the impact events. To obtain more realistic simulation conditions, loss of

volatile material needs to be incorporated into the simulated impact events. However, this

85

Table 3.5: The percentage of each element assumed to be lost from the melt produced byindividual impact events. Values are based on depletions observed in meteorite samplesand are taken from Davis (2006).

Element Tcond (K) % LostC 78 100.00N 131 97.69H 182 92.90S 704 49.90

Na 958 32.92P 1248 16.69Cr 1296 14.32O 1316 13.37Ni 1353 11.64Fe 1357 11.45Mg 1397 9.65Si 1529 4.16Ti 1593 1.75Ca 1659 0.00Al 1677 0.00

approach is currently computationally very demanding and is not yet feasible.

As expected, loss of material through impacts reduced the amount of volatile species

present in the final planetary bodies but did not significantly alter the abundance of more

refractory species. Table B.4 shows the abundances of the simulated planets after impact-

induced elemental loss has been incorporated. This loss of volatile elements can best be

seen in the planet normalized abundances shown in Figure 3.9. Normalized abundances

for the other six simulations are shown in Figures B.8 - B.14. Clear reductions in the

amount of volatile elements (specifically Na and S) can be seen, while negligible changes

are produced in the abundances of the more refractory elements (such as Fe, Cr and Mg).

These reductions in the abundance of the most volatile elements are unable to produce

final planetary abundances in exact agreement with the observed planetary abundances

within the Solar System but they do represent a substantial improvement, and indicate

86


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

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10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10

CJS1-4 (Venus)

CJS1-5 (Earth)

CJS1-6 (Mars)

EJS1-4 (Venus)

EJS1-5 (Earth)

EJS1-6 (Mars)


Figure 3.9: Normalized abundances for CJS1 and EJS1 simulated planets showing abun-dances after volatile loss was considered. The solid line indicates the normalized abun-dances before volatile loss during impacts was considered while the dashed line indi-cates the normalized abundance once volatile loss during impacts has been incorporated.All abundances were determined for disk conditions at t = 5×105 years. The terrestrialplanet each simulation is normalized to is shown in parentheses. Reference Solar Sys-tem planetary abundances were taken from Morgan and Anders (1980) (Venus), Kargeland Lewis (1993)(Earth) and Lodders and Fegley (1997) (Mars). Left: CJS1 terrestrialplanets. Right: EJS1 terrestrial planets.

87

that impact-induced melting and vaporization (and the associated loss of material) is an

important factor in determining the bulk elemental abundances of volatile species within

a planet.

The average fraction of the planet melted in each individual impact event is < 5% for

both simulations (2.8% for the CJS simulations, 3.5% for the EJS simulations). Only one

simulation (EJS1) produced an impact event large enough to melt and/or vaporize the en-

tire target body. This event was the 10th impact occurring on this body and thus occurred

early in the dynamical formation simulation (t = 9.72×106 years for the dynamical sim-

ulation). As such, it is likely that although the entire body would have been disrupted by

the event, a solid body may have reformed from the remaining material afterwards. More

detailed simulations are required to determine the full effects of large-scale impacts such

as this one on the terrestrial planet formation process.

3.3.6 Solar Pollution

Insignificant amounts of pollution of the Solar photosphere occurred during the terres-

trial planet formation simulations. A maximum of 0.135M⊕ of solid material was added

to the Sun in the CJS simulations, while the EJS simulations contributed a maximum

of 1.11M⊕. The ensemble-averaged resulting solar abundances are shown in Table 3.6.

The addition of solid material generated in the CJS simulations produced no observable

enrichment in the Solar spectrum. The EJS simulations, however, did produce a minor

enrichment of up to 0.02 dex for Ti and Al, 0.01 dex for C, N, Na, Mg, Al, Si, P, S, Ca,

Cr, Fe and Ni and no enrichment in O. Nonetheless, this enrichment is not large enough

to be definitively detected with current spectroscopic studies as many such studies pro-

duce stellar abundances with errors equivalent to or larger than the expected enrichment

(e.g. ±0.03 for Fischer and Valenti (2005)). As such, any Solar pollution produced by

terrestrial planet formation with the Solar System is believed to be negligible.

88

Table 3.6: Mean change in solar photospheric abundances produced by pollutionvia accretion of solid material during terrestrial planet formation. All solid mater-ial migrating to within 0.1AU from the Sun during the simulations of O’Brien et al.(2006) is assumed to be accreted. Change is defined as Abundanceafter planet formation -Abundancebefore planet formation.

Element SimulationCJS-1 CJS-2 CJS-3 CJS-4 EJS-1 EJS-2 EJS-3 EJS-4

Mg 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01O 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00S 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01Fe 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01Al 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01Ca 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01Na 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01Ni 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01Cr 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01P 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01Ti 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01Si 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01

89

3.4 Discussion

My simulations successfully produce terrestrial planets that are in excellent agreement

with the terrestrial planets of the Solar System, in terms of both their dynamics and their

bulk elemental abundances. Although current simulations are unable to capture the finer

details of planetary formation (such as the amount and composition of the late veneer

material), the success of these simulations on a broader scale provides us with increased

confidence in the dynamical models of O’Brien et al. (2006). Furthermore, it also serves

to validate the approach utilized here to combine detailed dynamical and chemical mod-

eling together. This will allow for reliable application of this approach not only to other

dynamical models but also to extrasolar planetary systems.

The final bulk elemental compositions of the simulated terrestrial planets for rock

forming elements are not strongly constrained by the orbital properties or evolution of

Jupiter and Saturn as can be seen by the strong similarities between the CJS and EJS

simulations. The only significant differences occur in the amount of water rich material

accreted onto the final planets. This suggests that the bulk chemical evolution of the

terrestrial planets is to a large extent independent of the evolution of the giant planets.

This conclusion, however, is only valid for late stage and in situ formation after the giant

planets have formed and undertaken the vast majority of their migration. Simulations are

currently running to examine the effects on planetary composition of formation occurring

during giant planet migration. As Jupiter and Saturn are not believed to have undergone

extensive migration based on recent studies (Gomes et al., 2005; Levison et al., 2005;

Morbidelli et al., 2005), the issue of migration is not a significant one for the Solar System.

However, it will be an important issue for extrasolar planetary systems where many are

thought to have experienced large amounts of migration.

The delivery of water and other volatile species to the final terrestrial planets appears

to be a normal outcome of terrestrial planet formation, implying that it is normal for such

planets to accrete significant amounts of water. As such, it negates the need for large-scale

90

delivery of water and other volatile species by such exotic processes as cometary impacts.

Later planetary processing (especially within the mantle) would have resulted in dis-

sociation of some of the primordial water, causing a significant amount of H to migrate to

the core of the Earth or alternatively to be lost from the planet. This migration, however,

would have left a large amount of OH in the mantle, thus increasing its redox state. This

process allows us to explain the evolution of the Earth’s redox state over time from the

initially reduced state produced by the current simulations to the present stratified redox

state. This conclusion, however, requires a more detailed experimental understanding of

the efficiency of H partioning within the mantle and core of the Earth, along with the

evolution of mantle processes and mixing.

It is interesting to note the order of magnitude difference between the CJS and EJS

simulations in the amount of solid material added to the Sun during terrestrial planet for-

mation. This may potentially have great bearing on extrasolar planetary host stars as many

known extrasolar planets are currently in eccentric orbits. If such an orbit always results

in a greater amount of solid material being accreted by the host star, then it may give

more weight to the pollution hypothesis which has previously been suggested to explain

the observed [Fe/H] enrichment (e.g. Laughlin 2000; Gonzalez et al. 2001; Murray et al.

2001). However, no correlation has been found between known planetary eccentricity and

the metallicity of the host star (e.g. Reid, 2002; Santos et al., 2003; Fischer and Valenti,

2005; Bond et al., 2006), suggesting that this is not a strong effect. I determined that

a negligible amount of solid material was added to the Solar photosphere during terres-

trial planet formation and that no observable elemental enrichment would be produced.

While similar simulations are needed for extrasolar planetary systems, the current simu-

lations support the conclusion that the observed metal enrichment in extrasolar host stars

is primordial in origin, established in the giant molecular cloud from which these systems

formed as has been concluded by other studies (such as Santos et al. 2001, 2003, 2005

and Fischer and Valenti 2005). Of course, this does not rule out the possibility that ex-

trasolar planetary host stars may have in fact accreted a giant planet during the formation

91

and migration process and thus display higher levels of pollution. Host star pollution for

extrasolar planetary systems is discussed further in Chapter 4.

Finally, biologically important elements are obviously of great interest, especially for

the Earth. Of the six major biogenic elements (H, C, N, O, S and P), four are accreted

in excess by the planets during their formation (H, O, S and P). Only C and N are not

accreted during planetary formation. Both species are primarily present as solids within

an equilibrium Solar nebula as clathrates (methane or ammonia trapped in a water ice

lattice) and organics. As these species only form in the outermost regions of the disk, they

could only be delivered to the final planets via cometary and meteorite impacts, migration

or temporal variations within the disk or some combination of all three. Therefore delivery

of material from the outer regions of the disk are necessary in the current models for life

to be able to develop.

Assuming the outer regions of the disk are the source for C and N, all of the biolog-

ically important elements are accreted in the form believed to be required required for

the early evolution of life. C and N are reduced in their clathrate forms and O would be

present in several forms (oxides, silicates and hydrous material). S is primarily accreted

in its reduced form as troilite (FeS) while P accreted both as schribersite (Fe3P) and phos-

phates, both of which can be utilized by early life. Therefore our results are in agreement

with current predictions for chemical requirements for the evolution of early life on Earth.

3.5 Summary

Bulk elemental abundances have been determined for the simulated terrestrial planets of

O’Brien et al. (2006). These abundances are in excellent agreement with observed plane-

tary values, indicating that the models of O’Brien et al. (2006) are successfully producing

planets comparable to those of the Solar System in terms of both their dynamical and

chemical properties, adding greater weight to their predictive properties. Simulated redox

states are also in agreement with those predicted for the early Earth. Although differences

92

do exist between the observed and predicted geochemical ratios, these are believed to be a

result of our assumption of equilibrium controlled compositions. Additionally, the current

simulations are unable to successfully reproduce the accretion of a late veneer of material

by the early Earth, in terms of both the chemistry and, in the case of the EJS simulations,

the amount.

Significant amounts of water are accreted in the present simulations, implying that

the terrestrial planets form “wet” and do not need significant water delivery from other

sources. N and C, however, do still need to be delivered to an early Earth by some other

process in order for life to develop.

Additionally, the bulk elemental abundances of the final planets in the current simu-

lations are not strongly dependent on the orbital properties of the giant planets with the

CJS and EJS simulations both producing comparable results. This suggests that although

the orbits of Jupiter and Saturn are of great dynamical importance to the evolution of the

terrestrial planets, they may not exert such a large influence over the chemical evolution

of the same planets in late stage in-situ formation.

Finally, the pollution of the outer layers of the Sun via solid material during planetary

formation produces a negligible photospheric elemental enrichment. Assuming similar

levels of pollution in other planetary systems, this in turn implies that the high metallicity

trend observed in extrasolar planetary systems is in fact primordial.

93

Figure 3.10: PEARLS BEFORE SWINE c© Stephan Pastis/Dist. by United Feature Syn-dicate, Inc. Originally published 4/2/2007.

94

CHAPTER 4

EXTRASOLAR PLANETARY SYSTEM SIMULATIONS

4.1 Introduction

Extrasolar terrestrial planets are a tantalizing prospect. Given that the number of plan-

ets in the galaxy is expected to correlate inversely with planetary mass, it is expected

that Earth-sized terrestrial planets are much more common than giant planets (Marcy

et al., 2000). Although still undetectable by current exoplanet searches, the possibility

of their existence in extrasolar planetary systems has been examined by several authors.

Many such studies have focussed on the long term dynamical stability of regions within

the planetary system where such planets could exist for geologic timescales (Barnes and

Raymond, 2004; Raymond and Barnes, 2005; Asghari et al., 2004). Several systems have

been found to posses such regions (e.g. Barnes and Raymond 2004), indicating that if they

are able to form, terrestrial planets may still be present within extrasolar planetary sys-

tems. Additionally, many of these systems appear to be ‘packed’, containing no available

space in which another planet could be inserted and still be dynamically stable (Barnes

and Raymond, 2004). If this same packing principle holds true for other systems then it

can be utilized to predict regions in which planets are likely to be detected. Analyses of

this nature are of great interest to future planet search missions as they assist in constrain-

ing future planet search targets. However, they provide little insight into the formation

mechanism of such planets and do not necessarily indicate the presence of a terrestrial

planetary companion.

Few other studies have gone one step further and undertaken detailed simulations of

terrestrial planet formation within specific systems. Raymond et al. (2005) considered

terrestrial planet formation in a series of hypothetical ‘hot Jupiter’ simulations and found

95

that terrestrial planets can indeed form in such systems provided the ‘hot Jupiter’ is lo-

cated within 0.5AU from the host star. Furthermore, such planets may even have water

contents comparable to that of the Earth. Terrestrial planets have been found to form even

in simulations of systems which have undergone large-scale migration of the known giant

planet (Mandell et al., 2007). Terrestrial planets were found to form both exterior and

interior to the giant planet after migration has occurred and many were located within the

habitable zone of the host star. As many extrasolar planets are believed to have experi-

enced such a migration, it is encouraging to still be able to form terrestrial planets within

these systems. To date, only Raymond et al. (2006) have undertaken terrestrial planet for-

mation simulations for specific planetary systems. They considered four known planetary

systems and found that terrestrial planets could form in one of the systems (55Cancri).

Small bodies comparable to asteroid sized objects would be stable in another (HD38529).

Although such simulations have not been undertaken for a large number of planetary sys-

tems, early studies have indicated that approximately one-third of extrasolar planetary

systems may be ‘habitable’, containing a terrestrial planet located within the habitable

zone of the system (Mandell et al., 2007) and that many more may still contain other

terrestrial bodies.

An even more intriguing question beyond whether or not such terrestrial planets could

exist within these systems is their potential chemical composition. Extrasolar planetary

host stars are already known to be chemical unusual (Gonzalez, 1997, 1998; Butler et al.,

2000; Gonzalez and Laws, 2000; Gonzalez et al., 1999; Gonzalez and Vanture, 1998;

Santos et al., 2000, 2001, 2004; Gonzalez et al., 2001; Smith et al., 2001; Reid, 2002;

Fischer and Valenti, 2005; Bond et al., 2006) (see Chapter 2), displaying systematic en-

richments in Fe and smaller, less statistically significant enrichments in other species such

as C, Si, Mg and Al (Gonzalez and Vanture, 1998; Gonzalez et al., 2001; Santos et al.,

2000; Bodaghee et al., 2003; Fischer and Valenti, 2005; Beirao et al., 2005; Bond et al.,

2006). Given that these enrichments are primordial in origin (Santos et al., 2001, 2003,

2005; Fischer and Valenti, 2005), it is thus natural to assume that the planet forming ma-

96

terial within these systems will be similarly enriched. Hints of such a correlation between

transiting giant planets and stellar metallicity have been observed (Guillot et al., 2006;

Burrows et al., 2007). Consequently, it is possible that terrestrial extrasolar planets may

have compositions reflecting the enrichments observed in the host stars. Furthermore,

several known host stars have been found to have C/O values above 0.8 (see Chapter 2).

Systems with high C/O ratios will contain large amounts of C phases (such as SiC, TiC

and graphite), resulting in any terrestrial planets within these systems being enriched in

C and potentially having compositions and mineralogies unlike any body yet observed

within our Solar System.

Despite the likely chemical peculiarities and the early successes of terrestrial planet

formation simulations, no studies of extrasolar terrestrial planet formation completed to

date have considered both the dynamics of formation and the detailed chemical composi-

tions of the final terrestrial planets produced. This present study addresses this issue by

simulating late-stage in-situ terrestrial planet formation within nine extrasolar planetary

systems while simultaneously determining the bulk elemental compositions of the plan-

ets produced. This is the first such study to consider both the dynamical and chemical

nature of potential extrasolar terrestrial planets and it represents a significant step towards

gaining a greater understanding of the full diversity of extrasolar terrestrial planets.

4.2 System Composition

Before considering detailed simulations of planetary formation and composition, we first

need to consider the geochemical trends observed in extrasolar planetary host stars.The

two most important elemental ratios for determining the mineralogy of extrasolar terres-

trial planets are C/O and Mg/Si. The ratio of C/O controls the distribution of Si among

carbide and oxide species. If the C/O ratio is greater than 0.8, Si exists in solid form

primarily as SiC. Additionally, significant amounts of solid C are also present as planet

building materials. For C/O values below 0.8, Si is present in rock-forming minerals as

97

SiO4, allowing for the formation of silicates. The silicate mineralogy is controlled by the

Mg/Si value. For Mg/Si values less than 1, Mg is in pyroxene (MgSiO3) and the excess Si

is present as other silicate species such as feldspars. For Mg/Si values ranging from 1 to 2,

Mg is distributed between olivine (Mg2SiO4) and pyroxene. For Mg/Si values extending

beyond 2, all available Si is consumed to form olivine with excess Mg available to bond

with other elements as MgO.

The photospheric C/O vs. Mg/Si values for known extrasolar planetary host stars are

shown in Figure 4.1, based on stellar abundances taken from Gilli et al. (2006) (Si and

Mg), Beirao et al. (2005) (Mg), Ecuvillon et al. (2004) (C) and Ecuvillon et al. (2006b)

(O). A conservative approach was taken in determining the errors shown in Figure 4.1

(bottom panel). The errors published for each elemental abundance were taken as being

the 2 σ errors (based on the method used to determine them) and were used to determine

the maximum and minimum abundance values possible with 2 σ confidence for each

system. The elemental ratios produced by these extremum abundances were thus taken as

the 2 σ range in ratio values and are shown as errors in Figure 4.1.

The mean values of Mg/Si and C/O for all extrasolar planetary systems for which

reliable abundances are available are 1.28 and 0.65 respectively, which are above solar

values (Mg/Si⊙ = 1.00 and C/O⊙ = 0.54). This non-solar average and observed variation

implies that a wide variety of terrestrial planet compositions are present within extrasolar

planetary systems and that not all of them can be expected to be identical to that of Earth.

Of the 62 systems shown, 13 have C/O values above 0.8, implying that carbide minerals

are important planet building materials in over 20% of planetary systems. The idea of C-

rich planets is not new (Kuchner and Seager, 2005) but the potential prevalence of these

bodies has not been previously recognized, nor have specific systems been identified as

likely C-rich planetary hosts. These data demonstrate that there are a significant number

of systems in which terrestrial planets have compositions vastly different to any body

observed in our Solar System.

However, a high degree of uncertainty is associated with the values shown in Fig-

98

Mg/Si

0.0 0.5 1.0 1.5 2.0 2.5

C/O

0.0

0.5

1.0

1.5

2.0

2.5

Mg/Si

0.0 0.5 1.0 1.5 2.0 2.5

C/O

0.0

0.5

1.0

1.5

2.0

2.5

Figure 4.1: Mg/Si vs. C/O for known planetary host stars with reliable stellar abundances.Stellar photospheric values were taken from Gilli et al. (2006) (Si, Mg), Beirao et al.(2005) (Mg), Ecuvillon et al. (2004) (C) and Ecuvillon et al. (2006b) (O). Solar valuesare shown by the red circle and were taken from Asplund et al. (2005). The dashedline indicates a C/O value of 0.8 and marks the transitions between a silicate-dominatedcomposition and a carbide-dominated composition. Top Panel: Stellar ratios with errorbars removed for clarity. Bottom Panel: Stellar ratios with 2-σ error bars included.

99

ure 4.1. The primary source of this error is errors in the stellar elemental abundances

themselves. Spectrally determined abundances are sensitive to continuum placement and

stellar atmospheric parameters such as Teff , log g, metallicity and microturbulence. The

uncertainty produced by each parameter is determined via sensitivity studies. Each para-

meter was varied in turn by a specified amount (±100 K for Teff ,±0.3 dex for log g,±0.3

dex for metallicity and ±0.05 dex for microturbulence) and the resulting variation in the

elemental abundance was determined. Thus the final error was obtained by summing in

quadrature the sensitivity errors, continuum placement error (typically 0.05 dex) and stan-

dard deviation of each mean abundance (where the elemental abundance was determined

from more than one spectral line):

σ2final = σ2

std + σ2continuum + σ2

Teff + σ2logg + σ2

[Fe/H] + σ2micro (4.1)

This results in an average error of ±0.04 for [Mg/H], ±0.07 for [Si/H], ±0.08 for

[C/H] and ±0.09 for [O/H]. These errors result in considerable percentage uncertainties

for the Mg/Si and C/O values of up to 124%. Although large, the errors will not de-

crease until we are able to improve the uncertainty on each individual stellar elemental

abundance.

Of the four elements considered here, O is the most troublesome and controversial.

Three different spectral lines are available for determining the photospheric O abundance

- the forbidden OI lines located at 6300 and 6363 A the OI triplet located between 7771

A and 7775 A and the OH lines located near 3100 A (Ecuvillon et al., 2006b). Previous

studies have found discrepancies between abundances obtained from different spectral

lines for the same star of up to 1 dex (Israelian et al., 2004). Each of these lines is sub-

ject to interferences from different stellar sources. The forbidden OI lines are weak and

blended with Ni, the OI triplet is influenced by non-local thermodynamic equilibrium

(non-LTE) effects and the OH lines are influenced by stellar surface features (Ecuvillon

100

et al., 2006b). Ecuvillon et al. (2006b) undertook a detailed examination of the correla-

tion between these different O indicators for a sample of 96 host and 59 non-host stars.

Their study showed that the discrepancies in abundances determined by the three differ-

ent indicators was less than 0.2dex for the majority of stars examined. The forbidden OI

and OH lines were found to be in excellent agreement with each other while abundances

obtained from the O triplet lines (with the appropriate NLTE corrections applied to them)

were systematically lower. However, all three indicators produced abundances in keeping

with the galactic evolutionary trends observed for lower metallicity (and thus younger)

stars (Ecuvillon et al., 2006b). The C/O ratios shown in Figure 4.1 are based on the O

abundances from Ecuvillon et al. (2006b) obtained from the forbidden OI spectral line

observed at 6300.3 A as abundances from this line are in agreement with the abundances

obtained from the OH line and produce a marginally better fit to stellar evolutionary mod-

els

Given the errors associated with each individual elemental abundance and thus also

ratio value, it is natural to consider the error associated with the dispersion seen in Figure

4.1. The observed dispersion is produced by both dispersion in the data and dispersion

due to errors. Thus it is probable that the real range in elemental ratios is less than is

shown in Figure 4.1 and fewer planetary systems have C/O values above 0.8. Based on

the errors described above and shown in Figure 4.1, only 2 of the 62 planetary systems

shown (3% of the sample) can be said with 2 σ confidence to have C/O values above 0.8.

This increases to just 3 planetary systems (5% of the sample) when I reduce the confidence

interval to 1 σ. It should be noted that such a drastically reduced C-rich population is a

worst case scenario, based on the assumption that all potentially C-rich systems identified

in Figure 4.1 have a true, error-free C/O ratio at the lower limit of their 2-sigma errors.

This is not likely to be true for all systems but allows for a conservative estimation of the

true C/O distribution.

Similar values are observed for the abundance ratios of both host and non-host stars

obtained in Chapter 2. Based on the values and errors listed in Tables A.1 and A.2 and

101

shown in Figure 4.2, only 2 of the 26 host stars (8% of the sample) and 2 of the 77

non-host stars (3% of the sample) can be said to have C/O values above 0.8 with 2 σ

confidence.

Thus it is probable that a reduced number of planetary systems will be C-rich while

most will be Solar-like in terms of their bulk elemental ratios. This represents a signif-

icant reduction in spread from that shown in Figure 4.1. If the real dispersion is this

small, then it implies that C-rich systems would be relatively rare and terrestrial extraso-

lar planets (if present) would be dominated by pyroxene and olivine in almost all known

planetary systems. Although a diminished distribution in stellar C/O values would reduce

the prevalence of the extremely C-rich condensation sequences of the present study, the

fact remains that several planetary systems would still contain significant amounts of C

and carbide phases as major planet building elements. Thus although potentially not com-

mon, the C-rich systems considered here still warrant detailed study and investigation.

Although it is highly desirable to compare Mg/Si and C/O values for host and non-

host star populations, sufficient data is currently unavailable for a large sample of non-host

stars. Although Gilli et al. (2006); Beirao et al. (2005); Ecuvillon et al. (2006b) do pro-

vide Mg, Si and O abundances for non-host stars, C abundances are provided by Ecuvil-

lon et al. (2004) for just 3 non-host stars in common with these previous studies. Due to

the potential of introducing systematic instrument and/or processing errors by combining

stellar abundances from a variety of sources and the lack of available abundances, a com-

parison between host and non-host stars was not undertaken based on values published

by these studies.

Instead, the stellar abundances determined in Chapter 2 and shown in Figure 4.2 were

compared. The C/O and Mg/Si distributions for both host and non-host stars are shown

in Figure 4.3. Both the host and non-host star populations display the same distributions.

The mean, median and standard deviation for both the host and non-host stars is shown

in Table 4.1. Given the excellent agreement between the two populations, I conclude

that known planetary host stars are not preferentially biased towards higher C/O or Mg/Si

102

Mg/Si

0.0 0.5 1.0 1.5 2.0 2.5

C/O

0.0

0.5

1.0

1.5

2.0

2.5

Mg/Si

0.0 0.5 1.0 1.5 2.0 2.5

C/O

0.0

0.5

1.0

1.5

2.0

2.5

Figure 4.2: Mg/Si vs. C/O for host and non-host stars based on abundances determinedin Chapter 2. Open circles indicate stars not currently known to harbor a planetary com-panion. Filled circles indicate known planetary host stars. Solar values are shown by thered circle and were taken from Asplund et al. (2005). The dashed line indicates a C/Ovalue of 0.8 and marks the transitions between a silicate-dominated composition and acarbide-dominated composition. Top Panel: Stellar ratios with error bars removed forclarity. Bottom Panel: Stellar ratios with 2-σ error bars included.

103

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

Mg/Si Ratio

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

15

20

25

30

C/O Ratio

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

15

20

25

30

Chapter 2

host stars

Chapter 2

host stars

Chapter 2

non-host stars

Chapter 2

non-host stars

Figure 4.3: C/O and Mg/Si distributions for host and non-host stars based on the abun-dances determined in Chapter 2 and shown in Table A.2. Left: C/O distributions for host(top) and non-host (bottom) stars. Right: Mg/Si distributions for host (top) and non-host(bottom) stars.

values compared to stars not known to harbor a planetary companion. This in turn implies

that the prevalence of C-rich planetary systems identified above is not statistically unusual

(in terms of stellar composition).

However, the Mg/Si and C/O values shown in Figure 4.3 should not be directly com-

pared to values obtained from abundances provided other similar spectroscopic studies

(such as those of Beirao et al. (2005) and Gilli et al. (2006)). As was previously discussed

in Chapter 2, systematic deviations from previously published abundances for the 29 host

stars in common with the studies of Beirao et al. (2005) and Gilli et al. (2006) were iden-

tified in the [Mg/H] values. The observed difference is due to the use of a smaller number

104

Table 4.1: Statistical analysis of the host and non-host star distributions of Mg/Si and C/O.All values are based on the abundances determined in Chapter 2. The quoted uncertaintyis the standard error in the mean.

Mean Median StandardDeviation

Mg/Si:Host Stars 0.83± 0.04 0.80 0.22

Non-Host Stars 0.80± 0.03 0.79 0.16

C/O:Host Stars 0.67± 0.03 0.68 0.23

Non-Host Stars 0.67± 0.03 0.69 0.23

of Mg spectral lines in the present study. This abundance shift acts to skew the Mg/Si

distribution towards lower values and thus prohibiting direct numerical comparison. This

can be seen in Figure 4.4 where the Mg/Si distributions for both host and non-host stars

are noticeably offset from previously published values. Additionally, the O abundances

of Chapter 2 were obtained from the O triplet located at 7771 A 7774 A and 7775 A. As

previously discussed, O abundances obtained from these spectral lines have been found

by Ecuvillon et al. (2006b) to be lower than those from the OI line located at 6300.3 A.

The resulting shift in C/O values, however, appears to be negligible based on the distri-

butions shown in Figure 4.4. Until the complete reasons for these offsets are understood

and corrected for (where possible), direct comparisons will be restricted to comparing

distributions only.

105

Previously published

host stars

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

15

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

15

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

15

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

15

Mg/Si Ratio

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

15

20

25

30

C/O Ratio

0.0 0.5 1.0 1.5 2.0 2.5

Nu

mb

er

of

sta

rs

0

5

10

15

20

25

30

Previously published

host stars

Chapter 2

host stars

Chapter 2

host stars

Chapter 2

non-host stars

Chapter 2

non-host stars

Figure 4.4: C/O and Mg/Si distributions for previously published host stars, along withvalues for host and non-host stars based on the abundances determined in Chapter 2 andshown in Table A.2. Left: C/O distributions for previously published host stars (top), hoststars from Chapter 2 (middle) and non-host stars from Chapter 2 (bottom). Right: Mg/Sidistributions for previously published host stars (top), host stars from Chapter 2 (middle)and non-host stars from Chapter 2 (bottom).

106

0 1 2 3 4 5 6 7

Semimajor Axis (AU)

55Cnc

GJ777A

HD4208

HD72659

HD142415

HD19994

HD108874

HD4203

HD177830

0 1 2 3 4 5 6 7

Semimajor Axis (AU)

Planetary Systems

55Cnc

GJ777A

HD4208

HD72659

HD142415

HD19994

HD108874

HD4203

HD177830

Figure 4.5: Location of known giant planets in the systems selected for study. The hor-izontal lines indicate the variation from periastron and apastron. The size of the circlesscales with the planetary Msini value. All planets are assumed to have zero inclination.All values taken from the Butler et al. (2006) catalog.

4.3 Simulations

4.3.1 Extrasolar Planetary Systems

Nine known extrasolar planetary systems spanning the entire spectrum of observed plane-

tary systems were selected for this study. By studying planetary systems with such a wide

range of both chemical and dynamical properties, I am exploring the full diversity of pos-

sible extrasolar terrestrial planets. The dynamical and chemical details of each system

are shown in Tables 4.2, (orbital parameters of known planetary companions), 4.3 (stellar

abundances in logarithmic units) and 4.4 (stellar abundances normalized to 106Si atoms),

while the known giant planet architecture is shown in Figure 4.5 and the C/O and Mg/Si

values are shown in Figure 4.6. Note that the innermost planet of 55Cnc was neglected in

our present simulations due to its location and low mass.

107

Table 4.2: Orbital parameters of known extrasolar planets for the systems studied. Valuestaken from the University of California catalog located at www.exoplanets.org

Planet M a e(MJupiter) (AU)

55Cnc-b 0.82 0.11 0.0255Cnc-c 0.17 0.24 0.0555Cnc-d 3.84 5.84 0.0855Cnc-e 0.02 0.04 0.0955Cnc-f 0.14 0.70 0.20

Gl777-b 1.55 4.02 0.35Gl777-c 0.06 0.13 0.07

HD4203-b 2.07 1.16 0.52

HD4208-b 0.81 1.64 0.01

HD19994-b 1.69 1.43 0.30

HD72659-b 3.30 4.76 0.26

HD108874-b 1.30 1.05 0.21HD108874-c 1.07 2.75 0.16

HD142415-b 1.69 1.07 0.50

HD177830-b 1.43 1.22 0.03

108

Tabl

e4.

3:Ta

rget

star

elem

enta

lab

unda

nces

inst

anda

rdlo

gari

thm

icun

its,

norm

aliz

edto

Han

dSo

lar

valu

es.

See

text

for

refe

renc

es.

Ele

men

t55

Cnc

Gl7

77A

HD

4203

HD

4208

HD

1999

4H

D72

659

HD

1088

74H

D17

7830

HD

1424

15[F

e/H

]0.

330.

240.

40−0

.24

0.24

0.03

0.23

0.33

0.21

[C/H

]0.

310.

290.

45−0

.01

0.39

−0.1

10.

210.

48−0

.02

[O/H

]0.

130.

220.

00−0

.14

0.11

0.11

−0.1

00.

38−0

.21

[Na/

H]

0.26

0.26

0.42

−0.2

20.

480.

070.

130.

370.

15[M

g/H

]0.

480.

330.

48−0

.12

0.21

0.11

0.27

0.56

0.17

[Al/H

]0.

470.

340.

51−0

.10

0.32

0.07

0.30

0.54

0.17

[Si/H

]0.

290.

240.

44−0

.23

0.23

0.05

0.14

0.31

0.15

[S/H

]0.

120.

100.

20−0

.38

−0.0

5−0

.23

0.14

0.31

0.12

[Ca/

H]

0.08

0.11

0.24

−0.3

10.

17−0

.03

0.01

−0.0

70.

13[T

i/H]

0.36

0.32

0.41

−0.1

40.

180.

130.

200.

310.

31[C

r/H

]0.

220.

170.

33−0

.28

0.20

−0.0

10.

150.

130.

18[N

i/H]

0.31

0.25

0.42

−0.2

50.

270.

010.

180.

390.

18

109

Tabl

e4.

4:Ta

rget

star

elem

enta

labu

ndan

ces

asnu

mbe

rofa

tom

san

dno

rmal

ized

to10

6Si

atom

s.Se

ete

xtfo

rref

eren

ces.

Ele

men

t55

Cnc

Gl7

77A

HD

4203

HD

4208

HD

1999

4H

D72

659

HD

1088

74H

D17

7830

HD

1424

15Fe

9.55×1

058.

71×1

057.

94×1

058.

51×1

058.

91×1

058.

32×1

051.

07×1

069.

12×1

051.

00×1

06

C7.

94×1

068.

51×1

067.

76×1

061.

26×1

071.

10×1

075.

25×1

068.

91×1

061.

12×1

075.

13×1

06

O9.

77×1

061.

35×1

075.

13×1

061.

74×1

071.

07×1

071.

62×1

078.

13×1

061.

66×1

076.

17×1

06

Na

4.27×1

044.

79×1

044.

37×1

044.

68×1

048.

13×1

044.

79×1

044.

47×1

045.

25×1

044.

57×1

04

Mg

1.62×1

061.

29×1

061.

15×1

061.

35×1

061.

00×1

061.

20×1

061.

41×1

061.

86×1

061.

10×1

06

Al

1.10×1

059.

12×1

048.

51×1

049.

77×1

048.

91×1

047.

59×1

041.

05×1

051.

23×1

057.

59×1

04

Si1.

00×1

061.

00×1

061.

00×1

061.

00×1

061.

00×1

061.

00×1

061.

00×1

061.

00×1

061.

00×1

06

Ca

3.89×1

044.

68×1

043.

98×1

045.

25×1

045.

50×1

045.

25×1

044.

68×1

042.

63×1

046.

03×1

04

Ti2.

88×1

032.

95×1

032.

29×1

033.

02×1

032.

19×1

032.

95×1

032.

82×1

032.

45×1

033.

55×1

03

Cr

1.15×1

041.

15×1

041.

05×1

041.

20×1

041.

26×1

041.

17×1

041.

38×1

048.

91×1

031.

45×1

04

Ni

5.50×1

045.

37×1

045.

01×1

045.

01×1

045.

75×1

044.

79×1

045.

75×1

046.

31×1

045.

62×1

04

110

Mg/Si

0.0 0.5 1.0 1.5 2.0 2.5

C/O

0.0

0.5

1.0

1.5

2.0

2.5

Figure 4.6: Mg/Si vs. C/O for planetary host stars studied. Filled circles indicate systemsselected for this study. Stellar photospheric values were taken from Gilli et al. (2006) (Si,Mg), Beirao et al. (2005) (Mg), Ecuvillon et al. (2004) (C) and Ecuvillon et al. (2006b)(O). Solar values are shown in red and were taken from Asplund et al. (2005). The dashedline indicates a C/O value of 0.8, the point at which the solid composition transitions frombeing silicate-dominated to being carbide-dominated.

4.3.2 Dynamical Simulations

In the current study, I build upon our recent success in simulating terrestrial planet forma-

tion within the Solar System (as discussed in Chapter 3) and apply the same methodology

here. N-body simulations of terrestrial planet accretion in each of the selected extrasolar

planetary systems are run using the SyMBA n-body integrator (Duncan et al., 1998). The

orbital parameters of the giant planets in each system are taken from the catalog of Butler

et al. (2006), and updated as additional data on these systems were obtained. Inclinations

of each of the giant planets are assumed to be zero since no such measurements have been

obtained for these systems. Due to the computational time required, current simulations

only contain an initial population of embryos (i.e. no planetesimal swarm is included).

This differs from the previous simulations of O’Brien et al. (2006) as used in Chapter 3.

111

As such, it is possible that differences between the current extrasolar dynamical simu-

lations and those of the Solar System as used in Chapter 3 will occur, most likely with

regards to the dynamical excitation of the system and accretion time.

The inclusion of a large swarm of planetesimals (∼1000 in the simulations of O’Brien

et al. (2006)) was found by O’Brien et al. (2006) to reduce the overall excitation of the

system when compared to previous Solar System simulations such as that of Chambers

and Wetherill (1998) and Chambers (2001). This is a result of the increased number

of gravitational interactions occurring during the formation process between the planets

and the large number of planetesimals. Each interaction acts to damp the eccentricity

of the planet while simultaneously exciting the planetesimal. Thus the resultant degree

of damping for the final planets is naturally increased in simulations containing a large

number of planetesimals. As such, the exclusion of the planetesimal swarm from the

present simulations may result in planets with a higher excitation.

The degree of radial mixing for simulations with and without planetesimals is also

of interest. O’Brien et al. (2006) found that all CJS simulations underwent a significant

degree of radial mixing, indicating that planets were not being produced from material

originally located adjacent to their final orbital positions. The simulations of Chambers

(2001) with a smaller planetesimal population were found to produce a lower degree of

radial mixing. However, the Chambers (2001) simulations only extended out to 2AU

while the simulations of O’Brien et al. (2006) extended out to 4AU, thus permitting a

larger degree of mixing to occur and not necessarily implying a connection between in-

creased numbers of planetesimals and radial mixing. A better comparison of the effects

of planetesimals on radial mixing within the dynamical simulations can be obtained by

comparing the EJS simulations of O’Brien et al. (2006) with Model C from Chambers and

Wetherill (1998) (with Jupiter and Saturn in their current orbital configurations and with

planetesimals initially present to 4AU). Chambers and Wetherill (1998) find that 31% of

embryos located between 2 and 3AU and 18% of embryos between 3 and 4AU are incor-

porated into the final planet. In contrast to this, O’Brien et al. (2006) finds that only trace

112

amounts of material from beyond 2.5AU are accreted by the final planet. No embryos

from beyond 2.5AU are accreted and 5 of the 14 planets produced by the EJS simulations

contain no planetesimals from this region either. The observed reduction in radial mixing

is believed to be due to interactions with the planetesimals forcing embryos into reso-

nances with the giant planets. From this point, it is relatively easy to remove the embryos

from the system through ejection or accretion by the Sun. The same effect is believed to

have produced the Kirkwood gaps within the asteroid belt within our Solar System. Thus

it appears that the inclusion of a planetesimal swarm in simulations with eccentric orbits

for Jupiter and Saturn reduces the degree of radial mixing occurring within the system.

As this configuration is the most analogous to the majority of known extrasolar planetary

systems, it is thought that a similar effect may be observed in simulations for extrasolar

planetary systems. Of course, this is highly dependent on the exact orbital parameters of

the planets present within the system. It is conceivable that planetesimals will be accreted

from a larger semimajor axis range, but the increase in radial mixing produced may be

offset by the embryos being accreted over a smaller range as gravitational interactions

with planetesimals damp their orbits.

To examine these effects in more detail, simulations were run for a hypothetical sys-

tem with a Jupiter-mass planet located at 1AU. Two sets of four simulations were run

- one with only embryos present and one with both embryos and ∼500 planetesimals

present. Surface mass density profiles that vary as r−3/2, normalized to 10 gcm−3 at 1

AU, were assumed and each simulation was run for 1×108 years. The median number

of planets formed in each set of simulations, 50% and 90% formation times and radial

mixing parameter are shown in Table 4.5. As in O’Brien et al. (2006), the extent of radial

mixing is characterized by σ where:

σ =Σimi|afin,i − ainit,i|/afin,i

Σimi

(4.2)

113

where mi is the initial mass of each embryo, ainit,i is the initial semi-major axis of each

embryo and afin,i is the final semi-major axis of each embryo (i.e. the semi-major axis of

the planet produced) (Chambers, 2001).

Based on the values shown in Table 4.5, it can be seen that the presence of a plan-

etesimal swarm acts to reduce the number of terrestrial planets produced. Three of the

four simulations run without planetesimals produced two terrestrial planets while each

of the four simulations run with both embryos and planetesimals present produced only

one terrestrial planet. Both planetary masses and formation timescales increased in the

simulations including planetesimals. The increased timescale in the presence of plan-

etesimals is in contrast to the result seen by Chambers and Wetherill (1998) and O’Brien

et al. (2006) for Solar System simulations. The precise cause of this difference is not clear

and requires further work. However, it is possible that in the planetesimal-free simula-

tions the more highly excited embryos are simply unable to interact and collide with each

other, thus resulting in a higher number of low mass terrestrial planets being produced

in a relatively short timeframe. The presence of planetesimals, however, acts to dampen

the excited embryos and produces a smaller number of larger planets. Additionally, the

planetesimals may also be inducing some degree of radial migration within the embryo

population, producing a pileup of material and thus a single, larger mass planet. Marginal

differences can be seen in the degree of radial mixing encountered within each simulation.

The embryo-only simulations experienced a smaller degree of mixing, primarily due to

the lack of both planetesimal-induced migration and accretion of planetesimal material

from a broader range of radii.

Caution should be used when extrapolating the results of the test simulations described

above to all extrasolar planetary systems considered here as variations in the precise struc-

ture of the system may influence the final results of any simulation. However, based on

the test simulations with and without planetesimals, we do not expect to see drastic dif-

ferences in the net results of the current study once planetesimals are included. The

increase in radial mixing is not substantial enough to drastically alter the bulk planetary

114

Table 4.5: Statistical analysis of the embryo and planetesimal and embryo only extrasolarplanetary system simulations. Number refers to the median number of terrestrial planetsproduced. σ is the median value of the radial mixing parameter (see text for definition).T50% and T90% is the median time required for the planet to accrete 50% and 90% of itsfinal mass respectively.

Embryos and EmbryosPlanetesimals Only

Number 1 2σ 0.35 0.24

T50% 1.80×106 7.55×105

T90% 3.63×106 1.51×106

abundances produced by the current approach and the difference in planetary size and

number is highly dependant on the exact system architecture. Thus I feel confident in

the approach applied here where system-specific simulations are run with a population of

embryos only.

For each extrasolar planetary system modeled, planetary embryos are distributed in

the zone between the star and the giant planets (or in the case where there are one or more

giant planets close to the host star, in the region between the inner and outer giant planets)

according to the relations between embryo mass, spacing, and orbital radius given by

Kokubo and Ida (2000). No embryos are initially located interior to 0.3 AU. The timestep

for the integration was set to at least 20× the orbital period of the innermost planet or

planetary embryo, or the orbital period of a body at 0.1 AU, whichever is smaller (this

corresponds to a 1 day timestep for an inner radius of 0.1 AU), and the simulations

are run for 100-250 Myr. Surface mass density profiles that vary as r−3/2, normalized

to 10 gcm−3 at 1 AU, were again assumed. For each system, a minimum of 4 accretion

simulations were run.

Migration of the giant planets is very likely to have occurred in all of these systems.

However, if migration occurred very early, prior to planetesimal and embryo formation,

then terrestrial planets could have potentially formed after migration, with the giant plan-

115

ets in their current configurations (e.g. Armitage 2003). Our simulations focus on this

scenario (termed here “in-situ formation”). If giant planet migration occurred after plan-

etesimals and embryos have formed, then our in-situ assumption does not apply and there

is likely to be radial migration of planetary embryos, driven by giant planet migration

(eg. Raymond et al. 2006; Mandell et al. 2007). However, as there is currently no clear

consensus as to the most common timing of planetary migration, and no evidence for the

specific systems that I propose to study, each of our simulations begin with the gas giants

already fully formed and located in their current positions.

4.3.3 Chemical Simulations

Once again, the chemical composition of material within the disk is assumed to be de-

termined by equilibrium condensation within the primordial stellar nebula. Equilibrium

condensation sequences for an identical list of elements as used in Chapter 3 (H, He, C,

N, O, Na, Mg, Al, Si, P, S, Ca, Ti, Cr, Fe and Ni) were obtained from the commercial

software package HSC Chemistry (v. 5.1) using the same list of gaseous and solid species

as previously listed in Table 3.2.

Observed stellar photospheric abundances were adopted as a proxy for the composi-

tion of the stellar nebula. Given the deviations observed in the stellar elemental abun-

dances of Chapter 2, elemental abundances for this study were taken from Gilli et al.

(2006); Beirao et al. (2005); Ecuvillon et al. (2004, 2006b). The input values used in

HSC Chemistry for each system are shown in Table 4.6. All species are initially assumed

to be in their elemental and gaseous form and no other species or elements are assumed

to be present within the system. It should be noted that all abundances applied here were

taken from the same research group and were obtained from the same spectra thus acting

to limit any possible systematic differences in abundances due to instrument or method-

ological differences between various studies. Similarly, stellar abundances were taken

from the references specified instead of using the values determined in Chapter 2 due to

the deviation in [Mg/H] values previously discussed.

116

The solar O abundance itself has experienced a ‘crisis’ in recent years (Ayres et al.,

2006) with several studies suggesting that a downward revision of the solar O value is

required (e.g. Ayres et al. 2006; Socas-Navarro and Norton 2007). This in turn would

act to drastically alter the observed O abundances for extrasolar planetary host stars as all

abundances are currently scaled against the solar value. However, realistic errors for the

suggested new O abundance are approximately 0.1 dex (Socas-Navarro and Norton, 2007)

and the abundances of the present study vary from [O/H] = 0.38 (HD 177830) to [O/H] =

−0.21 (HD 142415), a range of 0.59 dex. As our present study range is almost six times

larger than the errors of the revised O abundance, I feel confident in the compositional

variations identified here as being caused by variations in the stellar O abundances of

specific systems.

Neither N or P abundances have been obtained for extrasolar planetary host stars, pri-

marily due to the difficulty in finding unblended spectral lines to use within the visual

spectral range (where most studies have been focussed). For this present study, I over-

came this issue by obtaining approximate abundances for both elements based on the well

known odd-even effect. Caused by the increased stability of even atomic number nuclei

relative to odd-numbered nuclei, this effect produces the observed sawtooth pattern in the

Solar elemental abundances. As both Na and P are odd-numbered nuclides, extrasolar

abundances were obtained by fitting a linear trend through the solar abundances of odd

nuclides and then applying this same fit to observed extrasolar host star abundances of

Na and Al (odd nuclides). This approach assumes that extrasolar host stars will display

the same atomic sawtooth pattern, a valid assumption as host stars do not appear to have

undergone any form of systematic processing (such as pollution by a nearby supernova

event) to cause a significant deviation (see Chapter 2).

117

Tabl

e4.

6:H

SCC

hem

istr

yin

putv

alue

sfo

rthe

extr

asol

arpl

anet

ary

syst

ems

stud

ied.

All

inpu

tsar

een

tere

din

toth

esi

mul

atio

nsof

HSC

Che

mis

try

thei

rel

emen

tala

ndga

seou

sst

ate.

All

valu

esar

ein

mol

esan

dar

eba

sed

onth

est

ella

rab

unda

nce

valu

eslis

ted

inTa

bles

4.3

and

4.4.

Ele

men

tSy

stem

55C

ncG

l777

AH

D42

03H

D42

08H

D19

994

HD

7265

9H

D10

8874

HD

1778

30H

D14

2415

H1.

00×1

012

1.00×1

012

1.00×1

012

1.00×1

012

1.00×1

012

1.00×1

012

1.00×1

012

1.00×1

012

1.00×1

012

He

8.51×1

010

8.51×1

010

8.51×1

010

8.51×1

010

8.51×1

010

8.51×1

010

8.51×1

010

8.51×1

010

8.51×1

010

C5.

01×1

085.

25×1

086.

92×1

082.

40×1

086.

03×1

081.

91×1

083.

98×1

087.

41×1

082.

34×1

08

N1.

23×1

081.

29×1

081.

70×1

080.

59×1

081.

48×1

080.

47×1

080.

98×1

081.

82×1

080.

58×1

08

O6.

17×1

087.

59×1

084.

57×1

083.

31×1

085.

89×1

085.

89×1

083.

63×1

0810

.96×1

082.

82×1

08

Na

2.69×1

062.

69×1

063.

89×1

060.

89×1

064.

47×1

061.

74×1

062.

00×1

063.

47×1

062.

09×1

06

Mg

10.2

3×1

077.

24×1

0710

.23×1

072.

57×1

075.

50×1

074.

37×1

076.

31×1

0712

.30×1

075.

01×1

07

Al

6.92×1

065.

13×1

067.

59×1

061.

86×1

064.

90×1

062.

75×1

064.

68×1

068.

13×1

063.

47×1

06

Si6.

31×1

075.

62×1

078.

13×1

071.

91×1

075.

50×1

073.

63×1

074.

47×1

076.

61×1

074.

57×1

07

P6.

76×1

055.

01×1

057.

42×1

051.

82×1

054.

79×1

052.

69×1

054.

57×1

057.

95×1

053.

39×1

05

S1.

82×1

071.

74×1

072.

19×1

070.

58×1

071.

23×1

070.

81×1

071.

91×1

072.

82×1

071.

82×1

07

Ca

2.45×1

062.

63×1

063.

55×1

061.

00×1

063.

02×1

061.

91×1

062.

09×1

061.

74×1

062.

75×1

06

Ti1.

82×1

051.

66×1

052.

04×1

050.

58×1

051.

20×1

051.

07×1

051.

26×1

051.

62×1

051.

62×1

05

Cr

7.24×1

056.

46×1

059.

33×1

052.

29×1

056.

92×1

054.

27×1

056.

17×1

055.

89×1

056.

61×1

05

Fe6.

03×1

074.

90×1

077.

08×1

071.

62×1

074.

90×1

073.

02×1

074.

79×1

076.

03×1

074.

57×1

07

Ni

3.47×1

063.

02×1

064.

47×1

060.

95×1

063.

16×1

061.

74×1

062.

57×1

064.

17×1

062.

57×1

06

118

As for the Solar System simulations of Chapter 3, “nominal” radial pressure and tem-

perature profiles obtained from the Hersant et al. (2001) model were used to provide

chemical compositions with a spatial location within the disk. The profiles were altered

for the stellar mass of the host star obtained from the Simbad database1. Disk mass is

assumed to vary linearly with stellar mass. From Hersant et al. (2001), disk mass depends

on the mass accretion rate as roughly given by:

Mdisk ∝ M2/3R4/3 (4.3)

where Mdisk is the mass of the disk in solar masses, M is the mass accretion rate in solar

masses per year and is the radius of the disk in AU. Adopting a uniform initial disk radius,

the mass accretion rate for each of the extrasolar planetary systems can thus be scaled with

the mass of the host star via:

M ∝ M3/2star (4.4)

The resulting stellar accretion rates obtained are shown in Table 4.7. All other input

parameters for the Hersant et al. (2001) models (α and initial disk radius) remained un-

changed. It is important to note that the current approach does not include variations in

the midplane conditions produced by different chemical compositions (which would alter

parameters such as disk viscosity), nor does it include the effects of stellar luminosity

(which aren’t incorporated into the Hersant et al. (2001) model). Furthermore, opacity

changes due to varying disk composition are also likely to alter the midplane conditions.

As such, the scaling applied here is a simplistic approach to a complex issue but is valid

1accessed at http://simbad.u-strasbg.fr/simbad/

119

for the current aims of this study. For these reasons, the stellar masses considered were

restricted to those close to solar (ranging from 0.95 M⊙ to 1.48 M⊙) to prevent further

complications due to widely varying stellar and disk masses. Please see Section 3.2.2 for

a more detailed discussion of the Hersant et al. (2001) model. Midplane pressure and tem-

perature values were determined with an average radial separation of 0.01AU throughout

the study region. As in Chapter 3, an ensemble of planetary compositions were deter-

mined based on Hersant et al. (2001) disk conditions at seven different evolutionary times

(t = 2.5×105yr, 5×105yr, 1×106yr, 1.5×106yr, 2×106yr, 2.5×106yr, 3×106yr). How-

ever, as I previously found the best fit to known planetary values in the Solar System to

occur using disk conditions obtained for t = 5×105yr, our discussions will mostly focus

on compositions produced by disk conditions at this time. The midplane temperature and

pressure profiles for each system and “snapshot” time are displayed in Figures C.1 - C.9.

4.3.4 Combining Dynamics and Chemistry

The dynamical and chemical simulations were combined together as outlined in Chapter

3 whereby I assigned each embryo a composition based on its formation location and

assumed that it then contributed that same composition to the final terrestrial planet. Phase

changes and outgassing were neglected and all collisions were assumed to be ideal (i.e.

no mass loss occurred).


The issue of stellar pollution produced by terrestrial planet formation is of great interest

in extrasolar planetary systems. Pollution of the stellar photosphere via accretion of a

large amount of solid mass during planet formation and migration has been suggested as

a possible explanation for the observed metallicity trend for known host stars (Laughlin,

2000; Gonzalez et al., 2001; Murray et al., 2001). Thus I determined the amount of

material accreted by the host star during the current terrestrial planet simulations and

also determined the resulting change in spectroscopic photospheric abundance. As for

120

Table 4.7: Stellar accretion rates for the extrasolar host stars studied. Stellar masses wereobtained from the Simbad database. Solar values are the nominal model determined byHersant et al. (2001). See text for details on the scaling relations applied.

System Stellar Mass M(M⊙) (M⊙/year)

Solar 1.00 5.00×10−6

55Cnc 1.03 5.23×10−6

Gl777 1.04 5.30×10−6

HD4203 1.06 5.46×10−6

HD4208 0.93 4.48×10−6

HD19994 1.35 7.84×10−6

HD72659 0.95 4.63×10−6

HD108874 1.00 5.00×10−6

HD177830 1.48 9.00×10−6

HD142415 1.09 5.69×10−6

121

Table 4.8: Convective zone masses for each of the target stars. Teff values taken fromSantos et al. (2004). See text for details on the determination of MCZ .

System Teff MCZ

(K) (M⊙)

55Cnc 5279 0.0398

Gl777 5584 0.0316

HD4203 5636 0.0288

HD4208 5626 0.0251

HD19994 6190 0.0045

HD72659 5995 0.0112

HD72659 5995 0.0112

HD108874 5596 0.0321

HD142415 6045 0.0089

HD177830 4804 0.0501

the Solar System simulations, any solid material migrating to within 0.1AU from the

host star is assumed to have accreted onto the stellar photosphere. This material is then

assumed to have been uniformly mixed throughout the stellar photosphere and convective

zone. Decreasing convective zone mass with time, granulation within the photosphere

and gravitational settling and turbulence within the convective zone are again neglected,

resulting in the values determined here being the maximum expected enrichments.

The mass of each element accreted was determined in the same way as for terrestrial

planets. As a reminder, the resulting photospheric elemental abundance is given by:

[X/H] = log

fX

fX,⊙

(4.5)

122

where [X/H] is the resulting abundance of element X after accretion of terrestrial planet

material, fX is the mass abundance of element X in the stellar photosphere after accretion

and fX,⊙ is the mass abundance of element X in the Sun (from Murray et al. (2001)).

Note that [X/H] is still dependant on fX,⊙ as by definition it is taken relative to the Solar

abundance.

fX values for the extrasolar planetary host stars were obtained via the stellar abun-

dances of Gilli et al. (2006); Beirao et al. (2005); Ecuvillon et al. (2004, 2006b), as these

papers represent a comprehensive, internally consistent catalogue of photospheric abun-

dances for a large number of known planetary host stars. The mass of the convective zone

of a star is known to vary with its mass, effective temperature (Teff ) and, to some extent,

its metallicity. Values for the masses of the convective zone for each of the target stars

was thus obtained from Pinsonneault et al. (2001) using the Teff values from Santos et al.

(2004). The convective zone masses are shown in Table 4.8. fX,⊙ values were obtained

by utilizing the solar abundances of Asplund et al. (2005) and a current solar convective

zone mass of 0.03M⊙ (Murray et al., 2001).

4.4 Results

4.4.1 Dynamical

Terrestrial planets were found to form in all simulations. 17 of the 40 simulations pro-

duced two or more terrestrial planets within one system.The general architecture of the

resulting systems is shown in Figures 4.7 - 4.11. Several of these planets (e.g. those in the

simulation for HD4203) can be seen to simply be embryos that have survived for the dura-

tion of the simulation but have not accreted any additional material. The median number

of planets produced, along with their median masses, semimajor axes, eccentricities and

inclinations are summarized in Table 4.9.

123

Of the nine planetary systems examined, only one (HD72659) is found to produce

terrestrial planets with a median mass comparable to 1 M⊕ with six of the 11 planets

produced having masses equal to or greater than 1 M⊕. All other median planetary

masses are less than 1 M⊕ and only four out of 51 simulated planets have masses equal

to or greater than 1 M⊕ (excluding those of HD72659).

Similarly, with the exception of 55Cancri, all simulated planets have median semi-

major axes less than 1AU. This is believed to be a selection effect as I am currently only

simulating terrestrial planet formation interior to the known giant planets (i.e. between

the host star and the most distant known giant planet). Given that the majority of systems

studied are known to contain giant planets orbiting within 2AU of their host star, it is thus

expected that the terrestrial planets produced would be located in small orbits. 55Cancri

is unusual in that its outermost giant planet has a periapse larger than 5AU, a significant

increase over the other systems selected for study. This in turn dictated that the embryos

in the current simulations initially be located between 1 AU and 5AU, hence the larger

median semi-major axis. Thus it can be seen that the present simulations are in general

producing small terrestrial planets orbiting close to their host star.

It is also interesting to note that no radial trends in planetary mass or orbital parame-

ters can be seen. Similarly, no such trends with any of the orbital parameters and stellar

metallicity can be seen. However, as the dynamical simulations are all currently adopting

the same mass and surface density distribution, the stellar metallicity is not yet fully in-

corporated into the current simulations. As such, drawing any general conclusions based

on the lack of radial trends in the current simulations would be premature.

The planets themselves tended to accrete the vast majority of their mass from their

immediately surrounding area with only small amounts of radial mixing occurring. Mean

and median σ values are shown in Table 4.10. Only Gl777 and HD72659 display appre-

ciable amounts of radial mixing with all other systems producing σ values well below the

values observed for the Solar System simulations of O’Brien et al. (2006) and discussed

in Chapter 3. As such, the terrestrial planets in the current simulations are forming pri-

124

0 1 2 3 4 5 6 7Semimajor Axis (AU)

Final Planetary Systems - 55 Cnc









0.66

0.50

0.64 0.25

0.47 3.84 MJ0.8 0.2 0.1 MJ



0.66

0.50

0.64 0.25

0.47 3.84 MJ0.8 0.2 0.1 MJ



0.66

0.50

0.64 0.25

0.47 3.84 MJ0.8 0.2 0.1 MJ



0.66

0.50

0.64 0.25

0.47 3.84 MJ0.8 0.2 0.1 MJ

0 1 2 3 4 5Semimajor Axis (AU)

Final Planetary Systems - Gl 777









0.80

0.400.94

0.47 1.10

1.03 1.55 MJ0.06 MJ



0.80

0.400.94

0.47 1.10

1.03 1.55 MJ0.06 MJ



0.80

0.400.94

0.47 1.10

1.03 1.55 MJ0.06 MJ



0.80

0.400.94

0.47 1.10

1.03 1.55 MJ0.06 MJ

Figure 4.7: Schematic of the results of the dynamical simulations for 55Cancri (top panel)and Gl777 (bottom panel). Known giant planets are also shown with their masses inJupiter masses (MJ ). The horizontal lines indicate the range in distance from apastronto periastron. The vertical lines indicate variation in height above the midplane due toorbital inclination. Numerical values represent the mass of the planet in Earth masses.

125

0 0.5 1 1.5 2Semimajor Axis (AU)

Final Planetary Systems - HD4203









0.17

0.04

0.04

0.04 2.1 MJ



0.17

0.04

0.04

0.04 2.1 MJ



0.17

0.04

0.04

0.04 2.1 MJ



0.17

0.04

0.04

0.04 2.1 MJ











0.76 0.72

0.34 0.63 0.54

0.35 1.18 0.49

1.58 0.10 0.13 0.8 MJ



0.76 0.72

0.34 0.63 0.54

0.35 1.18 0.49

1.58 0.10 0.13 0.8 MJ



0.76 0.72

0.34 0.63 0.54

0.35 1.18 0.49

1.58 0.10 0.13 0.8 MJ



0.76 0.72

0.34 0.63 0.54

0.35 1.18 0.49

1.58 0.10 0.13 0.8 MJ

Figure 4.8: Schematic of the results of the dynamical simulations for HD4203 (top panel)and HD4208 (bottom panel). Known giant planets are also shown with their masses inJupiter masses (MJ ). The horizontal lines indicate the range in distance from apastronto periastron. The vertical lines indicate variation in height above the midplane due toorbital inclination. Numerical values represent the mass of the planet in Earth masses.

126











0.57

0.62

0.35 0.10 0.06

0.28 0.46 1.7 MJ



0.57

0.62

0.35 0.10 0.06

0.28 0.46 1.7 MJ



0.57

0.62

0.35 0.10 0.06

0.28 0.46 1.7 MJ



0.57

0.62

0.35 0.10 0.06

0.28 0.46 1.7 MJ











1.53 1.35

0.60 1.10 1.03

1.28 0.99 0.26

1.320.44 0.71 3.3 MJ



1.53 1.35

0.60 1.10 1.03

1.28 0.99 0.26

1.320.44 0.71 3.3 MJ



1.53 1.35

0.60 1.10 1.03

1.28 0.99 0.26

1.320.44 0.71 3.3 MJ



1.53 1.35

0.60 1.10 1.03

1.28 0.99 0.26

1.320.44 0.71 3.3 MJ

Figure 4.9: Schematic of the results of the dynamical simulations for HD19994 (toppanel) and HD72659 (bottom panel). Known giant planets are also shown with theirmasses in Jupiter masses (MJ ). The horizontal lines indicate the range in distance fromapastron to periastron. The vertical lines indicate variation in height above the midplanedue to orbital inclination. Numerical values represent the mass of the planet in Earthmasses.

127

0 0.5 1 1.5 2 2.5 3Semimajor Axis (AU)










0.34

0.46

0.18

0.40 0.13 1.3 MJ 1.07 MJ



0.34

0.46

0.18

0.40 0.13 1.3 MJ 1.07 MJ



0.34

0.46

0.18

0.40 0.13 1.3 MJ 1.07 MJ



0.34

0.46

0.18

0.40 0.13 1.3 MJ 1.07 MJ

0 0.2 0.4 0.6 0.8 1 1.2Semimajor Axis (AU)










0.14

0.04

0.13

0.05 1.7 MJ



0.14

0.04

0.13

0.05 1.7 MJ



0.14

0.04

0.13

0.05 1.7 MJ



0.14

0.04

0.13

0.05 1.7 MJ

Figure 4.10: Schematic of the results of the dynamical simulations for HD108874 (toppanel) and HD142415 (bottom panel). Known giant planets are also shown with theirmasses in Jupiter masses (MJ ). The horizontal lines indicate the range in distance fromapastron to periastron. The vertical lines indicate variation in height above the midplanedue to orbital inclination. Numerical values represent the mass of the planet in Earthmasses.

128

0 0.25 0.5 0.75 1 1.25 1.5Semimajor Axis (AU)










0.240.78

0.35 0.61 0.14

0.061.22

0.240.36 0.34 1.4 MJ



0.240.78

0.35 0.61 0.14

0.061.22

0.240.36 0.34 1.4 MJ



0.240.78

0.35 0.61 0.14

0.061.22

0.240.36 0.34 1.4 MJ



0.240.78

0.35 0.61 0.14

0.061.22

0.240.36 0.34 1.4 MJ

Figure 4.11: Schematic of the results of the dynamical simulations for HD177830.Known giant planets are also shown with their masses in Jupiter masses (MJ ). The hori-zontal lines indicate the range in distance from apastron to periastron. The vertical linesindicate variation in height above the midplane due to orbital inclination. Numerical val-ues represent the mass of the planet in Earth masses.

129

Table 4.9: Properties of the simulated extrasolar terrestrial planets for each system. Me-dian values are provided for the number of planets produced (N), planetary mass (M),semi-major axis (a), orbital eccentricity (e) and orbital inclination (i). The range in valuesfor each system is also provided in parentheses.

System N M a e i(M⊕) (AU) (◦)

55Cancri 1 0.51 2.00 0.15 6.28(0.67 − 0.25) (3.59 − 1.65) (0.30 − 0.11) (8.19 − 0.50)

Gl777 1.5 0.87 0.59 0.12 4.58(1.11 − 0.40) (0.89 − 0.45) (0.29 − 0.07) (16.18 − 0.33)

HD4203 1 0.04 0.32 0.31 1.22(0.17 − 0.04) (0.36 − 0.28) (0.39 − 0.27) (2.43 − 0.29)

HD4208 3 0.54 0.45 0.12 3.71(1.58 − 0.10) (1.19 − 0.27) (0.28 − 0.05) (8.91 − 1.59)

HD19994 1.5 0.35 0.37 0.12 2.02(0.63 − 0.07) (0.70 − 0.31) (0.19 − 0.10) (5.38 − 1.07)

HD72659 3 1.03 0.49 0.11 3.95(1.53 − 0.26) (0.97 − 0.29) (0.22 − 0.07) (8.87 − 1.46)

HD108874 1 0.34 0.35 0.16 2.19(0.47 − 0.13) (0.48 − 0.33) (0.19 − 0.13) (3.08 − 0.77)

HD142415 1 0.04 0.30 0.32 0.97(0.14 − 0.04) (0.33 − 0.25) (0.41 − 0.23) (1.49 − 0.41)

HD177830 2.5 0.35 0.45 0.06 1.72(1.22 − 0.06) (0.65 − 0.33) (0.17 − 0.02) (15.63 − 0.66)

130

Table 4.10: Degree of radial mixing for simulated systems. σ is the weighted measure ofradial migration defined in equation 4.2. The error on the mean is the rms error. Valuesfor the Solar System simulations of O’Brien et al. (2006) are provided for comparison.

System σMedian Mean

55Cnc 0.16 0.19 ± 0.22

Gl777 0.43 0.49 ± 0.52

HD4203 0.01 0.04 ± 0.08

HD4208 0.32 0.32 ± 0.32

HD19994 0.15 0.15 ± 0.15

HD72659 0.40 0.41 ± 0.41

HD108874 0.09 0.09 ± 0.09

HD142415 0.04 0.09 ± 0.13

HD177830 0.18 0.17 ± 0.20

Solar System - CJS 0.56 0.59 ± 0.59

Solar System - EJS 0.45 0.48 ± 0.48

marily from material located in the region immediately surrounding them and are thus

expected to have compositions reflecting any radial trends within the disk. These values,

however, are likely to increase significantly once the full effects of a planetesimal swarm

and orbital migration are incorporated into the planet formation simulations.

Terrestrial planets produced in the current simulations attain their final masses rela-

tively quickly. Median times to accrete 50% and 100% of the final planetary mass are

shown in Table 4.11. As one would intuitively expect, systems with the highest median

planetary masses (HD72659, Gl777) also had the highest median growth times (approxi-

131

Table 4.11: Median time required to accreted 50% and 100% of the final terrestrial planetmass. N is the number of planets considered in determining the median values. Onlyplanets that accreted two or more embryos are included.

System N Time (years)M50% M100%

55Cnc 4 3.70 ×105 3.34 ×106

Gl777 6 2.18 ×106 1.11 ×107

HD4203 1 3.03 ×102 1.63 ×104

HD4208 9 4.79 ×105 2.36 ×106

HD19994 5 1.52 ×105 6.92 ×105

HD72659 11 2.60 ×106 9.35 ×106

HD108874 4 1.02 ×105 4.05 ×105

HD142415 2 2.35 ×103 1.21 ×104

HD177830 8 3.94 ×105 1.53 ×106

mately 10Myr for the final planetary mass). Systems with lower median masses reached

their final planetary masses significantly faster (3Myr or less). Planetary formation times

have implications for planetary processes (such as differentiation and the resulting the

distribution of siderophile elements). The current growth times, however, are expected to

change once planetesimals are incorporated into the simulations as discussed in Section

4.3.2.

The above results need to be interpreted with caution as I am currently only consider-

ing late stage, in-situ terrestrial planet formation. That is, I am only considering formation

that has occurred after the known giant planets have formed and migrated to their current

orbits. As previously discussed, such an approach is currently valid as there is no con-

132

sensus on the timing or extent of migration within these systems and it provides us with

a valid starting point to consider the possible chemical composition of the system. How-

ever, migration could potentially remove sufficient mass from the planetary disk so as

to inhibit any terrestrial planet formation from occurring. Alternatively, migration of the

giant planets at a later time (i.e. after terrestrial planet formation has begun) may result

in the ejection of terrestrial planets from the system and radial redistribution of material

such that it deviates from the currently assumed surface density profile (Mandell et al.,

2007). These effects are believed to be of most importance in systems with close in giant

planets in very eccentric orbits, such as is the case for HD4203. Simulations addressing

these issues are currently running.

4.4.2 Chemical

The condensation sequences and abundances of solid species (normalized to the abun-

dance of the least abundant species) are shown in Figures 4.12 - 4.20 in order of increas-

ing C/O value. The 50% condensation temperatures (i.e. temperature at which half of the

species has condensed) for each of the systems studied is shown in Table 4.12. As they

are not the main focus of the current work, the equilibrium gas compositions are shown

in Figures D.1 - D.9 in Appendix D.

Two very distinct general types of condensation sequence are produced for the sys-

tems studied here - those resembling the Solar condensation sequence (Gl777, HD4208,

HD72659 and HD177830) and those in which C (and occasionally O) is drastically more

refractory in nature (55Cnc, HD4203, HD19994, HD108874 and HD142415). This com-

positional difference can be seen in Figures 4.18 - 4.20 where the high temperature (in-

nermost) region of the disk is dominated by SiC, TiC and C. Furthermore, the spatial

region where solid material is present increases with increasing C/O value. For HD72659

(the system with lowest C/O value), solids are present at temperatures below ∼1600 K

while for HD19994, solids are present below ∼1800 K. HD4203, the most C rich system

studied, has solids present below∼2300 K. The implications of these variations in the dis-

133

tribution of solid material are discussed in Section 4.5.9. The composition of terrestrial

planets produced in each of these general classes reflects these drastic compositional dif-

ferences and shall be discussed in turn. Unless otherwise stated, all compositions shown

are produced by disk conditions at t = 5×105 years. Compositional changes with disk

conditions will be discussed in Section 4.5.3 and compositions produced by disk condi-

tions at alternative times are presented in Figures E.1 - E.32.

134

Tabl

e4.

12:T

50%

conden

sati

on,C

/Oan

dM

g/Si

fore

xtra

sola

rpla

neta

rysy

stem

sst

udie

d.So

larv

alue

sar

eal

sosh

own

forc

ompa

ri-

son.

All

valu

esar

ein

K.

Ele

men

tSy

stem

HD

7265

9So

lar

HD

1778

30G

l777

AH

D42

0855

Cnc

HD

1424

15H

D19

994

HD

1088

74H

D42

03A

l16

5716

3916

7216

4015

7515

9415

1912

9813

0513

23C

<15

0<

150

<15

0<

150

<15

094

990

910

2192

310

64C

a15

3515

2715

2415

2214

6314

8214

2912

5312

8412

95C

r12

9513

0113

2113

1312

7213

2013

1013

1313

0413

23Fe

1333

1339

1359

1351

1310

1359

1348

1352

1350

1366

Mg

1355

1339

1362

1338

1286

1131

1112

1070

1061

1069

Na

939

941

815

909

916

857

846

866

848

857

Ni

1345

1351

1371

1363

1321

1370

1359

1363

1358

1375

O18

018

018

318

117

626

394

118

075

999

7P

1308

1039

1333

1338

1325

1372

1374

1389

1388

1403

S61

865

868

265

660

210

7010

5262

810

8210

91Si

1346

1329

1359

1321

1275

1137

1114

1430

1556

1637

Ti15

8715

8015

8315

7715

2115

3914

9917

7118

0318

24

C/O

0.32

0.54

0.68

0.69

0.72

0.81

0.83

1.02

1.10

1.51

Mg/

Si1.

201.

051.

861.

291.

351.

621.

101.

001.

411.

26

135

HD72659

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Nor

mal

ized

Abu

ndan

ce (

mol

e)

0.1

1

10

100

1000

10000

AlN C Ca2Al2SiO7 Ca3(PO4)2 CaMgSi2O6 CaAl12O19 CaAl2Si2O8CaTiO3 CaS FeCr2O4 Cr Fe Fe2SiO4 Fe3C Fe3O4 Fe3P FeS FeSiO3 H2O Mg2SiO4 Mg3Si2O5(OH)4 MgAl2O4 MgS MgSiO3 NaAlSi3O8 Ni SiC TiC TiN

Figure 4.12: Schematic of the output obtained from HSC Chemistry for HD72659 at apressure of 10−4 bar. Only solid species present within the system are shown. All abun-dances are normalized to the least abundant species present. Input elemental abundancesare shown in Table 4.6.

136

HD177830

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Nor

mal

ized

Abu

ndan

ce (

mol

e)

0.1

1

10

100

1000

10000



137

Gl777

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Nor

mal

ized

Abu

ndan

ce (

mol

e)

0.1

1

10

100

1000

10000


Figure 4.14: Schematic of the output obtained from HSC Chemistry for Gl777 at a pres-sure of 10−4 bar. Only solid species present within the system are shown. All abundancesare normalized to the least abundant species present. Input elemental abundances areshown in Table 4.6.

138

HD4208

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Nor

mal

ized

Abu

ndan

ce (

mol

e)

1e-1

1e+0

1e+1

1e+2

1e+3

1e+4

1e+5



139

55Cnc

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Nor

mal

ized

Abu

ndan

ce (

mol

e)

0.1

1

10

100

1000

10000


Figure 4.16: Schematic of the output obtained from HSC Chemistry for 55Cnc at a pres-sure of 10−4 bar. Only solid species present within the system are shown. All abundancesare normalized to the least abundant species present. Input elemental abundances areshown in Table 4.6.

140

HD142415

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Nor

mal

ized

Abu

ndan

ce (

mol

e)

0.1

1

10

100

1000

10000



141

HD19994

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Nor

mal

ized

Abu

ndan

ce (

mol

e)

0.1

1

10

100

1000

10000



142

HD108874

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Nor

mal

ized

Abu

ndan

ce (

mol

e)

0.1

1

10

100

1000

10000



143

HD4203

T (K)

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Nor

mal

ized

Abu

ndan

ce (

mol

e)

0.1

1

10

100

1000

10000



144

Earth-like Planets

Four systems (Gl777, HD4208, HD72659 and HD177830) were found to produce con-

densation sequences (and thus also terrestrial planets) comparable to those of the Solar

System. The final elemental abundances for all times studied are shown in Tables E.1 - E.4

while schematic representations of the abundances (for disk conditions at 5×105 years)

are shown in Figures 4.21 − 4.26. From these it can be seen that for Gl777, HD72659

and HD4208 the terrestrial planets produced are grossly similar in composition to known

terrestrial planets. Their compositions are dominated by O, Fe, Mg and Si with varying

amounts of minor elements (such as Al, Ca and Cr). Upon closer examination, however,

large and important differences emerge, primarily due to variations in the compositions

of the host star and thus the initial system itself.

Gl777: Gl777 produces the most Earth-like terrestrial planets of all of the systems

simulated (Figure 4.21). The final elemental abundances of the refractory lithophile and

siderophile elements are remarkably similar to those of Earth with the simulated plan-

ets displaying a marginal enrichment in Mg (∼3wt%), depletion in Si (∼1wt%), and Fe

(∼2wt%) compared to Earth values. Deviations from Earth abundances also occur for the

most volatile species (P, Na and S). This enrichment is likely an artifact of the fact that I

do not consider volatile loss during accretion, which is expected to be significant as for

the Solar System simulations.

The geochemical ratios of Mg/Si and Al/Si are also in excellent agreement with those

of the Earth, falling on the Earth fractionation trend and within the upper limit of values

estimated for the Earth (Drake and Righter, 2002) (see Figure 4.22). This increase in the

planetary Mg/Si values over the previous Solar System simulations of Chapter 3 is due to

the slight increase the Mg/Si value of Gl777 itself (Mg/Si⊙ = 1.05, Mg/SiGl777 = 1.29) .

In turn, this produces a system containing nearly equal amounts of olivine and pyroxene

(compared to the pyroxene dominated Solar disk) and thus results in Mg-enriched planets.

The Ca/Si values, however, are lower than those of Earth (Ca/SiGl777 = 0.06−0.07,

145

Ca/Si⊕ = 0.11), primarily due the fact that there is relatively less Ca within the system.

Ca and S are the two least enriched elements within Gl777 ([Ca/H] = 0.10 vs. [Al/H] =

0.34), resulting in a relative Ca and S depletion within the solid material. The variation in

the abundances of the host star are reflected in the lower Ca/Si value of the final planets

produced. This difference is certainly no larger than that observed for the Solar Sys-

tem simulations previously discussed and I feel confident in claiming that the terrestrial

planets of Gl777 are essentially Earth-like in their chemical composition.

It is also interesting to note Gl777 represents the average extrasolar planetary host

star values of Mg/Si and C/O (1.29 and 0.63 respectively). This result thus implies that

the “average” extrasolar planetary system contains terrestrial planets with compositions

extremely comparable to that of our own Solar System.

HD72659 & HD4208: More pronounced compositional variations can be seen in the

terrestrial planets of HD72659 and HD4208 (Figures 4.23 and 4.24). Although producing

planets with two of the highest radial mixing parameters for the extrasolar planetary sim-

ulations, clear radial compositional trends are evident. Planets located within ∼0.7AU

from the host star for HD72659 and within ∼0.5AU for HD4208 are primarily composed

of Al, Ca and O, indicating that these planets formed from the high-temperature Al and Ca

condensates (such as spinel and gehlenite) (see Figures 4.23 and 4.24). However, beyond

∼0.7AU and ∼0.5AU respectively, planets have compositions more closely correlating

with that of the Earth, dominated by O, Fe, Mg and Si.

As expected, this difference is reflected in the planetary geochemical ratios as the

planets located within the inner region have Al/Si and Ca/Si ratios well above and Mg/Si

values well below observed Solar System terrestrial planet values. However, for planets

located beyond the compositional transitional point, the reverse is true. In this region,

planetary Al/Si and Ca/Si values are below Earth values while Mg/Si is within the upper

limits of current Earth approximations (for HD72659) and in agreement with terrestrial

peridotites (for HD4208). A steady transition between these two regions is seen for both

systems (see Figure 4.25). This trend lies well above the observed Earth fractionation line

146

and is a result of the condensation of Mg-silicate species further out in the disk, combined

with relatively little radial mixing of material during the formation process.

The terrestrial planets of HD72659 and HD4208 can thus be characterized as being

essentially similar in composition to Ca- and Al-rich inclusions (CAI’s) (for the inner

planets) and Earth (for the outer planets).

HD177830: HD177830 has the highest Mg/Si (and Al/Si) ratio of any system sim-

ulated. This enrichment alters the compositions of major silicate species present within

the disk. While the Solar System should have condensed both olivine and pyroxene be-

tween 0.35 and 2.5 AU, HD177830 is dominated by olivine beyond 0.3 AU and contains

only a small region where pyroxene is predicted to coexist. This unusual composition is

reflected in the final planetary abundances as the planets contain large portions of Mg (up

to 23 wt%) (Figure 4.26) and have a mean Mg/Si value of 1.71, well above Earth values

(Mg/Si⊕ = 1.01).

Al is also similarly enriched (up to 18.07 wt%), again because of the high Al abun-

dance of the host star and thus the initial system itself. Other refractory and lithophile

elemental abundances within the final planets are comparable to that of the Solar System.

The planets of HD177830 can best be described as being Mg- and Al-rich Earths. Such a

Mg dominated planetary composition would undoubtedly alter the interior structure and

processes of the planets themselves. Such considerations will be discussed further in

Section 4.5.

147

Final Composition - Gl777 (0.5Myr)

Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other

Figure 4.21: Schematic of the bulk elemental planetary composition for Gl777. All valuesare wt% of the final simulated planet. Values are shown for the terrestrial planets producedin each of the four simulations run for the system. Size of bodies is not to scale.

148

Mars

fractionation

line


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Mg

/Si (

we

igh

t ra

tio

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4


Figure 4.22: Al/Si v. Mg/Si for planets of Gl777. Black circles indicate values for diskconditions at t = 2.5×105 years while red circles indicate values for disk conditions at t= 5×105 years. Values at all other times are concentrated at the 5×105 years values andomitted for clarity. Earth values are shown in green and are taken from Kargel and Lewis(1993) and McDonough and Sun (1995). Martian values are shown in pink and are takenfrom Lodders and Fegley (1997). Venus values are shown in light blue and are taken fromMorgan and Anders (1980).

149

Final Composition - HD72659 (0.5Myr)

Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other

Figure 4.23: Schematic of the bulk elemental planetary composition for HD72659. Allvalues are wt% of the final simulated planet. Values are shown for the terrestrial planetsproduced in each of the four simulations run for the system. Size of bodies is not to scale.

150


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


151

Mars

fractionation

line


0 1 2 3 4 5

Mg

/Si (

we

igh

t ra

tio

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4


Figure 4.25: Al/Si v. Mg/Si for the planets of HD4208 and HD72659. Black circlesindicate values for the terrestrial planets of HD72659 while red circles indicate values forthe terrestrial planets of HD4208. Values are for disk conditions at 5×105 years. Earthvalues are shown in green and are taken from Kargel and Lewis (1993) and McDonoughand Sun (1995). Martian values are shown in pink and are taken from Lodders and Fegley(1997). Venus values are shown in light blue and are taken from Morgan and Anders(1980).

152


Semimajor Axis (AU)

0.0 0.2 0.4 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


153

C-rich Planets

Far more profound mineralogical variations from Earth-like compositions occur in sys-

tems with C/O values above 0.8. The inner part of these systems are dominated by refrac-

tory carbon species such as graphite, SiC and TiC (e.g. see Figures 4.18 - 4.20). Five such

systems were selected for the current study (55Cnc, HD142415, HD19994, HD108874

and HD4203). The final elemental abundances for all times studied are shown in Tables

E.5 - E.9 while schematic representations of the abundances are shown in Figures 4.27

− 4.31. These planets clearly represent a completely different type of terrestrial body

unseen in our Solar System.

55Cnc: For disk conditions at t = 5×105 years, 55Cancri produced terrestrial planets

similar to those of HD177830 - essentially Earth-like in terms of major elements present

but with Mg/Si and Ca/Si values well above those of Earth and Ca/Si values well below.

(see Figure 4.27) This high planetary Mg abundance is caused by the fact that 55Cancri is

highly enriched in Mg ([Mg/H] = 0.48), resulting in olivine becoming the major silicate

species present within the disk and thus producing the high Mg/Si value observed.

Although the disk of 55Cancri is predicted to contain a C-rich zone, only one predicted

planetary composition for disk conditions at t = 5×105 years contains a significant amount

of C (see Figure 4.16). For disk conditions at later times, none of the simulated planets

are predicted to contain any C. This apparent C depletion is due to the location of the

planets within the disk. All of the terrestrial planets in 55Cnc are located between 1.5

and 4AU while the C-rich zone is located between ∼1100 and 750K, corresponding to a

radial distance of 0.6 and 1.35AU (for disk conditions in the Hersant et al. (2001) model at

5×105 years). Thus the primary feeding zones for each of the planets are located beyond

the C zone, resulting in Mg-rich Earth-like planets being produced. For disk conditions

at 2.5×105 years, however, the C zone extends from 0.92 to 2.11AU, producing planets

that contain up to 9.41 wt% C. The location of the C zone also implies that the four

inner known giant planets of the 55Cnc system (located at 0.038AU, 0.115AU, 0.24AU

154

and 0.781AU) should contain significant amounts of C, both in their solid cores and in

their atmospheres (depending on the exact time of their formation). Given the variation

in the location of the C rich zone, it is expected that C rich terrestrial planets would

also be produced in the current simulations at later times if temporal variations in solid

composition were incorporated.

HD142415: Although the disk of HD142415 does contain a C-rich zone, for the disk

conditions at t = 5×105 years the simulated terrestrial planets consist almost entirely of

refractory siderophile and lithophile species (Ti, Al, Ca and O) (see Figure 4.28). As

for 55Cnc, this is primarily due to their radial location within the system. All of the

planets of HD142415 are located within 0.35AU from their host star, well inside the C

zone which extends from 0.6 to 1.3AU (for disk conditions at 5×105 years). Thus their

location, combined with the small radial mixing observed for the HD142415 simulation,

results in planets consisting entirely of refractory species, resembling the CAI’s of the

Solar System.

At later times, however, the planetary composition changes to become more Earth-

like, with planets dominated by O, Fe, Mg and Si and a significant amount of C. Up to

12.44 wt% C is predicted to exist in the planets for the disk conditions at 3×106 years.

These planets are essentially C-enriched Earths, containing the same major elements in

the same geochemical ratios as Earth, but also an enhanced inventory of C, primarily

accreted as solid graphite. As for 55Cnc, it is expected that were I to incorporate giant

planet migration and temporal variations in composition into our models that I would see

C occurring in the terrestrial planets for all simulation times.

HD19994, HD108874 & HD4203: HD19994, HD108874 and HD4203 all have C/O

values above 1.0 (1.02, 1.10 and 1.51 respectively). In all three systems, the inner regions

of the disk are completely dominated by refractory species composed of C, SiC and TiC,

as opposed to the Ca and Al-rich inclusions characteristic of the earliest solids within our

Solar System. Significant amounts of metallic Fe are also present within these systems.

As all three systems produced terrestrial planets located within 0.7AU from their host star,

155

these unusual inner disk compositions produced terrestrial planets primarily composed of

C, Si and Fe. HD19994 produced terrestrial planets composed almost entirely of SiC and

metallic Fe and containing up to 60 wt% Si and between 16 and 21 wt% C, over 100 times

more C than is estimated for Earth (see Figure 4.29). The outermost terrestrial planet for

HD19994 does contain significant amounts of O and Mg, primarily as its feeding zone,

although still undoubtedly dominated by C, is also rich in pyroxene. This presence of a

Mg silicate species produces a slightly more varied composition for a single planet.

More extreme deviations occur when I consider the planets formed for HD108874

and HD4203. Both of these systems have considerably wider graphite dominated regions,

extending from 1.5AU to within 0.1AU (for disk conditions at 5×105 years). As a result,

terrestrial planets are found to be composed almost entirely of C, Si and Fe. HD108874

produced terrestrial planets containing between 9.58 and 29.30 wt% C, 13.29 and 51.36

wt% Si and 18.03 and 63.62 wt% Fe (see Figure 4.30). HD4203 was even more extreme,

producing terrestrial planets composed almost entirely of SiC and containing more than

50 wt% C (for midplane conditions at 5×105 years) (see Figure 4.31). At later times, Mg

and O are also present, again due to the incorporation of pyroxene and olivine into the

planetary feeding zones. It must be noted though that the terrestrial planets formed in the

HD4203 simulations are single embryos that survived for the duration of the simulation

but did not accrete any other solid material. As such, they are presumably more C-rich

than terrestrial planets forming for other systems as they have not been combined with

material drawn from any other region within the disk. Terrestrial planets within these

systems are unlikely to have compositions resembling that of any body we have previously

observed. The possible implications of these types of planetary compositions will be

discussed in Section 4.5.


The average change in stellar photospheric abundances produced by accretion for disk

conditions at 5×105 years are shown in Table 4.13. The majority of systems experienced

156

Final Composition - 55 Cnc (0.5 Myr)

Semimajor Axis (AU)

0 1 2 3 4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other

Figure 4.27: Schematic of the bulk elemental planetary composition for 55Cnc. All valuesare wt% of the final simulated planet. Values are shown for the terrestrial planets producedin each of the four simulations run for the system. Size of bodies is not to scale.

157


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

M g

S i

C

S

A l

C a

T i

O ther


158


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


159


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


160


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


161

minimal increases in photospheric abundances as a result of accretion during terrestrial

planet formation. The largest elemental enrichments occurred for the most refractory el-

ements (Al, Ca, Ti, Ni and Cr), primarily as a result of accretion of refractory material

initially located closest to the star itself, as one would intuitively expect. Only the sim-

ulations for HD142415 produced drastic increases in the predicted observed elemental

abundances, with simulations for HD19994 also producing significant enrichments for Ti

and Si. This is primarily due to the low estimated mass of the convective zone masses for

the host stars (MHD142415 = 0.0089M⊙, MHD19994 = 0.0045M⊙). However, as previously

discussed, mixing within the stellar radiative zone are not incorporated into the current

approach. As such, our current values are upper limits for those stars with low mass con-

vective zones and large radiative zones as is the case for HD142415 and HD19994. It

is also interesting to note that the two systems with the highest degree of radial mixing

(Gl777 and HD72659) both accreted the largest amount of solid material onto their host

stars.

With the exception of HD142415 and HD19994, all predicted abundance changes are

below the errors of current spectroscopic surveys (e.g. ±0.03 for Fischer and Valenti

(2005)), meaning that definitively observable elemental enrichments are not necessarily

produced by the current terrestrial planet formation simulations. Of course, inclusion

of planetesimals within the formation simulations and migration of the giant planets is

expected to increase the amount of material accreted by the host star and thus also the

predicted stellar abundances. However, these increases are expected to be no more than

a factor of two and would thus still result in only marginal increases in the observed

elemental abundances.

162

Tabl

e4.

13:C

hang

ein

host

star

phot

osph

eric

abun

danc

espr

oduc

edby

terr

estr

ialp

lane

tfor

mat

ion.

Syst

emM

ass

Acc

rete

dC

hang

ein

Abu

ndan

ce(M

⊕)

Mg

OS

FeA

lC

aN

aN

iC

rP

TiSi

C

55C

nc0.

140.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

000.

00G

l777

2.10

0.01

0.00

0.01

0.01

0.01

0.01

0.01

0.01

0.01

0.00

0.01

0.01

0.00

4203

0.63

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.01

0.01

0.00

4208

0.28

0.00

0.00

0.00

0.00

0.02

0.02

0.00

0.00

0.00

0.00

0.02

0.01

0.00

1999

40.

900.

020.

000.

000.

000.

030.

020.

000.

040.

040.

010.

070.

050.

0172

659

2.04

0.02

0.01

0.01

0.02

0.01

0.02

0.01

0.02

0.02

0.01

0.03

0.02

0.00

1424

150.

550.

000.

010.

000.

000.

160.

150.

000.

010.

000.

000.

290.

010.

0017

7830

0.24

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

163

4.5 Implications and Discussion

4.5.1 Frequency of Terrestrial Planets

As terrestrial planets formed in all systems studied, it implies that terrestrial planets are

ubiquitous within extrasolar planetary systems. This observation is not limited to those

systems dynamically similar to our own (i.e. with the innermost giant planet located

at 5AU). Systems containing multiple giant planets, along with those containing close-in

giant planets, are found to be capable of both forming and retaining at least one terrestrial-

sized planetary companion. Furthermore, many of the systems simulated produced mul-

tiple terrestrial planets. As Jovian-mass planets in close-in orbits are the most commonly

known type of extrasolar planetary system, it is encouraging to note that the current sim-

ulations are forming several terrestrial planets in such systems. Assuming sufficient mass

is retained after the known giant planets have formed and migrated to their current posi-

tions, these current simulations indicate that terrestrial planets are likely to form in a wide

variety of planetary architectures. These results provide further motivation for the devel-

opment of future terrestrial planet searches and argue for the expansion of such searches

to include a diverse range of dynamical structures beyond those most closely resembling

the Solar System.

4.5.2 Planetary Types

A broad range of possible planetary compositions have been produced. Four distinct

classes of planetary composition can be identified: Earth-like, Mg-rich Earth-like, refrac-

tory (compositions similar to CAI’s) and C-rich. These planetary types are primarily a

result of the compositional variations of the host stars and thus the system as a whole.

Based on their observed photospheric elemental abundances, the majority of known ex-

trasolar planetary systems are expected to produce terrestrial planets with compositions

similar to those within our own Solar System. Therefore, systems with elemental abun-

dances and ratios similar to these (e.g. Gl777) are ideal places to focus future “Earth-like”

164

planet searches.

On the other hand, this study also suggests that a large fraction of planetary systems

are much more C-rich than anything in our own system. This result implies that a similar

fraction of protoplanetary disks should contain high abundances of carbonaceous grains.

Min et al. (2005) have shown that for comets and protoplanetary disks a mass fraction of

20% carbon grains successfully reproduces both the infrared spectrum and the polariza-

tion of scattered light at optical wavelengths. Furthermore, infrared spectral features at

3.43 and 3.53 µm observed in protoplanetary disks have been identified as being produced

by nano-diamonds (Acke and van den Ancker, 2006). Such high abundances of carbon-

rich grains in nascent planetary systems is inconceivable if they have primary mineralogy

similar to our Solar System, thus implying that C-rich planetary systems may be more

common than previously thought. Future planetary formation and astrobiological studies

should consider the implications of a C-dominated composition.

4.5.3 Timing of Formation

Specific planetary compositions have been found to be highly dependent on the time se-

lected for the disk conditions. This is primarily due to the low degree of radial mixing

encountered within the simulations. As a result, as conditions within the area immedi-

ately adjacent to the planet evolve, the composition of the solid material and thus the

final planet itself drastically change. For disk conditions at later times, it can been from

Tables E.1 - E.9 that the compositions evolve to more closely resemble those of the So-

lar System. They become dominated by Mg silicate species and metallic Fe. Terrestrial

planets in Solar-like systems attain more hydrous material while those in C-rich sys-

tems accrete more C. Temporal variations in composition are most noteworthy for those

planets dominated by refractory compositions (such as the inner planets of HD72659 and

HD142415). Under later disk conditions, these planets experience a complete shift in their

composition, losing the majority of their refractory inventory to be composed primarily

of Mg-silicates (olivine and pyroxene). Therefore if solid condensation and planet forma-

165

tion occurred significantly later, I would expect to observe predominantly Mg-silicate and

metallic Fe planets with enrichments in other elements (such as C) depending on the exact

composition of the system. Although disk conditions at 5×105 years provide the “best fit”

for Solar System simulations and are thus utilized here, it remains to be seen whether or

not disk conditions at this time provide an accurate description of accretion conditions in

other planetary systems. Therefore, we require a more detailed understanding of the tim-

ing of condensation and planetesimal and embryo formation within protoplanetary disks

to be able to further constrain the predicted elemental abundances.

Similarly, as the disk evolves, the various condensation fronts migrate closer to the

host star. For example, the water ice line for Gl777 migrates from 7.29 AU for midplane

conditions at 2.5×105 years to 1.48AU for midplane conditions at 3×106 years. Similar

degrees of migration also occur for other species. In effect, this migration alters the mass

distribution within the disk, concentrating more mass in both the very closest regions of

the disk (< 1AU) and in the outer most water rich regions (> 3AU) producing a bi-modal

mass distribution. The full effects of this change will obviously require formation simu-

lations to be run with alternative mass distributions but it is thought that such conditions

will increase the efficiency of forming close-in terrestrial planets and/or the mass of the

resulting planets. Additionally, it will also allow for efficient terrestrial planet growth in

the outer regions, possibly to the extent of forming gas giant cores. It remains to be seen,

however, if sufficient solid mass would be retained during the evolutionary process for

Jovian-cores to develop.

4.5.4 Detection of Terrestrial Planets

The results of this study are of great importance for the design of terrestrial planet finding

surveys. Our simulations provide not only predictions of the location of terrestrial plan-

ets but also constrain their mass and bulk composition, thus aiding in detection. Based

on the present simulations, the masses of the terrestrial planets produced are certainly

too low to be detected by current radial velocity surveys. However, it is believed that

166

many of the simulated planets are in orbits that would place them within the prime tar-

get space for detection by the Kepler mission. Designed to detect extrasolar planets via

transit studies, Kepler is the first mission which will be capable of detecting Earth-mass

(and lower) extrasolar planets located within the habitable zone of a planetary system. It

will be able to detect an Earth mass body within 2AU from the host star and a Mars mass

body (0.1M⊕) within 0.4AU. The vast majority of the terrestrial planets formed here

(with the exception of the lowest mass, highest semimajor axis planets) are well within

this range and thus should be detectable if they are indeed present within these systems.

Only HD4203 and HD142415 produce no potentially detectable planets, based on their

predicted masses. Thus it is likely that I will have an independent check of extrasolar

terrestrial planet formation simulations within the next 5 years. Such information will

be vital for further refinement of planetary formation models for both giant and terres-

trial planets. Obtaining compositional checks, however, will be more difficult as the size

and location of the predicted planets will prohibit direct spectroscopic studies. It is also

unlikely that the terrestrial planets will contain atmospheres large enough to be detected

with transiting surveys. As such, specific extrasolar planetary chemical compositions will

remain unknown for the foreseeable future.

In addition to detection via transit surveys, attempts are also being made to obtain

direct images of extrasolar planetary systems. One such example is Darwin, a proposed

ESA space based mission that would utilize nulling interferometry in the infrared to di-

rectly search for terrestrial extrasolar planets. The compositional variations outlined here

are likely to influence our ability to successfully detect these planets. Carbon-rich aster-

oids are known to be highly non-reflective. For example, 624 Hektor (D-type asteroid)

has a geometric albedo of 0.025 while 10 Hygiea (C-type asteroid) has a geometric albedo

of 0.0717. As both of these asteroids are assumed to be carbon-rich, it is likely that the

carbon-rich planets identified here are similarly dark. Thus it is expected that searches

for these planets in the visible spectrum will be difficult due to the small amount of light

reflected by these bodies. However, a lower albedo results in greater thermal emission

167

from a body, suggesting that the infrared signature from these planets is much larger

than corresponding silicate planets and extends to shorter wavelengths, assuming that any

planetary atmosphere present reflects the composition of the solid body. As a result, in-

frared searches (such as that of Darwin) are ideally suited to detect carbon-rich terrestrial

planets and thus should be focused on stellar systems with compositions similar to that of

the C-rich stars identified here to maximize results.

4.5.5 Hydrous Species

None of the simulated terrestrial planets directly accrete any hydrous species (water or

serpentine) for disk conditions at 5×105 years. This is understandable as all of the planets

are located relatively close to their host star and well interior to the hydrous species region

of the disk. At later times, all planets formed for 55Cnc and only the outer most planets

of Gl777, HD72659 and HD4208 contain hydrous species. The planets of 55Cnc are

understandably more enriched in water as they are located further out in the system, thus

producing a greater overlap between their feeding zones and the water-rich region of the

disk. However, the majority of planets accrete dry and contain no primordial water for

the disk conditions simulated here. This will obviously influence not only planetary and

atmospheric processes but will also impact on the potential for life to develop on these

planets.

Cometary and asteroidal delivery of water has been widely suggested as the origin

of Earth’s water. However, it is questionable how effective such processes would be in

extrasolar planetary systems. Only 55Cnc has been found to be dynamically capable

of hosting an asteroid belt analogous to the belt in our own Solar System. Gl777 and

HD72659 both contain giant planets in orbits that would render any similar feature within

these planetary systems unstable, thus making its long term survival unlikely.

As described in Chapter 3, water can also be delivered to a planetary body via ad-

sorption onto solid grains within the disk. As this process has not been considered in our

current simulations, it is likely that there will be some water delivered during the forma-

168

tion process to the terrestrial planets produced in the Earth-like systems (Gl777, HD4208,

HD72659 and HD177830) as the solid grains are bathed in water vapor over the entire

span of the disk. This same process will likely not be as effective at delivering water to

the C-rich systems (55Cnc, HD4203, HD19994, HD108874 and HD142415) as they only

have water vapor present at temperatures below ∼800 K. The different distributions can

be seen when comparing the equilibrium gas compositions for HD 72659 (C/O = 0.32,

Figure 4.32) and HD 4203 (C/O = 1.51, Figure 4.33). This temperature range corresponds

to beyond a radial distance of ∼1.2AU for Hersant et al. (2001) midplane conditions at

2.5×105 years and∼0.2AU for Hersant et al. (2001) midplane conditions at 3×106 years.

As few terrestrial planets accrete material from beyond 1.2AU, it is expected that C-rich

planets forming early in the lifetime of the disk will remain dry without additional water

being delivered to the planets via adsorption.

Delivery of water by exogenous sources (such as comets and asteroids) would be re-

quired to produce an ocean-bearing planet within the C-rich systems. However, these

systems are predicted to contain less water ice and serpentine than their Solar-like com-

panions. This is due to the relative O depletions within the selected systems. [O/H] values

for the C-rich systems range from −0.21 to 0.13, depleted when compared both to other

elements within the same system and in comparison to the Solar-like systems which vary

from [O/H] = −0.14 to 0.38. These reduced O abundances result in the production of

smaller amounts of the water-bearing species and would thus make it increasingly diffi-

cult to provide water to a terrestrial planet within these systems. This variation in water

abundance can be seen most easily when comparing Figures 4.12 and 4.20. Thus it ap-

pears that terrestrial planets within Solar-like systems are likely to obtain some amount of

water (through temporal variations in composition, adsorption and exogenous delivery)

while those in C-rich systems are likely to remain dry.

169

HD72659

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

T vs Al(g)

T vs Al2O(g)

T vs AlH(g)

T vs Ca(g)

T vs CH4(g)

T vs CN(g)

T vs CO(g)

T vs CO2(g)

T vs Cr(g)

T vs CS(g)

T vs Fe(g)

T vs H(g)

T vs H2(g)

T vs H2O(g)

T vs H2S(g)

T vs HCN(g)

T vs He(g)

T vs HS(g)

T vs Mg(g)

T vs N2(g)

T vs Na(g)

T vs NaOH(g)

T vs NH3(g)

T vs Ni(g)

T vs O(g)

T vs P(g)

T vs PH(g)

T vs PN(g)

T vs PO(g)

T vs PS(g)

T vs S(g)

T vs S2(g)

T vs Si(g)

T vs SiH(g)

T vs SiO(g)

T vs SiS(g)

T vs SO(g)

T vs SO2(g)

T vs Ti(g)

T vs TiO(g)

T vs TiO2(g)

Figure 4.32: Schematic of the output obtained from HSC Chemistry for HD72659 at apressure of 10−4 bar. Only gaseous species present within the system are shown. Allabundances are normalized to the least abundant species present. Input elemental abun-dances are shown in Table 4.6.

170

HD4203

T (K)

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

Al(g)

Al2O(g)

AlH(g)

Ca(g)

CH4(g)

CN(g)

CO(g)

CO2(g)

Cr(g)

CS(g)

Fe(g)

H(g)

H2(g)

H2O(g)

H2S(g)

HCN(g)

He(g)

HS(g)

Mg(g)

N2(g)

Na(g)

NaOH(g)

NH3(g)

Ni(g)

O(g)

P(g)

PH(g)

PN(g)

PO(g)

PS(g)

S(g)

S2(g)

Si(g)

SiH(g)

SiO(g)

SiS(g)

SO(g)

SO2(g)

Ti(g)

TiO(g)

TiO2(g)

Figure 4.33: Schematic of the output obtained from HSC Chemistry for HD4203 at apressure of 10−4 bar. Only gaseous species present within the system are shown. Allabundances are normalized to the least abundant species present. Input elemental abun-dances are shown in Table 4.6.

171

4.5.6 Planetary Interiors and Processes

Given the wide variety of predicted planetary compositions, a similarly diverse range of

planetary interiors is also expected. To better quantify this, I examined four specific cases:

a 1.1M⊕ Earth-like planet (Gl777), a 0.61M⊕ Mg-rich Earth-like planet (HD177830),

a 1.1M⊕ refractory planet (HD4208) and a 0.47M⊕ C-rich planet (HD108874). Ap-

proximate interior structures for each were calculated using equilibrium mineralogy for

a global magma ocean with P = 27GPa and T = 2000◦C. Equilibrium compositions at

these conditions have been found to produce the best agreement between predicted and

observed siderophile abundances within the primitive upper mantle of the Earth (Drake,

2000). Elemental abundances were taken from the results discussed in Section 4.4.2. Re-

sulting mineral assemblages were sorted by density to define the compositional layers.

Approximate planetary radii were obtained from Sotin et al. (2007) based on planetary

mass. These planetary radii are based on silicate planetary equations of state and as such

are unlikely to completely describe the C-rich planets observed here. However, no stud-

ies have considered such assemblages, forcing us to assume a silicate based approximate

radius. Density variations at high pressures were not considered in defining the depths of

various layers. Large impacts (such as the moon forming impact) are also neglected. The

resulting interior structures (shown to scale) can be seen in Figure 4.34.

The interior mineralogy and structure of the planet orbiting Gl777 is similar to Earth.

It contains a pyroxene dominated crust (∼450 km deep) overlying an olivine mantle

(∼1500 km deep) with an F-Ni-S core (radius ∼ 4600 km). The crust is significantly

thicker than seen on Earth as I am currently neglecting density and phase changes. Given

its structure and comparable mineralogy, I would expect to observe planetary processes

similar to those seen on Earth. Melting conditions and magma compositions are expected

to be comparable and it is feasible that a liquid core would develop, resulting in the pro-

duction of a magnetic dynamo. Although I cannot make any specific statements regarding

the likelihood of plate tectonics without further detailed modelling, the thicker crust of

172

this planet will increase the magnitude of the shear stresses required for lithospheric de-

formation, one of the key requirements of tectonic activity (Valencia et al., 2007b). Even

if the crustal thickness does prohibit global tectonics, stagnant lid convection may occur

as is believed to have been the case on Mars. In general, based on their mass and composi-

tion, the terrestrial planets of Gl777 are likely to have structures and mineral assemblages

similar to those observed in our system.

The simulated planet for HD177830 is depleted in Si, relative to the Earth, resulting

in high spinel and olivine content in the mantle (resembling that of type I kimberlites) and

a thinner pyroxene and feldspathic crust than observed for Gl777 (∼190 km deep). Given

its small mass and size, unless significant amounts of radioactive material are accreted

or tidal heating is significant, it will be difficult to attain temperatures high enough to

produce large amounts of magmatic melt within the mantle. If produced, however, they

would have compositions similar to komatiite (dominated by olivine with trace amounts

of pyroxene and plagioclase). Volcanic eruptions would be comparable to basaltic flows

observed on Earth due to the low silica content of the melt. Similarly, driving mantle

convection also requires significant levels of melt production. Although more comparable

in thickness to the Earth’s crust, it is still questionable whether sufficient melt could be

produced to induce plate tectonics on this planet.

The terrestrial planet orbiting HD4208 is highly refractory in composition. The crust

is thick (∼800 km) and has a composition resembling continental crust (felsic upper, ul-

tramafic lower). Production of large amounts of melt within the mantle would be limited

by the highly refractory composition, even considering that the large core would pro-

duce a considerable amount of heat via potential energy release. Furthermore, given the

thickness of the crust, extrusive volcanism and plate tectonics are unlikely to occur as

high stress levels would be required to fracture the crust. Producing such stresses with-

out a vigorously convecting mantle would be challenging. Therefore, it is questionable

whether or not a planet with this composition and structure would be active. Given the

similar composition and size of the core, a magnetic dynamo is still expected to be pro-

173

duced within the core.

Finally, carbide planets are expected to form around HD108874. The resulting compo-

sition and structure is unlike any known planet. Its small size, refractory composition and

possible lack of radioactive elements (due to the potential absence of phosphate species,

common hosts for U and Th, and possible lack of carbonates, the common host of K) will

inhibit long-term geologic activity due to the difficulty in melting the mantle. Only large

amounts of heat due to core formation and/or tidal heating would be able to provide the

required mantle heating. Once all the primordial heat has been removed, it is unlikely

that the mantle would remain molten on geologic timescales. Until that time, given the

buoyancy of molten carbon, volcanic eruptions would be expected to be highly enriched

in C. The core is also expected to be molten, thus making it likely that a magnetic dynamo

would be produced (Gaidos and Selsis, 2007). In essence, although initially molten and

probably active, old carbide planets of this type would be geologically dead.

Recent studies have shown that coreless planets may be produced for compositions

with significant amounts of oxidized material (Elkins-Tanton and Seager, 2008). As pre-

viously discussed, none of the terrestrial planets directly accrete hydrous material for

midplane conditions at t = 5×105 years, nor are they highly oxidized. However, several

planets did accrete water and serpentine for later disk conditions. Additionally, adsorption

is also believed to contribute significant amounts of water to terrestrial planets in systems

with Solar-like compositions. Therefore, oxidized planetary compositions and thus core-

less planets may be produced for the Solar-like systems. To examine the effects of such a

water-rich compositions on the predicted structure, I determined the composition for the

same planet orbiting Gl777 but for disk conditions at t = 3×106 years. At this time, it

contains a sizeable amount of oxidized, hydrous material. The predicted interior structure

and composition is shown in Figure 4.35.

It is clear that for conditions at t = 5×105 years the composition is considerably more

oxidized. It is now dominated by olivine and troilite with minor amounts of feldspar,

diopside and water. No pyroxene is predicted. The crust is slightly thinner and now

174

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175

contains water. The core is also more oxidized, containing a large amount of magnetite

(Fe3O4).

Based on these simulations, I cannot definitively claim that core formation within

these planets will occur. Based on equilibrium assumptions, I would expect to see some

degree of core formation, albeit with an altered composition. However, based on the

simulations of Elkins-Tanton and Seager (2008), if the Fe fragments mixed throughout

the magma ocean are less than 1cm in size, oxidation of the Fe would occur before it

could sink and I would not expect to see any significant core development. If that were

to occur with the current simulated abundances, we would see a deep mantle composed

of primarily of olivine and iron oxides. Such a composition would prohibit the formation

of a magnetic dynamo and alter the rheology of the planet. Present models of planetary

formation are unable to simulate accretionary collisions in such detail. The different

rheology of a carbide magma ocean (as would be the case for the C-rich systems) may

also alter the size requirements for Fe fragments needed to form a core.

Similarly, incomplete mixing of material accreted at later times is likely to result

in deviations from the equilibrium picture presented here. For example, accretion of

oxidized and water-rich material late in the formation process may result in a stratified

redox state and water-rich crust as observed for the Earth. Unfortunately, it is not possible

to determine these effects with current models as it requires a level of understanding of

the impact and accretion process (e.g. mantle mixing, fragmentation) on small planetary

bodies that we currently do not have. These results are also key for super Earth studies

such as that of Valencia et al. (2007a) and O’Neill et al. (2007). Previous simulations have

assumed Earth-based compositions and structures. Based on the present simulations, a

wide variety of both are possible and will need to be considered.

4.5.7 Planet Habitability

The habitable zone of a planetary system is defined as being the range of orbital radii for

which water may be present on the surface of a planet. For the stars considered here, that

176

Gl777 t = 0.5Myr

Fe-Ni-S core

Olivine mantle

Pyroxene crust

Gl777 t = 3Myr

Fe-S and

Fe oxide core

Olivine mantle

Feldspar crust

Water ocean

Figure 4.35: Schematic of simulated interiors of Gl777 under two different disk condi-tions. Left: Planetary interior for disk conditions at t = 5×105 years. Right: Planetaryinterior for disk conditions at t = 3×106 years. Figures are to scale for planet and layersizes.

177

corresponds to radii from∼0.7AU to∼1.45AU. The vast majority of the planets produced

by the current simulations orbit interior to this region (exterior in the case of 55Cnc) and

thus are unlikely to be habitable. Only 6 planets are produced within the classical habit-

able zone, existing in orbits extending from 0.84AU to 1.19AU. All six of these planets

are formed in Solar-like systems (Gl777, HD4208 and HD72659) and have compositions

comparable to that of Earth. Neglecting possible variations in atmospheric compositions,

I feel that these systems (and others similar to them) are the ideal place to focus future

astrobiological searches as they not only contain planets with compositions similar to that

of Earth and are likely to obtain some amount of water during their evolution but also

exist in the biologically favorable region of the planetary system.

Of the five C-rich systems, only one produced a planet close to the habitable zone.

HD19994 formed a terrestrial planet at 0.70AU, just at the inner edge of the habitable

zone. All other planets are located well outside the required radii. As such, under the

current definition of habitable, I conclude that it is unlikely that any of the C-rich planets

formed in the current simulations would be capable of supporting life.

4.5.8 Biologically Important Elements

In addition to water, complex life (as we know it) also requires several key elements to

exist. The six essential elements are H, C, N, O, P and S. As was the case for the Solar

System simulations discussed in Chapter 3, none of the planets accreted any N. Given that

they also failed to accrete any water, the final planets are also laking in H. The terrestrial

planets formed in the Solar-like systems all contained various amounts of O, P and S but,

as for the Solar System simulations, were deficient in C. The most C-rich systems, on the

other hand, were lacking in O, P and S.

Thus it is clear that for life to develop on any of the terrestrial planets formed in the

current simulations, significant amounts of several elements must be supplied from ex-

ogenous sources within the system. All elements may be supplied from the outer, cooler

regions of the disk. Thus it is possible that migration, comets, meteorites and/or radial

178

mixing may produce planets with the necessary elements for life to develop. As for the

Solar System simulations, all biologically required elements would be introduced in a

form that could be utilized by early life. This is especially intriguing for those planets

located within the habitable zone. On the other hand, alternative pathways could be de-

veloped for the formation of an alternative biologic cycle without requiring the same six

elements.

4.5.9 Mass Distribution

Radial midplane mass distributions based on the equilibrium condensation sequence were

calculated for each system. As composition is correlated to a specific radial distance

within the midplane (via the Hersant et al. (2001) model), the total mass of solid material

present within a given radial distance within the disk is given by:

Mass of solid material = Σi2πr2i Msolid, i (4.6)

where Msolid, i is the mass of solid material determined by the chemical model to be lo-

cated at ri.

Based on this calculation, the most carbon-rich systems simulated have unexpected

differences in their mass distributions. The combination of a broad zone of refractory

carbon-bearing solids and the relatively small amount of water ice that condenses in these

systems suggests that C-rich systems have more solid mass located in the inner regions of

the disk than in the outer regions. This mass distribution is the opposite of that expected in

Solar-like systems. This can be seen in Figure 4.36 which shows the distribution of solid

mass within each system under the assumption of equilibrium and for disk conditions at t

= 5×105 years. Radial mixing of material is neglected.

It can be seen from Figure 4.36 (top panel) that the planetary systems with Solar-like

compositions have mass distributions essentially identical to that of the Solar System.

179

Only HD72659 displays any appreciable deviation, with marginally lower percentages

than the Solar System (<2% difference) over much of the disk. The increase in mass

observed for all systems at ∼0.6AU is due to the appearance of silicate species within the

disk while the increase at ∼4.8AU is due to the condensation of hydrous species. The

variation in slope between the different systems is due to different stellar elemental ratios

(especially Mg/Si) resulting in slightly different ratios of the dominate silicate species

present within the disk. These compositional variations produce marginally different mass

distributions.

Significant differences appear when considering the C-rich systems as seen in Fig-

ure 4.36 (bottom panel). It can be seen that all of the C-rich systems contain a greater

proportion of their mass within the inner disk than the Solar System does. Additionally,

due to the reduced amount of water ice present in these systems, the marked increase in

mass at ∼4.8AU observed in the Solar-like systems is not seen here. This increased mass

concentration suggests that protoplanets may form more easily in the inner regions of the

C-rich systems. As I cannot determine the exact amount of solid material present within

these disks, I am unable to say whether it would be possible to produce a Jovian-planetary

core in this region. However, if sufficient mass were present, it is conceivable that a giant

planet core composed of refractory C-rich species may be produced within several AU

of the host star, allowing for giant planet formation to occur much closer to the host star

than previously thought. Such a scenario would obviously alter the extent and nature of

planetary migration required within these systems as we would no longer need to migrate

a planet from 5AU into 1-2AU. Alternatively, if insufficient mass is available for Jovian

core formation, production of terrestrial planets in this region may proceed faster and with

greater ease, thus increasing the chance for planetary detection. The full implications of

these scenarios need to be examined by using alternative mass distributions for extrasolar

planetary formation simulations for both gas giant planets and smaller terrestrial planets.

180

Semimajor Axis (AU)

0 1 2 3 4 5

% o

f Sol

id M

ater

ial

0

20

40

60

80

100

SolarGl777HD4208HD177830HD72659

Semimajor Axis (AU)

0 1 2 3 4 5

% o

f Sol

id M

ater

ial

0

20

40

60

80

100

Solar55CncHD19994HD4203HD108874HD142415

Figure 4.36: Solid mass distribution within the disk for known extrasolar planetarysystems. The mass distribution for the Solar System is also shown for comparison.Top Panel: Distribution determined for Solar-like systems studied (Gl777, HD4208,HD72659, HD177830). Bottom Panel: Distribution determined for the C-rich systemsstudied (55Cnc, HD4203, HD19994, HD108874, HD142415).

181


As previously discussed, stellar photospheric pollution has been suggested as a possible

explanation for the observed high metallicity of extrasolar planetary host stars (Laughlin,

2000; Gonzalez et al., 2001; Murray et al., 2001). The current simulations, though, do

not support this hypothesis. Enrichments are produced primarily in Al, Ca and Ti, not

Fe as is required by the pollution theory. Furthermore, relatively small masses of solid

material are accreted by the host stars during planet formation, suggesting that insufficient

material is accreted to produce the observed enrichments. Thus unless migration of the

giant planets can systematically result in accretion of giant planets by the host star, I have

to agree with previous authors (e.g Santos et al. 2001, 2003, 2005; Fischer and Valenti

2005) and conclude that the observed host star enrichment is primordial in origin.

The current simulations also imply that enrichments due to stellar pollution are most

likely to be observed for the refractory elements in high mass stars with low convective

zone masses. This suggests that surveys for pollution effects caused by terrestrial planet

formation should focus on Ti, Al and Ca abundances in A-type and high mass F-type stars

as they are expected to have the lowest convective zone masses. However, more detailed

simulations of the fate of material accreted into radiative zones need to be undertaken to

support this hypothesis.

4.6 Summary

Terrestrial planet formation simulations have been undertaken for nine different extrasolar

planetary systems. Terrestrial planets were found to be ubiquitous, forming in all cases

examined. Almost half of the simulations produced multiple terrestrial planets. The simu-

lated planets are expected to be detectable by Kepler, thus allowing for future independent

verification of formation simulations.

The compositions of these planets are found to vary greatly, from those comparable to

Earth and CAI’s to other planets highly enriched in carbide phases. These compositional

182

variations are produced by deviations in the abundances of the host star and thus the

system as a whole. Based on this, it is expected that C-rich planets will comprise a

sizeable portion of extrasolar terrestrial planets and need to be considered in significantly

more detail. These compositions are highly dependant on the disk conditions selected for

study, requiring us to develop a more detailed understanding of the timing of planetary

formation within these systems.

Given the wide variety of compositions predicted, it is also likely that planetary min-

eralogies and processes within these planets will be altered from those of our own Solar

System. Compositions range from planets dominated by Fe and Mg-silicate species to

those composed almost entirely of Fe and C. These compositional variations are likely to

generate differences in delectability with C-rich planets being easier to detect via infrared

surveys due to their lower albedo.

The most habitable planets are expected to be those forming in systems with composi-

tions similar to Solar. Water delivery, composition and orbital location make these planets

ideal site for future biological surveys and studies. C-rich planets are likely to be lacking

water and located interior to the habitable zone, making such planets unfavorable for the

development of life as we know it.

Finally, pollution of the host star by the planetary formation process appears to

be negligible for the majority of systems. Enrichments are produced only for those

stars with the least massive convective zones and even then only in the most refractory

elements (Ti, Al and Ca). Therefore, it is unlikely that pollution is a viable explanation

for the currently observed host star metallicity trend. This also implies that pollution

studies should be undertaken for A-type and massive F-type stars as they are more likely

to display the preferential enrichment in Ti, Al and Ca that appears to be indicative of

terrestrial planet formation.

183

Figure 4.37: POOCH CAFE c© Paul Gilligan. Reprinted with permission of UNIVERSALPRESS SYNDICATE. All rights reserved. Originally published 8/12/2006.

184

CHAPTER 5

SUMMARY & CONCLUSIONS

A number of the questions posed in the introductory chapter of this dissertation have

begun to be answered. Extrasolar host star enrichments are primordial, not produced by

pollution or external processes or additions. Simulated extrasolar terrestrial planets have

been found to be common amongst systems and, based on their primordial enrichments,

are likely to have a wide diversity of compositions.

In Chapter 2, extrasolar planetary host stars were been found to be systematically

enriched over non-host stars in several r- and s- process elements. These enrichments,

however, are in keeping with general galactic chemical evolution trends. Thus although

enriched in a variety of elements, host stars (and presumably the rest of the planetary sys-

tem) are believed to have not undergone any unusual processing or alteration. Therefore,

the abundances we are observing today are primordial in nature. Furthermore, given the

apparent preference of planets to form around such stars, planet formation appears to be

a natural part of the stellar material evolution.

Given the primordial nature of the stellar photospheric enrichment, it is thus natural to

consider the composition of terrestrial planets forming within these systems. In Chapter

3, I determined the bulk elemental abundances of the simulated terrestrial planets pro-

duced by the Solar System simulations of O’Brien et al. (2006). These abundances are

in excellent agreement with observed planetary values, implying that the combination of

dynamical and chemical modeling is successfully reproducing the terrestrial planets of

the Solar System (to first order). These planets were also found to form wet, acquiring

sufficient water during their formation to not need significant delivery of material from

external sources, and with little dependance on the orbital properties of Jupiter and Saturn

(for the main rock forming elements only).

185

In Chapter 4, I expanded on these successes to finally consider terrestrial planet for-

mation in extrasolar planetary systems. Terrestrial planets were found to be ubiquitous,

forming in all simulations completed for each of the nine planetary systems considered.

The simulated terrestrial planets are generally found to be small (< 1M⊕) and are located

close to their host star. The compositions of these planets, however, are truly diverse,

ranging from Earth-like to refractory dominated and (most intriguingly) C-rich, domi-

nated by carbide species. As these compositions are a reflection of the host star elemental

abundances, stars with Solar elemental ratios are the best place to focus future Earth-like

planet searches as these systems are found to produce the most Earth-like terrestrial plan-

ets often located within the habitable zones of their systems and containing a significant

amount of water.

Finally, C should be a major planet building element in ∼20% of known extrasolar

planetary systems based on their host star photospheric compositions. Therefore it is

logical that carbide planets like those simulated here are likely to exist in a significant

number of planetary systems. These planets would be unlike anything we have previ-

ously observed and would produce an entirely different suite of planetary processes and

structures for future consideration.

Figure 5.1: CALVIN AND HOBBES c© 1993 Watterson. Dist. By UNIVERSAL PRESSSYNDICATE. Reprinted with permission. All rights reserved. Originally published2/11/1993.

186

APPENDIX A

STELLAR PHOTOSPHERIC ABUNDANCES

The full list of all stellar photospheric abundances determined in Chapter 2 for the target

stars of the Anglo-Australian Planet Search (AAPS) are provided in the following tables.

Internally consistent abundances for Fe, Si, C, O, Cr, Mg, Ba, Y, Zr, Eu and Nd are pro-

vided. Stellar abundances of O, Cr, Mg, Ba, Y, Zr, Eu and Nd were determined in Chapter

2 of this dissertation and the reader is referred to the text for more details. Abundances of

Fe, Si and C for the same stellar spectra were previously published in Bond et al. (2006)

and are reproduced here for ease of comparison discussion within the text.

Table A.1 lists the stellar elemental photospheric abundances of all target stars exam-

ined in Chapter 2. Abundances are given in the astronomical form of [X/H] (= logεX -

logεX,⊙). Solar values were taken from Asplund et al. (2005).

Table A.2 lists the stellar elemental photospheric abundances of all target stars exam-

ined in Chapter 2 in the cosmochemical form of number of atoms present. Values are

normalized to 106 Si atoms. Solar values were again taken from Asplund et al. (2005).

187Ta

ble

A.1

:St

ella

rabu

ndan

ces

obta

ined

fora

llA

APS

targ

etst

ars

with

viab

lete

mpl

ate

spct

ra.A

−in

dica

tes

that

ava

lue

coul

dno

tbe

obta

ined

from

the

spec

trum

.Sol

arva

lues

wer

e

take

nfr

omA

splu

ndet

al.(

2005

).

HD

[C/H

]1[S

i/H]1

[O/H

][C

r/H

][M

g/H

][B

a/H

][Y

/H]

[Zr/

H]

[Eu/

H]

[Nd/

H]

Hos

tSta

rs

2039

0.22±

0.16

0.28±

0.12

0.09±

0.04

0.25±

0.07

0.15±

0.07

0.14±

0.03

0.14±

0.09

0.06±

0.03

0.00±

0.02

0.23±

0.25

4308

−0.1

6±

0.08

−0.1

5±

0.06

−0.1

3±

0.02

−0.2

7±

0.02

−0.2

2±

0.09

−0.4

4±

0.02

−0.4

4±

0.08

−0.1

8±

0.03

−0.0

6±

0.01

−0.1

7±

0.16

1064

7−0

.14±

0.06

−0.2

2±

0.09

−0.1

4±

0.02

−0.1

4±

0.06

−0.1

5±

0.06

0.07±

0.03

−0.1

3±

0.12

−0.0

2±

0.04

−0.3

0±

0.01

−0.2

8±

0.20

1344

5−0

.17±

0.10

−0.3

2±

0.10

−0.2

2±

0.03

−0.1

8±

0.03

−0.2

7±

0.09

−0.4

8±

0.08

−0.3

5±

0.10

−−0

.43±

0.06

−0.0

6±

0.03

1705

10.

09±

0.11

0.09±

0.07

0.00±

0.01

0.08±

0.06

−0.1

3±

0.01

0.18±

0.08

0.00±

0.12

0.15±

0.04

−0.1

0±

0.03

0.07±

0.10

2078

2−0

.07±

0.10

−0.0

8±

0.05

−0.4

6±

0.04

0.12±

0.05

0.02±

0.07

−−0

.32±

0.08

−0.3

5±

0.05

−0.3

2±

0.06

−0.2

1±

0.05

2307

90.

01±

0.12

−0.0

3±

0.05

−0.2

4±

0.02

−0.1

6±

0.05

−0.3

3±

0.01

−0.2

2±

0.03

−0.1

9±

0.10

−0.0

5±

0.09

−0.1

8±

0.04

−0.0

5±

0.10

3017

70.

27±

0.09

0.43±

0.08

0.30±

0.06

0.30±

0.08

0.07±

0.02

−0.1

1±

0.03

0.03±

0.11

−0.0

4±

0.05

−0.

23±

0.04

3909

10.

03±

0.06

0.07±

0.03

−0.

15±

0.05

0.10±

0.03

−−

−0.0

4±

0.03

−0.1

1±

0.04

−0.0

4±

0.01

7064

2−

0.19±

0.11

0.08±

0.02

0.21±

0.05

0.09±

0.07

0.00±

0.03

0.11±

0.07

0.24±

0.04

−0.0

5±

0.02

−73

526

0.22±

0.09

0.26±

0.08

0.08±

0.07

0.12±

0.05

0.07±

0.09

0.05±

0.02

−0.0

8±

0.13

0.23±

0.05

0.22±

0.06

0.11±

0.04

7528

90.

12±

0.18

0.23±

0.05

0.01±

0.02

0.17±

0.04

0.00±

0.03

0.07±

0.10

0.02±

0.12

0.29±

0.04

0.04±

0.06

0.31±

0.05

8344

30.

30±

0.23

0.50±

0.02

0.27±

0.07

0.29±

0.06

0.16±

0.06

−0.1

6±

0.02

0.06±

0.06

−0.0

5±

0.04

−0.0

8±

0.03

0.05±

0.04

1021

170.

33±

0.13

0.29±

0.13

0.13±

0.04

0.22±

0.05

0.07±

0.08

0.11±

0.10

0.00±

0.08

0.23±

0.03

−0.

15±

0.05

1081

47−0

.05±

0.06

−0.0

2±

0.11

−0.0

7±

0.02

0.05±

0.05

−0.0

7±

0.02

0.04±

0.03

−0.0

3±

0.11

−0.0

7±

0.04

0.00±

0.02

−0.0

3±

0.10

1176

180.

01±

0.15

0.02±

0.06

−0.0

9±

0.02

−0.0

7±

0.05

−0.0

6±

0.08

0.09±

0.11

−0.1

1±

0.10

0.01±

0.03

−0.0

7±

0.01

0.11±

0.04

1349

870.

29±

0.10

0.32±

0.05

0.19±

0.04

0.30±

0.06

0.22±

0.09

0.31±

0.03

0.18±

0.08

0.21±

0.01

0.00±

0.03

0.27±

0.04

1424

150.

01±

0.04

−0.2±

0.13

−0.2

1±

0.01

−0.2

1±

0.05

−0.2

9±

0.01

0.11±

0.04

0.01±

0.10

−−0

.23±

0.03

0.11±

0.02

1548

57−0

.28±

0.07

−0.2

8±

0.11

−0.1

5±

0.03

−0.2

0±

0.04

−0.2

0±

0.03

−0.1

1±

0.09

−0.2

9±

0.08

−0.0

8±

0.04

−0.2

7±

0.07

−0.0

1±

0.02

1606

910.

31±

0.12

0.31±

0.07

0.15±

0.02

0.20±

0.06

0.14±

0.10

0.01±

0.05

0.00±

0.08

0.20±

0.04

−0.1

6±

0.08

0.18±

0.02

1644

270.

14±

0.09

0.11±

0.08

−0.0

2±

0.01

0.07±

0.03

−0.0

7±

0.01

−0.1

5±

0.03

−0.1

7±

0.10

−0.1

0±

0.05

−0.1

4±

0.04

0.12±

0.06

1799

490.

15±

0.02

0.10±

0.11

0.03±

0.05

0.14±

0.04

0.04±

0.01

−0.2

3±

0.03

0.16±

0.07

0.28±

0.08

−0.0

5±

0..0

40.

13±

0.10

1870

850.

08±

0.04

0.05±

0.03

−0.0

5±

0.02

−0.0

1±

0.05

−0.1

4±

0.01

0.05±

0.07

−0.0

6±

0.15

0.08±

0.02

−0.3

2±

0.07

−0.0

2±

0.11

1960

500.

20±

0.11

0.26±

0.06

0.17±

0.05

0.20±

0.06

0.19±

0.01

0.09±

0.04

0.09±

0.10

0.19±

0.05

−0.1

2±

0.04

0.02±

0.06

Con

tinue

don

next

page

188Ta

ble

A.1

–co

ntin

ued

from

prev

ious

page

HD

[C/H

][S

i/H]

[O/H

][C

r/H

][M

g/H

][B

a/H

][Y

/H]

[Zr/

H]

[Eu/

H]

[Nd/

H]

2084

870.

02±

0.02

−0.0

9±

0.10

−0.0

9±

0.01

0.02±

0.05

−0.1

0±

0.02

−0.0

6±

0.05

−0.0

6±

0.11

0.03±

0.03

−0.1

4±

0.07

−0.0

1±

0.04

2132

400.

18±

0.08

0.14±

0.06

0.00±

0.02

0.09±

0.04

−0.0

4±

0.04

0.07±

0.02

−0.0

1±

0.12

0.09±

0.03

0.14±

0.07

0.23±

0.05

2164

350.

17±

0.09

0.21±

0.07

0.21±

0.02

0.24±

0.04

0.18±

0.05

0.26±

0.09

0.19±

0.14

0.29±

0.05

0.00±

0.01

0.09±

0.15

2164

370.

23±

0.10

0.25±

0.08

0.12±

0.02

0.14±

0.05

0.09±

0.11

−0.0

7±

0.07

0.03±

0.10

0.02±

0.03

0.05±

0.04

0.22±

0.08

Non

-Hos

tSta

rs

1581

−0.2

8±

0.10

−0.1

4±

0.07

−0.3

0±

0.02

−0.1

8±

0.03

−0.2

8±

0.04

−0.1

4±

0.10

−0.2

8±

0.09

−0.1

0±

0.05

−0.3

6±

0.03

−0.1

9±

0.20

3823

−0.2

2±

0.08

−0.2

2±

0.15

−0.2

2±

0.01

−0.3

1±

0.05

−0.3

3±

0.03

−0.0

9±

0.05

−0.3

1±

0.10

−0.1

4±

0.12

−0.3

8±

0.09

−0.2

1±

0.20

7570

0.20±

0.14

0.18±

0.10

0.01±

0.01

0.07±

0.05

−0.0

1±

0.11

−0.1

2±

0.13

−0.0

3±

0.11

0.13±

0.08

−0.0

7±

0.04

−0.2

5±

0.27

9280

0.38±

0.19

0.28±

0.12

0.29±

0.05

0.15±

0.04

0.08±

0.08

−0.1

0±

0.07

−0.0

9±

0.09

−0.0

9±

0.04

−−0

.19±

0.08

1018

00.

06±

0.11

0.06±

0.04

−0.0

4±

0.03

0.02±

0.05

−0.0

6±

0.11

−0.0

6±

0.10

−0.1

1±

0.09

−0.0

4±

0.08

−0.1

7±

0.04

0.07±

0.05

1111

20.

18±

0.09

0.20±

0.07

0.02±

0.01

0.11±

0.04

−0.0

1±

0.04

−0.0

5±

0.08

−0.1

2±

0.11

0.02±

0.10

−0.1

2±

0.11

0.03±

0.06

1238

7−0

.05±

0.09

−0.0

8±

0.05

0.09±

0.03

−0.2

4±

0.04

−0.1

7±

0.08

−0.4

1±

0.12

−0.3

3±

0.09

−0.1

5±

0.04

−0.2

8±

0.07

−0.1

5±

0.06

1870

9−0

.26±

0.09

−0.1

8±

0.05

−0.2

7±

0.03

−0.2

4±

0.05

−0.2

4±

0.06

−0.2

1±

0.09

−0.3

5±

0.08

−0.2

1±

0.07

−0.2

8±

0.05

−0.2

0±

0.14

1963

2−0

.03±

0.09

0.05±

0.04

−0.0

7±

0.03

0.07±

0.04

−0.1

3±

0.08

−0.0

4±

0.04

−0.2

4±

0.10

−0.2

0±

0.05

−0.

08±

0.10

2020

1−0

.04±

0.12

0.09±

0.05

−0.1

3±

0.01

0.04±

0.05

−0.0

9±

0.08

0.07±

0.04

0.10±

0.08

0.13±

0.05

−0.

16±

0.08

2076

6−0

.19±

0.11

−0.1

6±

0.09

−0.2

8±

0.01

−0.2

1±

0.04

−0.2

6±

0.04

−0.4

0±

0.12

−0.4

0±

0.08

−0.2

7±

0.10

−−0

.04±

0.02

2079

4−0

.08±

0.09

−0.1

6±

0.07

−0.1

9±

0.01

−0.2

7±

0.04

−0.2

1±

0.09

−0.5

0±

0.13

−0.3

4±

0.09

−0.0

8±

0.08

−0.2

2±

0.04

−0.0

2±

0.03

2080

7−0

.19±

0.12

−0.1

8±

0.08

−0.2

7±

0.01

−0.2

6±

0.04

−0.2

6±

0.09

−0.3

9±

0.05

−0.2

8±

0.08

−0.1

3±

0.09

−0.3

0±

0.10

−0.0

3±

0.02

3029

5−

0.32±

0.16

0.31±

0.11

0.20±

0.05

0.06±

0.12

−0.0

2±

0.12

−0.1

0±

0.05

0.02±

0.06

−0.

03±

0.05

3182

70.

37±

0.12

0.52±

0.14

0.20±

0.07

0.20±

0.05

0.19±

0.13

−0.1

9±

0.08

−0.1

3±

0.03

−−

−33

811

0.03±

0.11

0.30±

0.06

0.01±

0.09

0.18±

0.07

0.09±

0.08

−−0

.15±

0.10

−−

−36

108

−0.1

3±

0.06

−0.1

9±

0.05

−0.2

4±

0.02

−0.2

1±

0.03

−0.3

3±

0.02

−0.0

9±

0.05

−0.3

4±

0.09

−0.0

9±

0.04

−0.2

6±

0.06

−0.0

9±

0.06

3828

3−0

.07±

0.03

−0.1

5±

0.03

−0.1

2±

0.01

−0.2

0±

0.04

−0.1

9±

0.12

−0.3

2±

0.03

−0.2

3±

0.07

−0.2

4±

0.05

−0.2

1±

0.07

−0.3

1±

0.09

3838

20.

03±

0.05

−0.0

1±

0.04

−0.1

0±

0.01

−0.0

7±

0.04

−0.1

7±

0.09

0.20±

0.12

−0.2

0±

0.08

0.04±

0.10

−0.1

2±

0.11

0.00±

0.01

3897

3−0

.01±

0.06

0.01±

0.09

−0.1

0±

0.01

−0.0

3±

0.04

−0.1

7±

0.06

−0.1

3±

0.02

−0.0

5±

0.08

0.01±

0.10

−0.2

0±

0.11

−0.1

2±

0.18

4290

20.

30±

0.13

0.32±

0.08

0.06±

0.08

0.20±

0.03

−0.0

5±

0.07

−0.

21±

0.08

−−

0.25±

0.08

4383

40.

04±

0.09

0.13±

0.09

0.00±

0.02

0.07±

0.04

−0.1±

0.06

0.04±

0.07

−0.0

6±

0.08

0.03±

0.03

0.12±

0.05

0.09±

0.03

Con

tinue

don

next

page

189Ta

ble

A.1

–co

ntin

ued

from

prev

ious

page

HD

[C/H

][S

i/H]

[O/H

][C

r/H

][M

g/H

][B

a/H

][Y

/H]

[Zr/

H]

[Eu/

H]

[Nd/

H]

4412

00.

13±

0.10

0.09±

0.07

−0.0

2±

0.01

−0.0

2±

0.05

0.01±

0.12

0.05±

0.09

−0.1

0±

0.12

0.03±

0.08

−0.1

8±

0.11

−0.0

4±

0.10

4459

40.

08±

0.05

0.15±

0.09

0.02±

0.02

−0.0

1±

0.15

−0.0

2±

0.11

0.05±

0.12

−0.0

4±

0.10

0.09±

0.15

0.05±

0.09

0.29±

0.18

4528

90.

12±

0.13

0.04±

0.05

0.00±

0.02

−0.0

3±

0.05

−0.0

2±

0.09

−0.0

6±

0.09

−0.1

6±

0.08

−0.0

5±

0.05

−0.2

8±

0.03

0.02±

0.01

4570

10.

24±

0.13

0.18±

0.07

0.10±

0.02

0.09±

0.06

0.02±

0.01

0.34±

0.04

0.25±

0.09

0.35±

0.08

−0.1

2±

0.06

0.00±

0.01

5244

70.

30±

0.18

0.24±

0.13

0.12±

0.02

0.10±

0.06

0.08±

0.12

0.07±

0.06

−0.2

1±

0.11

−0.1

3±

0.05

−−

5370

5−0

.08±

0.11

−0.1

2±

0.09

0.16±

0.02

−0.2

0±

0.02

−0.2±

0.06

−0.2

6±

0.02

−0.2

4±

0.05

−0.3

2±

0.08

−0.1

2±

0.04

0.11±

0.01

5370

6−0

.09±

0.08

−0.1

5±

0.08

−0.2

6±

0.02

−0.1

8±

0.04

−0.2

3±

0.06

−0.4

1±

0.04

−0.3

7±

0.07

0.01±

0.05

−0.1

4±

0.06

−0.0

9±

0.07

5572

0−0

.13±

0.14

−0.1

2±

0.09

−0.1

7±

0.02

−0.2

0±

0.02

−0.2

3±

0.08

−0.4

1±

0.04

−0.2

8±

0.04

0.05±

0.06

−0.0

6±

0.03

0.09±

0.04

5946

80.

07±

0.08

0.08±

0.09

−0.1

0±

0.05

0.10±

0.04

−0.1±

0.09

−0.1

2±

0.05

−0.1

0±

0.07

−0.0

8±

0.06

−−

6965

5−0

.12±

0.09

−0.1

4±

0.10

−0.2

6±

0.03

−0.2

4±

0.04

−0.3±

0.04

−0.2

3±

0.05

−0.3

0±

0.09

0.04±

0.05

−0.3

5±

0.07

−0.3

5±

0.25

7276

9−

0.34±

0.13

0.10±

0.02

0.22±

0.04

0.08±

0.10

−−0

.04±

0.08

−−0

.33±

0.07

−73

121

0.11±

0.08

0.05±

0.10

−0.0

5±

0.01

−0.0

3±

0.04

−0.0

5±

0.12

0.15±

0.05

−0.0

1±

0.12

0.03±

0.03

−0.1

5±

0.02

0.03±

0.01

7352

40.

11±

0.06

0.12±

0.04

−0.0

7±

0.01

0.08±

0.04

−0.0

2±

0.04

0.14±

0.08

0.16±

0.11

0.21±

0.09

0.07±

0.04

0.31±

0.05

7842

90.

02±

0.05

0.08±

0.09

−0.0

4±

0.04

0.05±

0.05

−0.1

0±

0.06

−0.1

0±

0.03

−0.1

6±

0.09

0.02±

0.05

−0.2

2±

0.03

0.11±

0.08

8063

50.

33±

0.19

0.44±

0.21

0.34±

0.10

0.23±

0.06

0.20±

0.02

0.01±

0.05

−0.0

3±

0.10

0.11±

0.07

−0.2

6±

0.09

−0.0

4±

0.01

8208

20.

02±

0.04

0.09±

0.06

−0.0

4±

0.03

0.08±

0.05

0.07±

0.16

0.19±

0.07

0.06±

0.22

0.06±

0.05

−0.0

9±

0.04

−0.3

7±

0.05

8352

9A−0

.2±

0.12

−0.2±

0.14

−0.2

5±

0.04

−0.2

3±

0.04

−0.2

4±

0.07

−0.1

9±

0.10

−0.3

2±

0.09

−0.0

2±

0.06

−−0

.05±

0.04

8681

90.

01±

0.06

−0.0

1±

0.06

−0.1

1±

0.01

−0.0

5±

0.04

−0.1

0±

0.12

−0.2

1±

0.11

−0.2

0±

0.10

−0.0

6±

0.09

−0.0

5±

0.06

−0.0

8±

0.04

8874

20.

00±

0.06

−0.0

4±

0.07

−0.1

3±

0.01

−0.0

3±

0.03

−0.1

3±

0.12

−0.1

0±

0.09

−0.1

5±

0.10

0.08±

0.06

−0.2

2±

0.08

−0.1

0±

0.07

9298

7−

0.07±

0.06

−0.0

6±

0.03

−0.0

1±

0.04

−0.0

6±

0.11

−0.2

5±

0.13

−0.2

7±

0.10

−0.0

1±

0.04

−−0

.06±

0.01

9338

50.

03±

0.10

0.01±

0.07

−0.1

2±

0.02

−0.0

1±

0.03

−0.0

2±

0.19

−0.1

1±

0.11

−0.1

7±

0.10

−0.0

6±

0.04

−0.0

8±

0.08

−0.1

1±

0.18

9642

3−

0.12±

0.07

−0.0

5±

0.02

0.08±

0.04

0.01±

0.14

−0.1

2±

0.04

−0.1

0±

0.08

0.04±

0.11

−0.4

2±

0.08

0.08±

0.04

1023

65−0

.18±

0.15

−0.1

9±

0.12

−0.2

1±

0.03

−0.2

6±

0.04

−0.2

6±

0.08

−0.3

5±

0.04

−0.3

6±

0.07

−0.2

0±

0.08

−0.2

8±

0.06

−0.1

1±

0.09

1053

280.

13±

0.08

0.16±

0.09

−0.0

5±

0.02

0.09±

0.04

0.05±

0.13

−0.3

0±

0.10

−0.0

6±

0.12

0.12±

0.05

−0.1

4±

0.07

0.06±

0.10

1064

53−0

.1±

0.09

0.07±

0.09

−0.0

2±

0.01

0.07±

0.05

−0.1

3±

0.03

−0.0

5±

0.05

−0.0

6±

0.10

0.11±

0.08

−0.

07±

0.06

1076

920.

00±

0.05

0.12±

0.08

−0.0

7±

0.01

0.10±

0.04

−0.0

4±

0.04

−0.0

8±

0.03

−0.1

0±

0.11

0.13±

0.04

−0.1

0±

0.05

0.05±

0.02

1083

090.

14±

0.06

0.13±

0.05

0.00±

0.04

0.09±

0.04

0.01±

0.09

−0.0

7±

0.02

−0.1

7±

0.08

0.00±

0.04

−0.2

4±

0.06

−0.0

7±

0.02

Con

tinue

don

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190Ta

ble

A.1

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from

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ious

page

HD

[C/H

][S

i/H]

[O/H

][C

r/H

][M

g/H

][B

a/H

][Y

/H]

[Zr/

H]

[Eu/

H]

[Nd/

H]

1146

13−

0.19±

0.06

0.03±

0.01

0.09±

0.04

−0.0

4±

0.06

−−0

.04±

0.10

0.17±

0.04

−0.1

7±

0.04

0.05±

0.01

1148

53−0

.17±

0.09

−0.2

1±

0.09

−0.2

8±

0.01

−0.2

2±

0.05

−0.2

8±

0.03

−0.2

4±

0.02

−0.3

0±

0.07

−0.2

5±

0.05

−0.3

7±

0.10

−0.0

4±

0.13

1228

62−0

.08±

0.12

−0.0

9±

0.08

−0.1

5±

0.02

−0.1

5±

0.04

−0.2

0±

0.07

−0.1

5±

0.06

−0.2

2±

0.10

−0.0

3±

0.03

−0.1

5±

0.04

−0.1

4±

0.14

1286

20−

0.22±

0.07

0.15±

0.02

0.10±

0.05

0.01±

0.02

−−0

.09±

0.10

−0.1

0±

0.05

−0.0

9±

0.10

−0.0

7±

0.01

1340

600.

05±

0.06

0.10±

0.07

−0.0

1±

0.02

0.04±

0.05

0.02±

0.14

0.02±

0.02

−0.0

4±

0.09

0.02±

0.04

−0.0

2±

0.09

0.00±

0.03

1343

30−0

.04±

0.13

0.07±

0.05

−0.0

5±

0.04

0.04±

0.04

−0.1

2±

0.04

0.04±

0.08

−0.1

3±

0.07

−0.

03±

0.02

0.04±

0.01

1409

010.

03±

0.05

0.11±

0.09

0.03±

0.03

0.09±

0.05

−0.0

4±

0.08

0.02±

0.03

0.02±

0.08

−0.0

2±

0.05

0.11±

0.04

0.14±

0.10

1431

14−0

.18±

0.11

−0.2

6±

0.09

−0.2

7±

0.04

−0.3

0±

0.06

−0.2

7±

0.06

−0.5

4±

0.04

−0.5

0±

0.08

−0.6

7±

0.10

−0.2

7±

0.12

−0.1

5±

0.04

1477

220.

05±

0.08

0.07±

0.08

−0.0

3±

0.02

0.02±

0.03

−0.1

0±

0.05

−0.0

6±

0.01

−0.1

5±

0.10

0.02±

0.06

−0.0

1±

0.04

0.03±

0.08

1559

74−0

.1±

0.12

−0.1

5±

0.07

−0.1

4±

0.02

−0.2

6±

0.09

−0.2

5±

0.01

0.12±

0.18

−0.2

1±

0.12

−0.0

9±

0.05

−0.3

6±

0.07

−16

1612

0.07±

0.09

0.17±

0.07

0.05±

0.01

0.11±

0.05

0.02±

0.06

0.00±

0.06

−0.0

7±

0.06

−0.0

5±

0.04

−0.2

7±

0.05

−0.1

6±

0.01

1775

650.

09±

0.08

0.07±

0.06

−0.0

5±

0.03

0.06±

0.03

−0.1

2±

0.07

−0.2

5±

0.04

−0.1

3±

0.09

−0.0

4±

0.05

−0.0

3±

0.09

0.07±

0.04

1838

77−0

.01±

0.08

−0.0

4±

0.05

−0.0

8±

0.03

−0.1

6±

0.03

0.13±

0.09

−0.2

3±

0.03

−0.2

4±

0.08

−0.1

2±

0.07

−0.

06±

0.01

1895

67−0

.33±

0.13

−0.1

6±

0.09

−0.2

5±

0.02

−0.2

4±

0.04

−0.2

7±

0.03

−0.2

7±

0.05

−0.3

7±

0.08

−0.0

8±

0.02

−0.1

5±

0.08

−0.0

4±

0.03

1928

650.

06±

0.15

0.03±

0.11

−0.0

5±

0.01

0.03±

0.05

0.01±

0.11

0.09±

0.02

−0.0

3±

0.17

0.00±

0.04

−0.1

9±

0.03

−0.1

6±

0.13

1931

93−0

.07±

0.11

−0.0

5±

0.09

−0.1

1±

0.02

−0.1

0±

0.04

−0.2

1±

0.04

−0.1

0±

0.05

−0.1

4±

0.10

0.09±

0.05

−0.3

4±

0.04

−0.0

3±

0.06

1933

07−0

.33±

0.19

−0.3

3±

0.05

−0.2

9±

0.01

−0.2

9±

0.04

−0.2

4±

0.11

−0.2

1±

0.10

−0.3

5±

0.11

−0.3

1±

0.09

−0.3

5±

0.04

−0.1

4±

0.07

1946

40−

0.01±

0.08

−0.1

1±

0.03

−0.0

2±

0.05

−0.1

2±

0.08

−0.1

7±

0.04

−0.1

5±

0.07

−0.0

9±

0.06

−0.2

7±

0.04

0.10±

0.11

1960

680.

16±

0.09

0.31±

0.14

0.05±

0.04

0.20±

0.04

0.13±

0.11

−0.0

7±

0.04

−0.0

1±

0.08

0.13±

0.04

0.03±

0.03

0.11±

0.04

1968

000.

36±

0.21

0.15±

0.14

0.03±

0.01

0.10±

0.03

−0.0

3±

0.09

0.28±

0.10

−0.0

5±

0.10

0.16±

0.09

0.05±

0.02

0.06±

0.07

1991

900.

21±

0.13

0.15±

0.08

−0.0

2±

0.02

0.08±

0.03

−0.0

2±

0.06

−0.1

3±

0.03

−0.1

0±

0.09

0.04±

0.04

−0.2

7±

0.08

−0.0

2±

0.03

1992

88−0

.41±

0.15

−0.4

4±

0.10

−0.4

1±

0.01

−0.5

4±

0.04

−0.4

3±

0.02

−0.4

8±

0.03

−0.5

1±

0.09

−0.3

3±

0.04

−0.2

7±

0.07

−0.1

8±

0.04

1995

09−

−0.2

4±

0.10

−0.3

4±

0.02

−0.3

5±

0.06

−0.3

6±

0.03

−0.2

9±

0.05

−0.3

1±

0.10

−0.1

1±

0.06

−−0

.03±

0.11

2026

28−0

.15±

0.10

−0.0

4±

0.09

−0.1

6±

0.05

0.00±

0.04

−0.1

4±

0.12

0.11±

0.17

−0.1

1±

0.11

0.14±

0.04

−0.1

9±

0.07

0.13±

0.01

2043

850.

07±

0.13

0.03±

0.07

−0.3

3±

0.02

−0.0

1±

0.04

−0.0

7±

0.09

−0.1

6±

0.03

−0.1

5±

0.10

0.04±

0.04

−0.

05±

0.04

2055

36−0

.03±

0.08

0.03±

0.06

−0.1

3±

0.01

−0.0

1±

0.05

−0.1

6±

0.02

−0.2

4±

0.05

−0.2

0±

0.07

−0.1

4±

0.04

−0.2

3±

0.03

0.25±

0.06

2077

000.

13±

0.11

0.15±

0.01

0.07±

0.04

0.05±

0.04

0.06±

0.10

−0.0

3±

0.06

−0.1

2±

0.07

−0.0

3±

0.03

−0.1

2±

0.02

0.11±

0.08

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[C/H

][S

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[O/H

][C

r/H

][M

g/H

][B

a/H

][Y

/H]

[Zr/

H]

[Eu/

H]

[Nd/

H]

2096

53−0

.08±

0.13

−0.0

8±

0.07

−0.1

5±

0.03

−0.1

2±

0.03

−0.1

4±

0.12

−0.1

7±

0.01

−0.2

3±

0.10

−0.0

4±

0.03

−0.2

3±

0.04

−0.0

4±

0.01

2089

98−0

.08±

0.06

−0.1

6±

0.11

−0.1

6±

0.01

−0.3

0±

0.04

0.19±

0.07

−0.3

9±

0.11

−0.4

1±

0.09

−0.2

4±

0.04

−0.4

1±

0.03

−0.1

5±

0.01

2109

18−0

.02±

0.08

−0.0

6±

0.05

−0.1

2±

0.01

−0.1

0±

0.03

−0.1

5±

0.07

−0.1

6±

0.01

−0.2

3±

0.09

−0.0

5±

0.04

−0.1

7±

0.07

0.13±

0.05

2113

170.

25±

0.09

0.25±

0.08

0.11±

0.01

0.15±

0.04

0.07±

0.08

0.02±

0.08

−0.0

6±

0.11

0.17±

0.01

0.10±

0.06

0.05±

0.11

2126

18−0

.19±

0.12

0.00±

0.07

−0.1

3±

0.01

0.00±

0.04

−0.1

1±

0.09

−0.1

8±

0.04

−0.1

8±

0.09

0.03±

0.06

−0.2

8±

0.07

0.04±

0.10

2123

30−

0.03±

0.06

−0.0

6±

0.01

0.02±

0.04

−0.1

0±

0.06

0.06±

0.02

−0.0

9±

0.10

0.10±

0.09

−0.0

6±

0.04

0.20±

0.02

2127

080.

27±

0.14

0.28±

0.08

0.16±

0.02

0.18±

0.05

0.00±

0.05

0.01±

0.04

−0.0

3±

0.07

0.20±

0.03

0.01±

0.01

0.23±

0.11

2147

59−

0.26±

0.11

0.06±

0.03

0.18±

0.06

−0.0

1±

0.03

0.11±

0.08

0.02±

0.07

−0.0

1±

0.04

−0.3

1±

0.01

0.02±

0.03

2149

530.

09±

0.06

0.02±

0.07

−0.0

3±

0.01

−0.0

3±

0.03

−0.1

1±

0.09

0.06±

0.07

−0.0

8±

0.12

0.01±

0.01

0.06±

0.05

−0.1

0±

0.14

2179

58−

0.32±

0.07

0.13±

0.06

0.14±

0.04

0.13±

0.15

−0.1

4±

0.02

−0.1

2±

0.14

−0.2

8±

0.09

−0.

30±

0.13

2190

77−

−0.0

9±

0.06

−0.1

8±

0.02

−0.1

3±

0.04

−0.1

8±

0.08

−0.2

9±

0.11

−0.3

4±

0.08

−0.1

5±

0.04

−0.1

6±

0.06

0.02±

0.01

2205

070.

15±

0.09

0.04±

0.08

0.04±

0.03

−0.0

3±

0.04

−0.0

1±

0.10

−0.2

3±

0.13

−0.2

4±

0.09

−0.0

6±

0.08

−0.1

7±

0.03

0.03±

0.01

2214

20−

0.33±

0.05

0.11±

0.02

0.20±

0.04

0.08±

0.05

−0.0

1±

0.09

−0.0

1±

0.10

0.17±

0.04

0.05±

0.03

0.21±

0.11

2231

710.

19±

0.13

0.09±

0.06

0.03±

0.02

0.04±

0.04

−0.0

8±

0.04

0.04±

0.02

−0.1

0±

0.10

0.05±

0.05

−0.0

1±

0.03

0.01±

0.06

1 Can

dSi

abun

danc

esw

ere

prev

ious

lyde

term

ined

fort

hesa

me

spec

tra

and

publ

ishe

din

Bon

det

al.(

2006

).

192Ta

ble

A.2

:Ste

llara

bund

ance

sfo

rall

AA

PSta

rget

star

sw

ithvi

able

tem

plat

esp

ectr

ano

rmal

ized

to10

6Si

atom

s.A−

indi

cate

sth

ata

valu

eco

uld

notb

eob

tain

edfr

omth

esp

ectr

um.S

olar

valu

esar

eba

sed

onth

eab

unda

nces

inA

splu

ndet

al.(

2005

).

HD

FeC

1O

Mg

Cr

YZ

rB

aN

dE

u

Hos

tSta

rs

Sola

r8.

71x1

057.

59x1

061.

41x1

071.

05x1

061.

35x1

045.

0112

.02

4.57

0.87

0.10

2039

1.00

x106

6.61

x106

9.12

x106

7.76

x105

1.26

x104

3.63

7.24

3.31

0.78

0.05

4308

8.32

x105

7.41

x106

1.48

x107

8.91

x105

1.02

x104

2.57

11.2

22.

340.

830.

13

1064

79.

77x1

059.

12x1

061.

70x1

071.

23x1

061.

62x1

046.

1718

.88

8.91

0.76

0.09

1344

58.

32x1

051.

07x1

071.

78x1

071.

17x1

061.

86x1

044.

68−

3.16

1.57

0.08

1705

17.

94x1

057.

59x1

061.

15x1

076.

31x1

051.

32x1

044.

0713

.80

5.62

0.83

0.07

2307

91.

07x1

067.

76x1

069.

77x1

065.

89x1

051.

12x1

043.

8912

.88

3.31

0.93

0.08

3017

76.

76x1

055.

25x1

061.

05x1

074.

57x1

051.

00x1

042.

004.

071.

320.

55−

3909

11.

05x1

066.

92x1

06−

1.12

x106

1.62

x104

−9.

33−

0.68

0.07

7064

21.

00x1

06−

1.10

x107

8.32

x105

1.41

x104

4.17

13.4

92.

95−

0.06

7352

66.

17x1

056.

92x1

069.

33x1

066.

76x1

059.

77x1

032.

2911

.22

2.82

0.62

0.09

7528

96.

76x1

055.

89x1

068.

51x1

066.

17x1

051.

17x1

043.

0913

.80

3.16

1.05

0.07

8344

34.

68x1

054.

79x1

068.

32x1

064.

79x1

058.

32x1

031.

823.

39−

0.31

−10

2117

6.76

x105

8.32

x106

9.77

x106

6.31

x105

1.15

x104

2.57

10.4

73.

020.

63−

1081

478.

71x1

057.

08x1

061.

26x1

079.

33x1

051.

58x1

044.

9010

.79

5.25

0.85

0.11

1176

180.

76x1

067.

41x1

061.

10x1

078.

71x1

051.

10x1

043.

7211

.75

5.37

1.07

0.08

1349

876.

17x1

057.

08x1

061.

05x1

078.

32x1

051.

29x1

043.

639.

334.

470.

780.

05

1424

151.

45x1

061.

23x1

071.

38x1

078.

51x1

051.

32x1

048.

13−

9.33

1.77

0.10

Con

tinue

don

next

page

193Ta

ble

A.2

–co

ntin

ued

from

prev

ious

page

HD

FeC

OM

gC

rY

Zr

Ba

Nd

Eu

1548

578.

91x1

057.

59x1

061.

91x1

071.

26x1

061.

62x1

044.

9019

.05

6.76

1.62

0.10

1606

916.

46x1

057.

59x1

069.

77x1

067.

08x1

051.

05x1

042.

459.

332.

290.

650.

03

1644

276.

61x1

058.

13x1

061.

05x1

076.

92x1

051.

23x1

042.

637.

412.

510.

890.

06

1799

499.

12x1

058.

51x1

061.

20x1

079.

12x1

051.

48x1

045.

7518

.20

2.14

0.93

0.07

1870

857.

59x1

058.

13x1

061.

12x1

076.

76x1

051.

17x1

043.

8912

.88

4.57

0.74

0.04

1960

505.

89x1

056.

61x1

06−

8.91

x105

1.17

x104

3.39

10.2

33.

090.

500.

04

2084

879.

12x1

059.

77x1

061.

41x1

071.

02x1

061.

74x1

045.

3715

.85

4.90

1.05

0.09

2132

400.

78x1

068.

32x1

061.

02x1

076.

92x1

051.

20x1

043.

5510

.72

3.89

1.07

0.10

2164

356.

61x1

056.

92x1

061.

41x1

079.

77x1

051.

45x1

044.

7914

.45

5.13

0.66

0.06

2164

376.

61x1

057.

24x1

061.

05x1

077.

24x1

051.

05x1

043.

027.

082.

190.

810.

06

Non

-Hos

tSta

rs

1581

7.24

x105

5.50

x106

9.77

x106

7.59

x105

1.23

x104

3.63

13.1

84.

570.

780.

06

3823

7.24

x105

7.59

x106

1.41

x107

8.13

x105

1.10

x104

4.07

14.4

56.

170.

890.

07

7570

0.68

x106

7.94

x106

9.55

x106

6.76

x105

1.05

x104

3.09

10.7

22.

290.

320.

06

9280

0.62

x106

9.55

x106

1.45

x107

6.61

x105

1.00

x104

2.14

5.13

1.91

0.30

−10

180

7.41

x105

7.59

x106

1.12

x107

7.94

x105

1.23

x104

3.39

9.55

3.47

0.89

0.06

1111

20.

65x1

067.

24x1

069.

33x1

066.

46x1

051.

10x1

042.

407.

942.

570.

590.

05

1238

75.

89x1

058.

13x1

062.

09x1

078.

51x1

059.

33x1

032.

8210

.23

2.14

0.74

0.06

1870

97.

76x1

056.

31x1

061.

15x1

079.

12x1

051.

17x1

043.

3911

.22

4.27

0.83

0.08

1963

26.

31x1

056.

31x1

061.

07x1

076.

92x1

051.

41x1

042.

576.

763.

720.

93−

2020

17.

41x1

055.

62x1

068.

51x1

066.

92x1

051.

20x1

045.

1313

.18

4.37

1.02

−C

ontin

ued

onne

xtpa

ge

194Ta

ble

A.2

–co

ntin

ued

from

prev

ious

page

HD

FeC

OM

gC

rY

Zr

Ba

Nd

Eu

2076

67.

59x1

057.

08x1

061.

07x1

078.

32x1

051.

20x1

042.

889.

332.

631.

15−

2078

27.

94x1

05−

5.25

x106

1.17

x106

1.91

x104

2.57

5.75

−0.

580.

05

2079

46.

03x1

059.

12x1

061.

32x1

079.

33x1

051.

05x1

043.

3114

.45

2.09

1.20

0.09

2080

77.

41x1

057.

41x1

061.

15x1

078.

71x1

051.

12x1

043.

9813

.49

2.82

1.23

0.08

3029

50.

59x1

06−

1.38

x107

5.75

x105

1.02

x104

1.91

6.03

2.09

0.45

−31

827

0.42

x106

5.37

x106

6.76

x106

4.90

x105

6.46

x103

1.12

−0.

89−

−33

811

0.62

x106

4.07

x106

7.24

x106

6.46

x105

1.02

x104

1.78

−−

−−

3610

87.

76x1

058.

71x1

061.

26x1

077.

59x1

051.

29x1

043.

5515

.14

5.75

1.10

0.09

3828

37.

08x1

059.

12x1

061.

51x1

079.

55x1

051.

20x1

044.

179.

773.

090.

600.

09

3838

27.

24x1

058.

32x1

061.

15x1

077.

24x1

051.

17x1

043.

2413

.49

7.41

0.89

0.08

3897

37.

24x1

057.

24x1

061.

10x1

076.

92x1

051.

23x1

044.

3712

.02

3.31

0.65

0.06

4290

20.

62x1

067.

24x1

067.

76x1

064.

47x1

051.

02x1

043.

89−

−0.

74−

4383

40.

74x1

066.

17x1

061.

05x1

076.

17x1

051.

17x1

043.

249.

553.

720.

790.

10

4412

07.

24x1

058.

32x1

061.

10x1

078.

71x1

051.

05x1

043.

2410

.47

4.17

0.65

0.05

4459

46.

76x1

056.

46x1

061.

05x1

077.

08x1

059.

33x1

033.

2410

.47

3.63

1.20

0.08

4528

96.

92x1

059.

12x1

061.

29x1

079.

12x1

051.

15x1

043.

169.

773.

630.

830.

05

4570

10.

68x1

068.

71x1

061.

17x1

077.

24x1

051.

10x1

045.

8917

.78

6.61

0.58

0.05

5244

70.

60x1

068.

71x1

061.

07x1

077.

24x1

059.

77x1

031.

785.

133.

09−

−53

705

6.76

x105

8.32

x106

2.69

x107

8.71

x105

1.12

x104

3.80

7.59

3.31

1.48

0.10

5370

66.

92x1

058.

71x1

061.

10x1

078.

71x1

051.

26x1

043.

0217

.38

2.51

1.00

0.10

5572

06.

17x1

057.

41x1

061.

26x1

078.

13x1

051.

12x1

043.

4717

.78

2.34

1.41

0.12

Con

tinue

don

next

page

195Ta

ble

A.2

–co

ntin

ued

from

prev

ious

page

HD

FeC

OM

gC

rY

Zr

Ba

Nd

Eu

5946

88.

13x1

057.

41x1

069.

33x1

066.

92x1

051.

41x1

043.

318.

322.

88−

−69

655

7.24

x105

7.94

x106

1.07

x107

7.24

x105

1.07

x104

3.47

18.2

03.

720.

540.

06

7276

90.

55x1

06−

8.13

x106

5.75

x105

1.02

x104

2.09

−−

−0.

02

7312

17.

41x1

058.

71x1

061.

12x1

078.

32x1

051.

12x1

044.

3711

.48

5.75

0.83

0.06

7352

40.

81x1

067.

41x1

069.

12x1

067.

59x1

051.

23x1

045.

5014

.79

4.79

1.35

0.09

7842

97.

41x1

056.

61x1

061.

07x1

076.

92x1

051.

26x1

042.

8810

.47

3.02

0.93

0.05

8063

50.

48x1

065.

89x1

061.

12x1

076.

03x1

058.

32x1

031.

705.

621.

700.

290.

02

8208

26.

61x1

056.

46x1

061.

05x1

071.

00x1

061.

32x1

044.

6811

.22

5.75

0.30

0.07

8352

9A8.

71x1

057.

59x1

061.

26x1

079.

55x1

051.

26x1

043.

8018

.20

4.68

1.23

−86

819

7.24

x105

7.94

x106

1.12

x107

8.51

x105

1.23

x104

3.24

10.7

22.

880.

740.

09

8874

27.

59x1

058.

32x1

061.

15x1

078.

51x1

051.

38x1

043.

8915

.85

3.98

0.76

0.07

9298

76.

17x1

05−

1.05

x107

7.76

x105

1.12

x104

2.29

10.0

02.

190.

65−

9338

57.

08x1

057.

94x1

061.

05x1

079.

77x1

051.

29x1

043.

3110

.23

3.47

0.66

0.08

9642

36.

76x1

05−

9.55

x106

8.13

x105

1.23

x104

3.02

10.0

02.

630.

790.

03

1023

657.

08x1

057.

76x1

061.

35x1

078.

91x1

051.

15x1

043.

3911

.75

3.16

1.05

0.08

1053

286.

76x1

057.

08x1

068.

71x1

068.

13x1

051.

15x1

043.

0210

.96

1.58

0.69

0.05

1064

537.

24x1

055.

13x1

061.

15x1

076.

61x1

051.

35x1

043.

7213

.18

3.47

0.87

−10

7692

6.03

x105

5.75

x106

9.12

x106

7.24

x105

1.29

x104

3.02

12.3

02.

880.

740.

06

1083

095.

89x1

057.

76x1

061.

05x1

077.

94x1

051.

23x1

042.

518.

912.

880.

550.

04

1146

130.

65x1

06−

9.77

x106

6.17

x105

1.07

x104

2.95

11.4

8−

0.63

0.04

1148

539.

33x1

058.

32x1

061.

20x1

078.

91x1

051.

32x1

044.

0710

.96

4.27

1.29

0.07

Con

tinue

don

next

page

196Ta

ble

A.2

–co

ntin

ued

from

prev

ious

page

HD

FeC

OM

gC

rY

Zr

Ba

Nd

Eu

1228

627.

59x1

057.

76x1

061.

23x1

078.

13x1

051.

17x1

043.

7213

.80

3.98

0.78

0.09

1286

205.

62x1

05−

1.20

x107

6.46

x105

1.02

x104

2.45

5.75

−0.

450.

05

1340

607.

41x1

056.

76x1

061.

10x1

078.

71x1

051.

17x1

043.

6310

.00

3.80

0.69

0.08

1343

307.

08x1

055.

89x1

061.

07x1

076.

76x1

051.

26x1

043.

16−

4.27

0.81

0.09

1409

017.

59x1

056.

31x1

061.

17x1

077.

41x1

051.

29x1

044.

078.

913.

720.

930.

10

1431

146.

31x1

059.

12x1

061.

38x1

071.

02x1

061.

23x1

042.

884.

682.

401.

120.

10

1477

226.

76x1

057.

24x1

061.

12x1

077.

08x1

051.

20x1

043.

0210

.72

3.39

0.79

0.09

1559

747.

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Con

tinue

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next

page

197Ta

ble

A.2

–co

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ued

from

prev

ious

page

HD

FeC

OM

gC

rY

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Ba

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2026

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60x1

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8.51

x106

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x105

1.00

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2.09

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2231

717.

24x1

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2410

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4.07

0.72

0.08

1 Cab

unda

nces

wer

epr

evio

usly

dete

rmin

edfo

rthe

sam

esp

ectr

aan

dpu

blis

hed

inB

ond

etal

.(20

06).

198

APPENDIX B

SOLAR SYSTEM TERRESTRIAL PLANET ABUNDANCES

Bulk elemental abundances were determined in Chapter 3 for all of the terrestrial planets

produced in the simulations of O’Brien et al. (2006). Planetary abundances were obtained

for seven different sets of midplane conditions at various disk evolutionary times (t =

2.5×105yr, 5×105yr, 1×106yr, 1.5×106yr, 2×106yr, 2.5×106yr and 3×106yr). Appendix

B contains the graphical and numerical results of each of these simulations.

Figures B.1 - B.7 show the normalized abundances for each planet produced by the

simulations of O’Brien et al. (2006). Normalized abundances are shown for each of the

seven sets of disk conditions examined. The terrestrial planet to which each simulated

planet was normalized was determined based on the semi-major axis of the terrestrial

planet and is shown in parentheses in the upper left of each plot. Figures B.1 and B.4 were

previously shown as Figure 3.3 in the text and are included here again for completeness.

The complete assemblage of all predicted bulk elemental abundances for each of the

simulated planets and for each of the seven different sets of disk conditions examined are

provided in Table B.1. Values are provided as bulk wt% of the final planet for each set

of disk conditions. Note that planetary numbers start at 4 and increase with increasing

distance from the Sun.

Table B.2 lists the ensemble-averaged bulk elemental abundances for the terrestrial

planets of the O’Brien et al. (2006) simulations. Abundances are averaged over all seven

sets of disk conditions simulated (from t = 2.5×105 to t = 3×106 years).

Table B.3 lists the difference in bulk elemental abundances between the first and last

set of disk conditions examined. As such, this table provides the range in each elemental

abundance for the terrestrial planets of O’Brien et al. (2006). The difference is defined as

AbundanceDisk at 3×106 yr − AbundanceDisk at 2.5×105 yr.

199

A first order approximation of planetary abundances incorporating volatile loss during

the accretion process was also undertaken (see Section 3.3.5). Figures B.8 - B.14 show

the normalized abundances for each planet produced by the simulations of O’Brien et al.

(2006) both with and without volatile loss incorporated. All abundances are determined

for disk conditions at 5×105 years. The terrestrial planet each simulation is normalized to

is shown in parentheses. Reference Solar System planetary abundances were taken from

Morgan and Anders (1980) (Venus), Kargel and Lewis (1993)(Earth) and Lodders and

Fegley (1997) (Mars). Figures B.8 and B.11 were previously shown as Figure 3.9 and are

included here again for completeness.

Table B.4 lists the bulk elemental abundances predicted for the terrestrial planets of

the O’Brien et al. (2006) simulations after volatile loss during impact events has been

incorporated. Abundances are listed as wt% for all planets for each of the seven disk

conditions examined.

200


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10

CJS1-4 (Venus)

CJS1-5 (Earth)

CJS1-6 (Mars)

Increasing volatility

Figure B.1: Normalized planetary abundances for CJS1 simulated terrestrial planets. Val-ues are shown for each of seven time steps considered with the following color scheme:black = 2.5×105 years, red = 5×105 years, green = 1×106 years, pink = 1.5×106 years,light blue = 2×106 years, yellow = 2.5×106 years and dark blue = 3×106 years.

201


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


CJS2-4 (Venus)

CJS2-5 (Venus)

CJS2-6 (Earth)

CJS2-7 (Mars)

Figure B.2: Normalized planetary abundances for CJS2 simulated terrestrial planets. Val-ues are shown for each of seven time steps considered with the following color scheme:black = 2.5×105 years, red = 5×105 years, green = 1×106 years, pink = 1.5×106 years,light blue = 2×106 years, yellow = 2.5×106 years and dark blue = 3×106 years.

202


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10

CJS3-4 (Venus)

CJS3-5 (Earth)

CJS3-6 (Mars)

CJS4-4 (Venus)

CJS4-5 (Mars)



Figure B.3: Normalized planetary abundances for CJS3 and CJS4 simulated terrestrialplanets. Values are shown for each of seven time steps considered with the followingcolor scheme: black = 2.5×105 years, red = 5×105 years, green = 1×106 years, pink =1.5×106 years, light blue = 2×106 years, yellow = 2.5×106 years and dark blue = 3×106

years. Left: CJS3 simulation results. Right: CJS4 simulation results.

203


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10

EJS1-4 (Venus)

EJS1-5 (Earth)

EJS1-6 (Mars)


Figure B.4: Normalized planetary abundances for EJS1 simulated terrestrial planets. Val-ues are shown for each of seven time steps considered with the following color scheme:black = 2.5×105 years, red = 5×105 years, green = 1×106 years, pink = 1.5×106 years,light blue = 2×106 years, yellow = 2.5×106 years and dark blue = 3×106 years.

204


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


EJS2-4 (Venus)

EJS2-5 (Venus)

EJS2-6 (Earth)

EJS2-7 (Mars)


205


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


EJS3-4 (Venus)

EJS3-5 (Earth)

EJS3-6 (Mars)

EJS3-7 (Mars)


206


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.01

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10EJS4-4 (Venus)

EJS4-5 (Venus)

EJS4-6 (Earth)

EJS4-7 (Mars)



207Ta

ble

B.1

:Pr

edic

ted

bulk

plan

etar

yab

unda

nces

for

the

terr

estr

ial

plan

ets

ofth

eO

’Bri

enet

al.(

2006

)si

mul

atio

ns.

All

valu

esar

ew

t%of

the

final

plan

et.C

JSde

note

sth

esi

mul

atio

nsof

O’B

rien

etal

.(20

06)w

ithJu

pite

rand

Satu

rnin

the

circ

ular

orbi

tspr

edic

ted

byth

eN

ice

mod

elw

hile

EJS

deno

tes

the

resu

ltsof

the

sim

ulat

ions

with

Jupi

tera

ndSa

turn

inth

eirc

urre

ntel

liptic

alor

bits

.Pla

neta

rynu

mbe

rsst

arta

t4an

din

crea

sew

ith

incr

easi

ngdi

stan

cefr

omth

eSu

n.

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

CM

g/Si

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=2.

5×10

5ye

ars

CJS

1-4

0.00

14.8

432

.05

2.16

27.6

41.

652.

390.

311.

790.

380.

090.

0916

.61

0.00

0.00

0.89

CJS

1-5

0.00

14.8

631

.94

1.61

28.1

21.

662.

410.

351.

790.

400.

110.

0916

.66

0.00

0.00

0.89

CJS

1-6

0.00

14.7

331

.43

3.34

28.0

81.

271.

840.

581.

780.

410.

130.

0716

.34

0.00

0.00

0.90

CJS

2-4

0.00

8.29

38.7

60.

589.

2311

.24

16.1

20.

090.

600.

120.

030.

6614

.27

0.00

0.00

0.58

CJS

2-5

0.00

14.8

932

.06

0.78

28.4

11.

772.

580.

331.

800.

410.

090.

1016

.77

0.00

0.00

0.89

CJS

2-6

0.00

14.6

032

.19

2.18

27.0

91.

942.

810.

351.

740.

370.

100.

1116

.52

0.00

0.00

0.88

CJS

2-7

0.00

14.5

730

.84

4.98

27.8

31.

121.

630.

601.

760.

400.

140.

0616

.09

0.00

0.00

0.91

CJS

3-4

0.00

10.6

136

.45

1.56

15.6

67.

7011

.07

0.17

1.04

0.20

0.05

0.45

15.0

40.

000.

000.

71

CJS

3-5

0.00

14.8

831

.66

2.22

28.3

41.

432.

070.

421.

800.

410.

110.

0816

.59

0.00

0.00

0.90

CJS

3-6

0.00

14.2

430

.99

5.98

27.2

21.

181.

710.

581.

730.

390.

130.

0615

.78

0.00

0.00

0.90

CJS

4-4

0.00

12.4

134

.61

1.13

20.7

65.

357.

700.

211.

340.

280.

070.

3115

.83

0.00

0.00

0.78

CJS

4-5

0.00

14.6

931

.03

4.07

28.0

71.

191.

730.

571.

780.

400.

130.

0616

.26

0.00

0.00

0.90

Con

tinue

don

next

page

208Ta

ble

B.1

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

CM

g/Si

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

EJS

1-4

0.00

14.4

832

.91

0.31

26.5

32.

693.

900.

111.

730.

350.

070.

1516

.77

0.00

0.00

0.86

EJS

1-5

0.00

11.9

734

.92

1.22

19.6

45.

908.

470.

291.

250.

280.

080.

3415

.64

0.00

0.00

0.77

EJS

1-6

0.00

14.7

930

.70

4.18

28.2

51.

131.

650.

571.

790.

410.

130.

0616

.34

0.00

0.00

0.91

EJS

2-4

0.00

8.74

35.8

40.

6515

.95

9.42

13.5

90.

241.

020.

220.

070.

5513

.71

0.00

0.00

0.64

EJS

2-5

0.00

13.5

734

.63

0.82

21.6

14.

326.

200.

181.

420.

280.

050.

2516

.67

0.00

0.00

0.81

EJS

2-6

0.00

15.2

032

.07

0.36

28.9

11.

492.

170.

411.

830.

420.

120.

0816

.95

0.00

0.00

0.90

EJS

2-7

0.00

14.1

929

.84

7.57

27.1

61.

091.

580.

591.

720.

390.

130.

0615

.68

0.00

0.00

0.91

EJS

3-4

0.00

10.6

035

.36

0.25

18.5

47.

5110

.85

0.10

1.22

0.23

0.04

0.44

14.8

70.

000.

000.

71

EJS

3-5

0.00

15.2

732

.20

0.22

28.7

81.

562.

280.

211.

830.

410.

100.

0817

.05

0.00

0.00

0.90

EJS

3-6

0.00

14.6

032

.95

1.81

25.2

62.

413.

440.

501.

610.

360.

120.

1416

.81

0.00

0.00

0.87

EJS

3-7

0.00

13.7

932

.30

6.89

25.8

51.

261.

820.

541.

640.

370.

130.

0715

.35

0.00

0.00

0.90

EJS

4-4

0.00

10.8

636

.60

0.14

16.0

47.

8411

.27

0.08

1.07

0.20

0.03

0.46

15.4

10.

000.

000.

71

EJS

4-5

0.00

14.3

332

.71

0.13

26.9

72.

804.

050.

091.

720.

380.

040.

1616

.62

0.00

0.00

0.86

EJS

4-6

0.00

15.3

631

.87

0.48

29.3

61.

181.

720.

581.

860.

420.

140.

0616

.97

0.00

0.00

0.91

EJS

4-7

0.00

14.9

131

.31

2.72

28.2

91.

341.

950.

501.

790.

410.

130.

0716

.56

0.00

0.00

0.90

Con

tinue

don

next

page

209Ta

ble

B.1

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

CM

g/Si

wt%

wt%

wt%

wt%

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FeA

lC

aN

aN

iC

rP

TiSi

NC

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

CJS

1−4

1.05

12.9

137

.09

4.87

24.5

21.

101.

600.

461.

560.

350.

110.

0714

.31

0.00

0.00

CJS

1−5

0.75

12.6

735

.89

5.42

25.2

71.

101.

600.

511.

600.

360.

120.

0714

.67

0.00

0.00

CJS

1−6

1.64

11.8

840

.35

5.64

22.6

80.

931.

350.

491.

440.

330.

110.

0613

.13

0.00

0.00

CJS

2−4

0.21

13.1

133

.49

4.54

23.9

12.

804.

040.

431.

520.

340.

110.

1615

.35

0.00

0.00

CJS

2−5

0.53

13.4

734

.76

4.52

25.5

91.

392.

020.

471.

620.

370.

120.

0715

.05

0.00

0.00

CJS

2−6

0.82

12.5

836

.54

4.54

23.8

41.

952.

830.

451.

510.

340.

110.

0714

.37

0.00

0.00

CJS

2−7

2.08

11.2

842

.60

5.62

21.5

40.

861.

260.

461.

370.

310.

110.

0512

.45

0.00

0.00

CJS

3−4

0.54

12.7

135

.33

4.33

23.4

72.

583.

720.

441.

490.

330.

110.

1214

.80

0.00

0.00

CJS

3−5

0.88

12.4

736

.85

4.64

23.6

81.

922.

790.

451.

500.

340.

110.

0614

.25

0.00

0.00

CJS

3−6

2.24

9.97

44.4

24.

6218

.25

2.67

3.88

0.38

1.17

0.26

0.10

0.05

11.9

20.

000.

00

CJS

4−4

0.42

13.2

334

.43

4.43

24.7

12.

072.

990.

461.

570.

350.

110.

1015

.11

0.00

0.00

CJS

4−5

1.53

11.1

540

.53

4.73

20.8

82.

383.

450.

411.

330.

300.

110.

0613

.06

0.00

0.00

Con

tinue

don

next

page

222Ta

ble

B.2

–co

ntin

ued

from

prev

ious

page

Plan

etH

Mg

OS

FeA

lC

aN

aN

iC

rP

TiSi

NC

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

EJS

1−4

0.14

13.9

832

.54

5.24

26.5

51.

321.

920.

501.

690.

380.

120.

0815

.56

0.00

0.00

EJS

1−5

0.58

13.0

835

.09

5.12

24.5

11.

722.

500.

481.

550.

350.

110.

1014

.80

0.00

0.00

EJS

1−6

1.18

12.4

438

.02

5.98

23.7

70.

951.

390.

511.

510.

340.

110.

0613

.74

0.00

0.00

EJS

2−4

0.17

13.9

932

.50

5.51

26.6

51.

181.

710.

531.

690.

380.

120.

0715

.50

0.00

0.00

EJS

2−5

0.21

13.9

132

.88

5.20

26.3

91.

311.

900.

481.

680.

380.

120.

0815

.48

0.00

0.00

EJS

2−6

0.30

13.2

633

.82

5.86

24.8

71.

732.

500.

521.

580.

360.

120.

1114

.99

0.00

0.00

EJS

2−7

3.24

9.85

48.6

24.

7518

.81

0.75

1.10

0.40

1.19

0.27

0.10

0.05

10.8

80.

000.

00

EJS

3−4

0.12

13.3

132

.71

4.90

25.2

52.

333.

370.

501.

600.

360.

120.

1415

.30

0.00

0.00

EJS

3−5

0.13

13.7

832

.85

5.61

25.7

21.

522.

210.

511.

640.

370.

120.

0915

.46

0.00

0.00

EJS

3−6

0.76

13.2

036

.02

4.82

24.8

41.

241.

800.

491.

570.

360.

120.

0914

.71

0.00

0.00

EJS

3−7

3.09

9.67

47.5

73.

7019

.35

1.33

1.29

0.49

0.77

0.24

0.09

1.19

11.0

60.

000.

16

EJS

4−4

0.07

13.6

832

.35

4.77

25.8

32.

042.

960.

471.

640.

370.

110.

1215

.58

0.00

0.00

EJS

4−5

0.08

14.1

832

.16

5.17

26.9

91.

181.

720.

521.

710.

390.

120.

0715

.70

0.00

0.00

EJS

4−6

0.36

13.4

534

.03

6.20

25.3

31.

221.

760.

541.

610.

370.

120.

0714

.96

0.00

0.00

EJS

4−7

1.06

12.5

037

.49

6.36

23.8

10.

991.

430.

511.

510.

340.

120.

0613

.82

0.00

0.00

223Ta

ble

B.3

:Diff

eren

cein

abun

danc

ebe

twee

nt=

2.5×

105yr

and

t=3×

106yr

.Diff

eren

ceis

defin

edas

Abu

ndan

ce3×

106−

Abu

ndan

ce2.5×

105.

Plan

etH

Mg

OS

FeA

lC

aN

aN

iC

rP

TiSi

NC

CJS

1−4

1.99

−3.4

89.

863.

91−

5.95

−0.

78−

1.13

0.16

−0.

41−

0.06

0.01

−0.

04−

4.07

0.00

0.00

CJS

1−5

1.70

−3.2

69.

064.

60−

5.98

−0.

77−

1.12

0.12

−0.

38−

0.08

−0.

01−

0.04

−3.

860.

000.

00

CJS

1−6

4.20

−6.1

922

.18

1.24

−11

.78

−0.

61−

0.89

−0.

23−

0.75

−0.

17−

0.06

−0.

03−

6.92

0.00

0.00

CJS

2−4

0.57

4.86

−4.

336.

4515

.91

−10

.23

−14

.65

0.45

0.99

0.24

0.08

−0.

600.

260.

000.

00

CJS

2−5

2.11

−3.

8011

.02

5.17

−7.

23−

0.93

−1.

340.

13−

0.46

−0.

100.

01−

0.05

−4.

520.

000.

00

CJS

2−6

2.04

−3.

4210

.52

3.82

−5.

74−

1.08

−1.

570.

12−

0.39

−0.

06−

0.00

−0.

06−

4.18

0.00

0.00

CJS

2−7

4.86

−6.

8025

.93

−0.

81−

13.0

0−

0.52

−0.

76−

0.28

−0.

82−

0.19

−0.

07−

0.02

−7.

520.

000.

00

CJS

3−4

0.62

2.35

−1.

105.

379.

09−

6.71

−9.

630.

360.

530.

160.

06−

0.39

−0.

720.

000.

00

CJS

3−5

2.55

−4.3

313

.65

3.44

−8.

19−

0.62

−0.

900.

02−

0.52

−0.

12−

0.02

−0.

03−

4.94

0.00

0.00

CJS

3−6

5.47

−7.1

928

.68

−2.

20−

13.7

5−

0.64

−0.

93−

0.29

−0.

87−

0.20

−0.

07−

0.03

−7.

990.

000.

00

CJS

4−4

1.13

−0.0

73.

265.

482.

82−

4.40

−6.

320.

300.

150.

060.

04−

0.25

−2.

200.

000.

00

CJS

4−5

4.26

−6.2

222

.85

0.47

−11

.90

−0.

54−

0.79

−0.

22−

0.75

−0.

17−

0.06

−0.

02−

6.91

0.00

0.00

Con

tinue

don

next

page

224Ta

ble

B.3

–co

ntin

ued

from

prev

ious

page

Plan

etH

Mg

OS

FeA

lC

aN

aN

iC

rP

TiSi

NC

EJS

1−4

0.49

−1.4

02.

006.

69−

1.56

−1.

69−

2.44

0.43

−0.

150.

010.

05−

0.09

−2.

330.

000.

00

EJS

1−5

1.66

−0.2

75.

575.

062.

73−

5.00

−7.

170.

200.

160.

050.

03−

0.29

−2.

720.

000.

00

EJS

1−6

2.01

−3.6

412

.16

1.81

−6.

94−

0.28

−0.

41−

0.11

−0.

44−

0.10

−0.

04−

0.01

−4.

020.

000.

00

EJS

2−4

0.31

4.64

−2.

236.

489.

60−

8.39

−12

.10

0.32

0.60

0.15

0.05

−0.

491.

070.

000.

00

EJS

2−5

0.46

−0.3

8−

0.26

6.24

3.57

−3.

31−

4.72

0.37

0.18

0.08

0.06

−0.

19−

2.11

0.00

0.00

EJS

2−6

1.31

−3.1

77.

196.

09−

5.94

−0.

57−

0.83

0.09

−0.

38−

0.08

−0.

02−

0.02

−3.

670.

000.

00

EJS

2−7

5.57

−7.3

530

.79

−3.

90−

14.1

0−

0.56

−0.

82−

0.30

−0.

89−

0.20

−0.

07−

0.02

−8.

120.

000.

00

EJS

3−4

0.44

2.66

−1.

326.

856.

79−

6.49

−9.

370.

450.

380.

130.

08−

0.38

−0.

220.

000.

00

EJS

3−5

0.50

−2.2

42.

926.

77−

3.90

−0.

57−

0.82

0.32

−0.

26−

0.05

0.01

−0.

02−

2.66

0.00

0.00

EJS

3−6

2.88

−4.4

714

.12

3.62

−5.

92−

1.63

−2.

32−

0.08

−0.

38−

0.08

−0.

03−

0.09

−5.

630.

000.

00

EJS

3−7

5.37

−6.5

326

.44

−2.

99−

11.9

9−

0.70

−1.

01−

0.24

−0.

76−

0.17

−0.

06−

0.03

−7.

330.

000.

00

EJS

4−4

0.25

2.61

−3.

427.

079.

69−

6.81

−9.

770.

480.

560.

170.

08−

0.40

−0.

530.

000.

00

EJS

4−5

0.36

−1.0

41.

346.

97−

1.63

−1.

78−

2.57

0.46

−0.

11−

0.01

0.07

−0.

10−

1.96

0.00

0.00

EJS

4−6

1.23

−3.2

87.

116.

01−

6.23

−0.

25−

0.37

−0.

08−

0.40

−0.

09−

0.03

−0.

01−

3.62

0.00

0.00

EJS

4−7

3.20

−5.1

917

.47

2.49

−9.

74−

0.60

−0.

87−

0.10

−0.

62−

0.14

−0.

05−

0.03

−5.

830.

000.

00

225


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10

CJS1-4 (Venus)

CJS1-5 (Earth)

CJS1-6 (Mars)


Figure B.8: Normalized planetary abundances for CJS1 simulated terrestrial planets. Thesolid line indicates the normalized abundances before volatile loss during impacts wasconsidered while the dashed line indicates the normalized abundance once volatile lossduring impacts has been incorporated. All abundances were determined for disk condi-tions at t = 5×105 years. The terrestrial planet each simulation is normalized to is shownin parentheses.

226


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


CJS2-4 (Venus)

CJS2-5 (Venus)

CJS2-6 (Earth)

CJS2-7 (Mars)

Figure B.9: Normalized planetary abundances for CJS2 simulated terrestrial planets. Thesolid line indicates the normalized abundances before volatile loss during impacts wasconsidered while the dashed line indicates the normalized abundance once volatile lossduring impacts has been incorporated. All abundances were determined for disk condi-tions at t = 5×105 years. The terrestrial planet each simulation is normalized to is shownin parentheses.

227


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10

CJS3-4 (Venus)

CJS3-5 (Earth)

CJS3-6 (Mars)

CJS4-4 (Venus)

CJS4-5 (Mars)



Figure B.10: Normalized planetary abundances for CJS3 and CJS4 simulated terrestrialplanets. The solid line indicates the normalized abundances before volatile loss duringimpacts was considered while the dashed line indicates the normalized abundance oncevolatile loss during impacts has been incorporated. All abundances were determined fordisk conditions at t = 5×105 years. The terrestrial planet each simulation is normalizedto is shown in parentheses.

228


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10

EJS1-4 (Venus)

EJS1-5 (Earth)

EJS1-6 (Mars)


Figure B.11: Normalized planetary abundances for EJS1 simulated terrestrial planets.The solid line indicates the normalized abundances before volatile loss during impactswas considered while the dashed line indicates the normalized abundance once volatileloss during impacts has been incorporated. All abundances were determined for diskconditions at t = 5×105 years. The terrestrial planet each simulation is normalized to isshown in parentheses.

229


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


EJS2-4 (Venus)

EJS2-5 (Venus)

EJS2-6 (Earth)

EJS2-7 (Mars)


230


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


EJS3-4 (Venus)

EJS3-5 (Earth)

EJS3-6 (Mars)

EJS3-7 (Mars)


231


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10


No

rma

lize

d A

bu

nd

an

ce

0.1

1

10

EJS4-4 (Venus)

EJS4-5 (Venus)

EJS4-6 (Earth)

EJS4-7 (Mars)



232Ta

ble

B.4

:Fin

albu

lkpl

anet

ary

abun

danc

esaf

terv

olat

ilelo

ssin

impa

cts

has

been

inco

rpor

ated

.All

valu

esar

ein

wt%

.

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=2.

5×10

5ye

ars

CJS

1-4

0.00

11.7

323

.13

0.62

20.9

11.

652.

390.

141.

350.

270.

060.

0915

.02

0.00

0.00

CJS

1-5

0.00

12.5

225

.19

0.65

22.9

51.

662.

410.

201.

450.

310.

080.

0915

.48

0.00

0.00

CJS

1-6

0.00

12.5

625

.19

1.43

23.2

41.

271.

840.

341.

470.

320.

100.

0615

.26

0.00

0.00

CJS

2-4

0.00

6.55

27.9

80.

176.

9811

.24

16.1

20.

040.

450.

090.

020.

6312

.90

0.00

0.00

CJS

2-5

0.00

13.1

827

.06

0.41

24.5

61.

772.

580.

221.

560.

340.

070.

0915

.91

0.00

0.00

CJS

2-6

0.00

11.7

623

.82

0.68

20.9

41.

942.

810.

161.

340.

270.

070.

1015

.06

0.00

0.00

CJS

2-7

0.00

12.5

425

.05

2.23

23.2

91.

121.

630.

351.

470.

320.

100.

0615

.09

0.00

0.00

CJS

3-4

0.00

7.98

24.5

30.

3311

.16

7.70

11.0

70.

060.

740.

130.

030.

4313

.31

0.00

0.00

CJS

3-5

0.00

11.9

223

.24

0.66

21.7

61.

432.

070.

191.

370.

290.

080.

0715

.08

0.00

0.00

CJS

3-6

0.00

12.8

426

.84

3.42

24.0

71.

181.

710.

401.

520.

340.

110.

0615

.09

0.00

0.00

CJS

4-4

0.00

8.91

21.8

10.

1813

.99

5.35

7.70

0.06

0.90

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9.79

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2-5

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10.2

420

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2-6

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224

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0613

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EJS

2-7

5.26

7.12

59.2

93.

8113

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0.55

0.80

0.29

0.86

0.20

0.13

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3-4

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10.5

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1.24

18.9

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091.

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3-5

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EJS

3-6

0.06

10.5

626

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EJS

3-7

4.36

7.33

56.9

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6613

.94

0.57

0.83

0.29

0.88

0.20

0.09

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4-4

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10.5

620

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1.28

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4-5

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10.9

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EJS

4-6

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12.1

828

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4.22

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81.

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EJS

4-7

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11.7

828

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3.61

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CJS

1-4

0.15

9.38

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1-6

0.39

9.51

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5617

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0.26

1.11

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2-4

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0.13

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1.13

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CJS

2-7

0.66

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CJS

3-4

0.05

9.45

24.9

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0.23

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CJS

3-5

0.11

9.77

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51.

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0.93

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1.13

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CJS

3-6

1.45

7.54

47.0

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5614

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0.64

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0.24

0.89

0.20

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CJS

4-4

0.02

9.27

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4-5

0.18

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EJS

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EJS

1-6

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0.23

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EJS

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2-6

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2-7

5.51

6.83

60.5

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0.76

0.28

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3-4

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921

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3-5

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3-6

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824

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EJS

3-7

4.45

7.20

57.4

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6113

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0.56

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0.29

0.87

0.20

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4-4

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10.3

320

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10.7

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4-6

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11.9

929

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EJS

4-7

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733

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CJS

1-4

0.17

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0.55

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2-4

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CJS

2-7

0.84

7.54

42.8

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1013

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0.21

0.88

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CJS

3-4

0.05

9.28

25.4

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0.22

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CJS

3-5

0.18

8.99

31.2

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0.22

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CJS

3-6

1.49

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47.5

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5213

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0.63

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0.24

0.88

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8.67

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CJS

4-4

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CJS

4-5

0.25

7.48

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EJS

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1-5

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EJS

1-6

0.59

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2-5

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2-6

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EJS

2-7

5.51

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6413

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0.52

0.76

0.28

0.83

0.19

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3-4

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EJS

3-6

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1.09

0.23

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11.7

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EJS

3-7

4.59

7.18

57.3

83.

6013

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0.56

0.81

0.28

0.86

0.20

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4-4

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10.6

723

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4-6

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831

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EJS

4-7

0.65

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page

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B.4

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prev

ious

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HM

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year

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CJS

1-4

0.18

8.98

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51.

7516

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CJS

1-5

0.29

9.78

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CJS

1-6

0.82

7.28

42.9

81.

9613

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0.65

0.95

0.20

0.85

0.19

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0.04

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CJS

2-4

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CJS

2-5

0.63

9.82

36.3

53.

1318

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0.85

1.24

0.30

1.16

0.26

0.08

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11.6

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CJS

2-6

0.21

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31.6

01.

8716

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0.22

1.04

0.22

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CJS

2-7

1.01

6.68

46.1

11.

8612

.41

0.59

0.87

0.19

0.78

0.17

0.05

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8.04

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CJS

3-4

0.03

9.75

23.7

81.

4717

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0.99

1.45

0.20

1.11

0.23

0.07

0.06

12.6

70.

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CJS

3-5

0.23

8.45

33.2

61.

6915

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0.81

1.18

0.20

0.98

0.21

0.06

0.05

10.5

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CJS

3-6

1.82

6.36

51.6

72.

1611

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0.54

0.79

0.20

0.75

0.17

0.05

0.03

7.45

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CJS

4-4

0.03

8.86

23.8

61.

0615

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0.95

1.38

0.16

1.00

0.21

0.06

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11.8

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CJS

4-5

0.32

6.68

38.7

41.

2412

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0.65

0.94

0.15

0.77

0.16

0.05

0.04

8.45

0.00

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tinue

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245Ta

ble

B.4

–co

ntin

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from

prev

ious

page

Sim

ulat

ion

HM

gO

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wt%

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EJS

1-4

0.01

9.21

21.4

71.

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1.46

0.16

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0.21

0.06

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EJS

1-5

0.01

8.53

26.0

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0.90

1.31

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0.20

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0.05

11.3

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EJS

1-6

0.34

9.52

34.3

72.

4917

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0.85

1.24

0.26

1.12

0.24

0.07

0.05

11.5

10.

000.

00

EJS

2-4

0.01

9.21

20.0

00.

9716

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1.02

1.49

0.15

1.03

0.21

0.06

0.06

12.5

90.

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EJS

2-5

0.02

9.69

22.3

91.

3717

.45

1.01

1.47

0.19

1.10

0.23

0.07

0.06

12.7

60.

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00

EJS

2-6

0.18

9.91

30.0

22.

3018

.26

0.92

1.34

0.25

1.15

0.25

0.07

0.05

12.2

20.

000.

00

EJS

2-7

5.51

6.84

60.5

33.

6413

.04

0.52

0.76

0.28

0.83

0.19

0.06

0.03

7.55

0.00

0.00

EJS

3-4

0.02

9.80

22.3

51.

4217

.67

1.02

1.48

0.19

1.11

0.23

0.07

0.06

12.8

60.

000.

00

EJS

3-5

0.13

11.5

229

.60

3.59

21.5

01.

001.

450.

351.

360.

300.

090.

0613

.65

0.00

0.00

EJS

3-6

0.32

8.19

35.1

01.

7515

.05

0.78

1.13

0.20

0.95

0.20

0.06

0.04

10.2

10.

000.

00

EJS

3-7

4.60

7.15

57.4

73.

5913

.61

0.56

0.81

0.28

0.86

0.20

0.06

0.03

7.97

0.00

0.00

EJS

4-4

0.01

10.0

121

.95

1.45

18.0

81.

031.

500.

201.

140.

240.

070.

0613

.10

0.00

0.00

EJS

4-5

0.03

10.4

224

.33

1.99

19.0

01.

021.

480.

241.

200.

260.

080.

0613

.21

0.00

0.00

EJS

4-6

0.44

10.9

133

.80

3.79

20.4

70.

931.

350.

351.

290.

290.

090.

0512

.78

0.00

0.00

EJS

4-7

0.82

8.57

40.9

82.

6315

.99

0.74

1.08

0.26

1.01

0.22

0.07

0.04

10.1

70.

000.

00

246

APPENDIX C

MIDPLANE TEMPERATURE AND PRESSURE PROFILES

In Chapter 4, midplane temperature and pressure profiles were used to obtain the radial

compositional variation within each of the systems studied. The profiles were obtained

from the Hersant et al. (2001) model and were scaled with host star (and thus also disk)

mass. The scaling was achieved by altering the mass accretion rate (M ) of the host star

by the following relationship:

M ∝ M3/2disk ∝ M

3/2star (C.1)

Appendix C displays the radial pressure and temperature profiles obtained for each

of the planetary systems examined. Midplane conditions are shown for seven differ-

ent evolutionary stages of disk evolution (t = 2.5×105yr, 5×105yr, 1×106yr, 1.5×106yr,

2×106yr, 2.5×106yr and 3×106yr) in Figures C.1 - C.9. All profiles were obtained from

the Hersant et al. (2001) models for the “nominal” conditions (M = 5×10−6M⊙yr−1,

Rinital = 17 AU and α = 0.009). Profiles are shown in order of increasing HD number.

247

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

55Cnc

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

Figure C.1: Midplane temperature and pressure profile for 55Cnc for all seven sets of diskconditions simulated. Profiles were obtained from the “nominal” model of Hersant et al.(2001).

248

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

Gl777

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

Figure C.2: Midplane temperature and pressure profile for Gl777 for all seven sets of diskconditions simulated. Profiles were obtained from the “nominal” model of Hersant et al.(2001).

249

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

HD4203

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

Figure C.3: Midplane temperature and pressure profile for HD4203 for all seven sets ofdisk conditions simulated. Profiles were obtained from the “nominal” model of Hersantet al. (2001).

250

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

HD4208

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr


251

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

HD19994

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr


252

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

HD72659

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr


253

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

HD108874

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr


254

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

HD177830

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr


255

Radius (AU)

0 1 2 3 4 5

T (

K)

0

500

1000

1500

2000

2500

3000

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr

HD142415

Radius (AU)

0 1 2 3 4 5

P (

atm

)

1e-8

1e-7

1e-6

1e-5

1e-4

1e-3

1e-2

1e-1

0.25 Myr

0.5 Myr

1 Myr

1.5 Myr

2 Myr

2.5 Myr

3 Myr


256

APPENDIX D

HSC CHEMISTRY GAS ABUNDANCES

The equilibrium calculations of HSC Chemistry determine the equilibrium composition

of both solid and gaseous species present within the disk. The solid species compositions

obtained for each system were previously shown in Figures 4.12 - 4.20. Appendix D

contains the same plots for the gaseous species only.

Figures D.1 - D.9 show the equilibrium gaseous composition for each of the nine ex-

trasolar planetary systems studied in order of increasing C/O value. The abundances are

normalized to the least abundant species present and were obtained from the input molar

abundances listed in Table 4.6. Values are shown for a pressure of 10−4 bar. Although

pressure was varied in the simulations of Chapter 4 from 10−2 bar to 10−9 bar in accor-

dance with the midplane models of Hersant et al. (2001), these variations do not alter the

general structure and composition shown in the following figures.

257

HD72659

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

T vs Al(g)

T vs Al2O(g)

T vs AlH(g)

T vs Ca(g)

T vs CH4(g)

T vs CN(g)

T vs CO(g)

T vs CO2(g)

T vs Cr(g)

T vs CS(g)

T vs Fe(g)

T vs H(g)

T vs H2(g)

T vs H2O(g)

T vs H2S(g)

T vs HCN(g)

T vs He(g)

T vs HS(g)

T vs Mg(g)

T vs N2(g)

T vs Na(g)

T vs NaOH(g)

T vs NH3(g)

T vs Ni(g)

T vs O(g)

T vs P(g)

T vs PH(g)

T vs PN(g)

T vs PO(g)

T vs PS(g)

T vs S(g)

T vs S2(g)

T vs Si(g)

T vs SiH(g)

T vs SiO(g)

T vs SiS(g)

T vs SO(g)

T vs SO2(g)

T vs Ti(g)

T vs TiO(g)

T vs TiO2(g)

Figure D.1: Schematic of the output obtained from HSC Chemistry for HD72659 at apressure of 10−4 bar. Only gaseous species present within the system are shown. Allabundances are normalized to the least abundant species present. Input elemental abun-dances are shown in Table 4.6.

258

HD177830

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

T vs Al(g)

T vs Al2O(g)

T vs AlH(g)

T vs Ca(g)

T vs CH4(g)

T vs CN(g)

T vs CO(g)

T vs CO2(g)

T vs Cr(g)

T vs CS(g)

T vs Fe(g)

T vs H(g)

T vs H2(g)

T vs H2O(g)

T vs H2S(g)

T vs HCN(g)

T vs He(g)

T vs HS(g)

T vs Mg(g)

T vs N2(g)

T vs Na(g)

T vs NaOH(g)

T vs NH3(g)

T vs Ni(g)

T vs O(g)

T vs P(g)

T vs PH(g)

T vs PN(g)

T vs PO(g)

T vs PS(g)

T vs S(g)

T vs S2(g)

T vs Si(g)

T vs SiH(g)

T vs SiO(g)

T vs SiS(g)

T vs SO(g)

T vs SO2(g)

T vs Ti(g)

T vs TiO(g)

T vs TiO2(g)


259

Gl 777

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

Al(g)

Al2O(g)

AlH(g)

Ca(g)

CH4(g)

CN(g)

CO(g)

CO2(g)

Cr(g)

CS(g)

Fe(g)

H(g)

H2(g)

H2O(g)

H2S(g)

HCN(g)

He(g)

HS(g)

Mg(g)

N2(g)

Na(g)

NaOH(g)

NH3(g)

Ni(g)

O(g)

P(g)

PH(g)

PN(g)

PO(g)

PS(g)

S(g)

S2(g)

Si(g)

SiH(g)

SiO(g)

SiS(g)

SO(g)

SO2(g)

Ti(g)

TiO(g)

TiO2(g)

Figure D.3: Schematic of the output obtained from HSC Chemistry for Gl777 at a pres-sure of 10−4 bar. Only gaseous species present within the system are shown. All abun-dances are normalized to the least abundant species present. Input elemental abundancesare shown in Table 4.6.

260

HD4208

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

T vs Al(g)

T vs Al2O(g)

T vs AlH(g)

T vs Ca(g)

T vs CH4(g)

T vs CN(g)

T vs CO(g)

T vs CO2(g)

T vs Cr(g)

T vs CS(g)

T vs Fe(g)

T vs H(g)

T vs H2(g)

T vs H2O(g)

T vs H2S(g)

T vs HCN(g)

T vs He(g)

T vs HS(g)

T vs Mg(g)

T vs N2(g)

T vs Na(g)

T vs NaOH(g)

T vs NH3(g)

T vs Ni(g)

T vs O(g)

T vs P(g)

T vs PH(g)

T vs PN(g)

T vs PO(g)

T vs PS(g)

T vs S(g)

T vs S2(g)

T vs Si(g)

T vs SiH(g)

T vs SiO(g)

T vs SiS(g)

T vs SO(g)

T vs SO2(g)

T vs Ti(g)

T vs TiO(g)

T vs TiO2(g)


261

55Cnc

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

Al(g)

Al2O(g)

AlH(g)

Ca(g)

CH4(g)

CN(g)

CO(g)

CO2(g)

Cr(g)

CS(g)

Fe(g)

H(g)

H2(g)

H2O(g)

H2S(g)

HCN(g)

He(g)

HS(g)

Mg(g)

N2(g)

Na(g)

NaOH(g)

NH3(g)

Ni(g)

O(g)

P(g)

PH(g)

PN(g)

PO(g)

PS(g)

S(g)

S2(g)

Si(g)

SiH(g)

SiO(g)

SiS(g)

SO(g)

SO2(g)

Ti(g)

TiO(g)

TiO2(g)

Figure D.5: Schematic of the output obtained from HSC Chemistry for 55Cnc at a pres-sure of 10−4 bar. Only gaseous species present within the system are shown. All abun-dances are normalized to the least abundant species present. Input elemental abundancesare shown in Table 4.6.

262

HD142415

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

Al(g)

Al2O(g)

AlH(g)

Ca(g)

CH4(g)

CN(g)

CO(g)

CO2(g)

Cr(g)

CS(g)

Fe(g)

H(g)

H2(g)

H2O(g)

H2S(g)

HCN(g)

He(g)

HS(g)

Mg(g)

N2(g)

Na(g)

NaOH(g)

NH3(g)

Ni(g)

O(g)

P(g)

PH(g)

PN(g)

PO(g)

PS(g)

S(g)

S2(g)

Si(g)

SiH(g)

SiO(g)

SiS(g)

SO(g)

SO2(g)

Ti(g)

TiO(g)

TiO2(g)


263

HD19994

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

Al(g)

Al2O(g)

AlH(g)

Ca(g)

CH4(g)

CN(g)

CO(g)

CO2(g)

Cr(g)

CS(g)

Fe(g)

H(g)

H2(g)

H2O(g)

H2S(g)

HCN(g)

He(g)

HS(g)

Mg(g)

N2(g)

Na(g)

NaOH(g)

NH3(g)

Ni(g)

O(g)

P(g)

PH(g)

PN(g)

PO(g)

PS(g)

S(g)

S2(g)

Si(g)

SiH(g)

SiO(g)

SiS(g)

SO(g)

SO2(g)

Ti(g)

TiO(g)

TiO2(g)


264

HD108874

T (K)

200 400 600 800 1000 1200 1400 1600 1800

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

Al(g)

Al2O(g)

AlH(g)

Ca(g)

CH4(g)

CN(g)

CO(g)

CO2(g)

Cr(g)

CS(g)

Fe(g)

H(g)

H2(g)

H2O(g)

H2S(g)

HCN(g)

He(g)

HS(g)

Mg(g)

N2(g)

Na(g)

NaOH(g)

NH3(g)

Ni(g)

O(g)

P(g)

PH(g)

PN(g)

PO(g)

PS(g)

S(g)

S2(g)

Si(g)

SiH(g)

SiO(g)

SiS(g)

SO(g)

SO2(g)

Ti(g)

TiO(g)

TiO2(g)


265

HD4203

T (K)

200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Norm

aliz

ed

Ab

un

da

nce

(m

ole

)

1

10

100

1000

10000

Al(g)

Al2O(g)

AlH(g)

Ca(g)

CH4(g)

CN(g)

CO(g)

CO2(g)

Cr(g)

CS(g)

Fe(g)

H(g)

H2(g)

H2O(g)

H2S(g)

HCN(g)

He(g)

HS(g)

Mg(g)

N2(g)

Na(g)

NaOH(g)

NH3(g)

Ni(g)

O(g)

P(g)

PH(g)

PN(g)

PO(g)

PS(g)

S(g)

S2(g)

Si(g)

SiH(g)

SiO(g)

SiS(g)

SO(g)

SO2(g)

Ti(g)

TiO(g)

TiO2(g)


266

APPENDIX E

EXTRASOLAR TERRESTRIAL PLANET ABUDNANCES

In Chapter 4, predicted bulk elemental abundances were determined for the terrestrial

planets simulated to form in nine different extrasolar planetary systems. Abundances

were determined for midplane conditions from the models of Hersant et al. (2001) at

seven different disk evolutionary times (t = 2.5×105yr, 5×105yr, 1×106yr, 1.5×106yr,

2×106yr, 2.5×106yr and 3×106yr). Appendix E contains the graphical and numerical

results of these simulations. Planetary systems are presented in order of increasing C/O

value.

Figures E.1 - E.32 provide a schematic depiction of the bulk planetary compositions

(in wt%). The composition of planets produced in each of the four simulations completed

for each system are shown for each set of disk conditions examined.

Tables E.1 through E.9 list the bulk elemental abundances for the simulated terrestrial

planets produced in each system. Abundances are listed as wt% of the final predicted

planet for all seven sets of disk conditions examined.

267

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0

Sim. 1

Sim. 2

Sim. 3

Sim. 4


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other

Figure E.1: Schematic of the bulk elemental planetary composition for Gl777. All valuesare wt% of the final simulated planet. Values are shown for the terrestrial planets producedin each of the four simulations run for the system. Size of bodies is not to scale. Top Panel:Compositions based on disk conditions at t = 2.5×105 years. Bottom Panel: Compositionsbased on disk conditions at t = 5×105 years.

268

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0

Sim. 1

Sim. 2

Sim. 3

Sim. 4

Figure E.2: Schematic of the bulk elemental planetary composition for Gl777. All valuesare wt% of the final simulated planet. Values are shown for the terrestrial planets producedin each of the four simulations run for the system. Size of bodies is not to scale. Top Panel:Compositions based on disk conditions at t = 1×106 years. Bottom Panel: Compositionsbased on disk conditions at t = 1.5×106 years.

269

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0

Sim. 1

Sim. 2

Sim. 3

Sim. 4

Figure E.3: Schematic of the bulk elemental planetary composition for Gl777. All valuesare wt% of the final simulated planet. Values are shown for the terrestrial planets producedin each of the four simulations run for the system. Size of bodies is not to scale. Top Panel:Compositions based on disk conditions at t = 2×106 years. Bottom Panel: Compositionsbased on disk conditions at t = 2.5×106 years.

270

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0

Sim. 1

Sim. 2

Sim. 3

Sim. 4

Figure E.4: Schematic of the bulk elemental planetary composition for Gl777. All valuesare wt% of the final simulated planet. Values are shown for the terrestrial planets pro-duced in each of the four simulations run for the system. Size of bodies is not to scale.Compositions based on disk conditions at t = 3×106 years.

271


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other

Figure E.5: Schematic of the bulk elemental planetary composition for HD4208. Allvalues are wt% of the final simulated planet. Values are shown for the terrestrial planetsproduced in each of the four simulations run for the system. Size of bodies is not to scale.Top Panel: Compositions based on disk conditions at t = 2.5×105 years. Bottom Panel:Compositions based on disk conditions at t = 5×105 years.

272

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

Figure E.6: Schematic of the bulk elemental planetary composition for HD4208. Allvalues are wt% of the final simulated planet. Values are shown for the terrestrial planetsproduced in each of the four simulations run for the system. Size of bodies is not to scale.Top Panel: Compositions based on disk conditions at t = 1×106 years. Bottom Panel:Compositions based on disk conditions at t = 1.5×106 years.

273

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Sim. 1

Sim. 2

Sim. 3

Sim. 4


274

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

Figure E.8: Schematic of the bulk elemental planetary composition for HD4208. Allvalues are wt% of the final simulated planet. Values are shown for the terrestrial planetsproduced in each of the four simulations run for the system. Size of bodies is not to scale.Compositions based on disk conditions at t = 3×106 years.

275

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sim. 1

Sim. 2

Sim. 3

Sim. 4


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


276

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sim. 1

Sim. 2

Sim. 3

Sim. 4


277

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sim. 1

Sim. 2

Sim. 3

Sim. 4


278

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Sim. 1

Sim. 2

Sim. 3

Sim. 4


279


Semimajor Axis (AU)

0.0 0.2 0.4 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


280


Semimajor Axis (AU)

0.0 0.2 0.4 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


281


Semimajor Axis (AU)

0.0 0.2 0.4 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.2 0.4 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


282


Semimajor Axis (AU)

0.0 0.2 0.4 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


283

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0 1 2 3 4

Sim. 1

Sim. 2

Sim. 3

Sim. 4


Semimajor Axis (AU)

0 1 2 3 4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other

Figure E.17: Schematic of the bulk elemental planetary composition for HD55Cnc. Allvalues are wt% of the final simulated planet. Values are shown for the terrestrial planetsproduced in each of the four simulations run for the system. Size of bodies is not to scale.Top Panel: Compositions based on disk conditions at t = 2.5×105 years. Bottom Panel:Compositions based on disk conditions at t = 5×105 years.

284

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0 1 2 3 4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0 1 2 3 4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

Figure E.18: Schematic of the bulk elemental planetary composition for HD55Cnc. Allvalues are wt% of the final simulated planet. Values are shown for the terrestrial planetsproduced in each of the four simulations run for the system. Size of bodies is not to scale.Top Panel: Compositions based on disk conditions at t = 1×106 years. Bottom Panel:Compositions based on disk conditions at t = 1.5×106 years.

285

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0 1 2 3 4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0 1 2 3 4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

Figure E.19: Schematic of the bulk elemental planetary composition for HD55Cnc. Allvalues are wt% of the final simulated planet. Values are shown for the terrestrial planetsproduced in each of the four simulations run for the system. Size of bodies is not to scale.Top Panel: Compositions based on disk conditions at t = 2×106 years. Bottom Panel:Compositions based on disk conditions at t = 2.5×106 years.

286

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0 1 2 3 4

Sim. 1

Sim. 2

Sim. 3

Sim. 4

Figure E.20: Schematic of the bulk elemental planetary composition for HD55Cnc. Allvalues are wt% of the final simulated planet. Values are shown for the terrestrial planetsproduced in each of the four simulations run for the system. Size of bodies is not to scale.Compositions based on disk conditions at t = 3×106 years.

287


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

M g

S i

C

S

A l

C a

T i

O ther


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

M g

S i

C

S

A l

C a

T i

O ther


288

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4


289

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4


290

O

Fe

Mg

Si

C

S

Al

Ca

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4


291

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


292


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


293


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


294


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


295

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5

Sim. 1

Sim. 2

Sim. 3

Sim. 4


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


296

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5

Sim. 1

Sim. 2

Sim. 3

Sim. 4


297

O

Fe

Mg

Si

C

S

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5

Sim. 1

Sim. 2

Sim. 3

Sim. 4

O

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Si

C

S

Other


Semimajor Axis (AU)

0.0 0.1 0.2 0.3 0.4 0.5

Sim. 1

Sim. 2

Sim. 3

Sim. 4


298

O

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Mg

Si

C

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Sim. 1

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308Ta

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next

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309Ta

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prev

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page

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ulat

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310Ta

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page

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next

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311Ta

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next

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312Ta

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314Ta

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315Ta

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316Ta

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317Ta

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318Ta

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319Ta

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19.2

71.

070.

560.

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170.

220.

120.

0510

.18

0.00

0.00

3-4

1.40

15.9

842

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3.75

21.6

51.

200.

630.

101.

310.

240.

130.

0611

.43

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3-5

3.31

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851

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17.4

50.

970.

510.

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200.

110.

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00

4-4

1.59

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042

.88

3.67

21.1

91.

170.

620.

231.

280.

240.

130.

0511

.15

0.00

0.00

Con

tinue

don

next

page

330Ta

ble

E.5

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

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wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

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t=3×

106

year

s

1-4

2.74

13.8

248

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3.24

18.7

11.

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210.

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00

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12.9

351

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00.

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510.

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200.

110.

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00

3-4

2.64

13.9

848

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18.9

21.

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210.

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00

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3.31

12.8

851

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3.02

17.4

50.

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059.

210.

000.

00

4-4

1.65

15.5

443

.26

3.65

21.0

81.

170.

620.

231.

280.

240.

130.

0511

.11

0.00

0.00

331Ta

ble

E.6

:Pre

dict

edbu

lkel

emen

talp

lane

tary

abun

danc

esfo

rHD

1424

15.A

llva

lues

are

inw

t%.

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=2.

5×10

5ye

ars

1-3

0.00

0.00

45.9

00.

000.

0040

.18

8.69

0.00

0.00

0.00

0.00

2.44

2.79

0.00

0.00

2-3

0.00

0.00

48.2

00.

000.

0049

.18

0.00

0.00

0.00

0.00

0.00

2.62

0.00

0.00

0.00

3-3

0.00

0.00

47.7

80.

000.

0048

.08

1.12

0.00

0.00

0.00

0.00

3.02

0.00

0.00

0.00

4-3

0.00

0.00

48.2

00.

000.

0049

.21

0.00

0.00

0.00

0.00

0.00

2.59

0.00

0.00

0.00

5-3

0.00

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48.2

00.

000.

0049

.18

0.00

0.00

0.00

0.00

0.00

2.62

0.00

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0.00

6-3

0.00

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48.2

00.

000.

0049

.20

0.00

0.00

0.00

0.00

0.00

2.60

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7-3

0.00

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00.

000.

0049

.18

0.00

0.00

0.00

0.00

0.00

2.62

0.00

0.00

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8-3

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48.2

00.

000.

0049

.19

0.00

0.00

0.00

0.00

0.00

2.60

0.00

0.00

0.00

Con

tinue

don

next

page

332Ta

ble

E.6

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

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Cr

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wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=5×

105

year

s

1-3

0.00

0.66

23.4

50.

0028

.92

8.28

16.1

30.

002.

290.

140.

1714

.70

3.32

1.94

0.00

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0.00

0.00

25.0

90.

000.

000.

0020

.95

0.00

0.00

0.00

0.00

47.4

20.

006.

540.

00

3-3

0.00

0.00

36.4

50.

000.

0016

.25

22.8

00.

000.

000.

000.

0017

.15

5.22

2.12

0.00

4-3

0.00

0.00

41.9

40.

000.

0024

.50

23.8

00.

000.

000.

000.

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017.

750.

000.

00

5-3

0.00

0.00

25.0

90.

000.

000.

0020

.95

0.00

0.00

0.00

0.00

47.4

20.

006.

540.

00

6-3

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1.11

33.1

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.62

23.2

50.

000.

000.

000.

0024

.36

4.25

3.23

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7-3

0.00

0.00

25.0

90.

000.

000.

0020

.95

0.00

0.00

0.00

0.00

47.4

20.

006.

540.

00

8-3

0.00

0.00

42.4

60.

000.

0026

.71

21.6

80.

000.

000.

000.

002.

206.

950.

000.

00

Con

tinue

don

next

page

333Ta

ble

E.6

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

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t=1×

106

year

s

1-3

0.00

7.21

17.0

60.

4053

.18

1.98

2.34

0.00

3.18

0.67

0.22

0.14

8.59

0.03

5.00

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0.00

3.11

10.8

30.

0070

.30

2.67

3.15

0.00

4.25

0.82

0.30

0.14

4.42

0.00

0.00

3-3

0.00

4.48

11.5

90.

0065

.80

2.57

3.04

0.00

4.04

0.74

0.28

0.19

6.43

0.00

0.84

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0.00

3.25

11.9

50.

0068

.18

2.50

2.95

0.00

4.04

0.91

0.28

0.21

5.67

0.06

0.00

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0.00

3.11

10.8

30.

0070

.30

2.67

3.15

0.00

4.25

0.82

0.30

0.14

4.42

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3.37

11.1

60.

0069

.58

2.60

3.08

0.00

4.17

0.86

0.29

0.18

4.69

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3.11

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30.

0070

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2.67

3.15

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4.25

0.82

0.30

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4.42

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78.4

43.

303.

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710.

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271.

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00

Con

tinue

don

next

page

334Ta

ble

E.6

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

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Ni

Cr

PTi

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wt%

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wt%

wt%

wt%

wt%

wt%

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wt%

wt%

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t=1.

5×10

6ye

ars

1-3

0.00

13.0

426

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0.99

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61.

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300.

221.

780.

410.

120.

0914

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0.00

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8

2-3

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12.4

724

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1.08

31.1

51.

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350.

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420.

130.

0913

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11.5

4

3-3

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13.4

723

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1.10

31.7

21.

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870.

430.

130.

1014

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10.5

1

4-3

0.00

12.5

425

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11.

061.

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0914

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6

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724

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51.

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4

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12.4

125

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9

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51.

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350.

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0913

.82

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4

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12.4

724

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1.08

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51.

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350.

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0913

.82

0.00

11.5

4

Con

tinue

don

next

page

335Ta

ble

E.6

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

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Al

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wt%

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wt%

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wt%

wt%

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wt%

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t=2×

106

year

s

1-3

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13.2

526

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4

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13.3

526

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0.98

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81.

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220.

431.

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0914

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0.03

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6

3-3

0.00

13.4

626

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0.63

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91.

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391.

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0814

.33

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1

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13.5

426

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531.

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926

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3

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13.3

526

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431.

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91.

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3

Con

tinue

don

next

page

336Ta

ble

E.6

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

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Al

Ca

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PTi

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wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

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wt%

wt%

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1-3

0.00

14.0

828

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2.73

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91.

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551.

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827

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29.0

71.

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260.

551.

720.

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120.

0914

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9.68

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13.5

326

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1.08

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31.

041.

220.

531.

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0814

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14.0

328

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81.

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41.

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120.

0614

.51

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3

Con

tinue

don

next

page

337Ta

ble

E.6

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

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Al

Ca

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PTi

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wt%

wt%

wt%

wt%

wt%

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wt%

wt%

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wt%

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wt%

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106

year

s

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13.5

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225

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511.

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0813

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426

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511.

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511.

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225

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4

338Ta

ble

E.7

:Pre

dict

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tary

abun

danc

esfo

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1999

4.A

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are

inw

t%.

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ulat

ion

HM

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Ni

Cr

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wt%

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wt%

wt%

wt%

wt%

wt%

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wt%

wt%

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wt%

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1-3

0.00

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0.00

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1.03

0.00

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0.00

0.13

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0.51

69.4

20.

0028

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0.00

0.00

0.00

0.00

0.00

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0.53

69.5

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0029

.89

3-3

0.00

0.00

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1.69

0.00

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0.21

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0.50

69.3

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3-4

0.00

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0.52

69.5

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3-5

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51.3

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2433

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2

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0.00

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0.00

0.00

0.00

0.00

0.00

0.00

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0.54

69.5

70.

0029

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4-4

0.00

0.00

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1.30

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0.00

0.00

0.16

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0.00

0.50

69.3

80.

0028

.66

Con

tinue

don

next

page

339Ta

ble

E.7

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

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Al

Ca

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wt%

wt%

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wt%

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wt%

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t=5×

105

year

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27.7

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810.

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190.

3251

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18.6

5

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0.37

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0.51

32.7

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410.

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300.

230.

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2845

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3554

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20.5

9

3-4

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11.7

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19.9

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3060

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17.3

9

4-4

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2.55

4.18

0.35

36.7

10.

820.

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2435

.57

0.00

16.5

7

Con

tinue

don

next

page

340Ta

ble

E.7

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

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Ca

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Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=1×

106

year

s

1-3

0.00

7.93

14.6

80.

7238

.77

1.69

1.18

0.12

2.68

0.48

0.22

0.08

17.2

70.

0114

.17

2-3

0.00

7.65

14.5

81.

3538

.70

1.84

1.23

0.22

2.65

0.48

0.21

0.08

16.6

30.

2514

.13

3-3

0.00

7.83

15.2

61.

3537

.64

1.81

1.52

0.03

2.56

0.49

0.21

0.08

16.7

30.

1614

.34

3-4

0.00

9.03

18.1

10.

6933

.67

1.63

1.49

0.54

2.28

0.44

0.18

0.07

17.3

80.

0014

.49

3-5

0.00

11.7

125

.12

1.29

23.9

51.

161.

060.

901.

620.

320.

130.

0513

.53

0.00

19.1

5

4-3

0.00

3.25

6.32

1.35

51.8

82.

441.

020.

003.

570.

630.

290.

1118

.67

0.36

10.1

0

4-4

0.00

11.5

223

.16

0.64

27.0

01.

301.

190.

381.

830.

360.

150.

0514

.62

0.01

17.8

0

Con

tinue

don

next

page

341Ta

ble

E.7

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=1.

5×10

6ye

ars

1-3

0.00

12.0

524

.78

0.53

24.8

11.

201.

100.

621.

680.

330.

130.

0513

.84

0.01

18.8

8

2-3

0.00

11.9

625

.07

0.58

24.7

21.

151.

090.

581.

680.

330.

130.

0513

.75

0.00

18.9

0

3-3

0.00

11.9

525

.09

0.41

24.6

11.

151.

090.

611.

670.

320.

130.

0513

.79

0.01

19.1

1

3-4

0.00

11.7

624

.94

1.61

24.1

11.

171.

070.

791.

640.

320.

130.

0513

.61

0.01

18.8

0

3-5

0.00

13.2

328

.56

3.71

27.0

61.

311.

201.

021.

840.

360.

150.

0615

.28

0.00

6.24

4-3

0.00

11.8

924

.57

0.74

24.8

21.

151.

100.

251.

680.

330.

130.

0513

.66

0.01

19.6

2

4-4

0.00

11.9

225

.38

1.07

24.3

91.

181.

080.

881.

650.

320.

130.

0513

.78

0.00

18.1

6

Con

tinue

don

next

page

342Ta

ble

E.7

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=2×

106

year

s

1-3

0.00

11.9

925

.62

0.76

24.5

21.

191.

090.

881.

660.

320.

130.

0513

.85

0.00

17.9

3

2-3

0.00

11.9

425

.50

1.09

24.4

41.

181.

080.

901.

660.

320.

130.

0513

.80

0.00

17.8

9

3-3

0.00

11.9

525

.55

0.55

24.4

61.

181.

080.

911.

660.

320.

130.

0513

.81

0.00

18.3

3

3-4

0.00

12.5

426

.98

2.08

25.6

71.

241.

130.

961.

740.

340.

140.

0514

.48

0.00

12.6

5

3-5

0.00

14.0

730

.38

4.15

28.8

41.

391.

271.

081.

950.

380.

160.

0616

.26

0.00

0.00

4-3

0.00

12.0

225

.54

0.20

24.6

21.

191.

090.

901.

670.

320.

130.

0413

.90

0.00

18.3

7

4-4

0.00

12.4

926

.85

2.05

25.5

31.

231.

130.

961.

730.

340.

140.

0514

.42

0.00

13.0

7

Con

tinue

don

next

page

343Ta

ble

E.7

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=2.

5×10

6ye

ars

1-3

0.00

12.1

826

.16

1.73

24.9

11.

201.

100.

941.

690.

330.

140.

0514

.07

0.00

15.5

2

2-3

0.00

12.4

026

.66

1.87

25.3

61.

231.

120.

951.

720.

330.

140.

0514

.32

0.00

13.8

3

3-3

0.00

11.9

125

.57

1.64

24.3

71.

181.

080.

921.

650.

320.

130.

0513

.76

0.00

17.4

1

3-4

0.00

13.0

928

.20

2.88

26.7

91.

301.

181.

011.

820.

350.

150.

0615

.13

0.00

8.05

3-5

0.00

14.0

830

.40

4.15

28.8

01.

391.

271.

081.

950.

380.

160.

0616

.27

0.00

0.00

4-3

0.00

12.1

025

.93

0.50

24.7

41.

201.

090.

931.

680.

330.

130.

0513

.98

0.00

17.3

5

4-4

0.00

12.7

127

.38

3.05

26.0

11.

261.

150.

981.

760.

340.

140.

0514

.69

0.00

10.4

6

Con

tinue

don

next

page

344Ta

ble

E.7

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=3×

106

year

s

1-3

0.00

12.5

627

.03

2.75

25.7

01.

241.

140.

971.

740.

340.

140.

0514

.51

0.00

11.8

4

2-3

0.00

12.7

527

.43

2.79

26.0

81.

261.

150.

981.

770.

340.

140.

0514

.72

0.00

10.5

4

3-3

0.00

12.3

826

.66

2.81

25.3

31.

221.

120.

951.

720.

330.

140.

0514

.31

0.00

12.9

7

3-4

0.00

13.1

228

.26

3.50

26.8

31.

301.

191.

011.

820.

350.

150.

0615

.16

0.00

7.26

3-5

0.00

13.0

635

.45

3.85

26.7

21.

291.

181.

001.

810.

350.

140.

0615

.09

0.00

0.00

4-3

0.00

11.7

925

.31

1.67

24.1

11.

171.

070.

911.

640.

320.

130.

0513

.62

0.00

18.2

2

4-4

0.00

13.3

828

.86

3.72

27.3

81.

321.

211.

031.

860.

360.

150.

0615

.46

0.00

5.22

345Ta

ble

E.8

:Pre

dict

edbu

lkel

emen

talp

lane

tary

abun

danc

esfo

rHD

1088

74.A

llva

lues

are

inw

t%.

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=2.

5×10

5ye

ars

1-4

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.56

64.5

30.

0034

.91

2-4

0.00

0.00

0.00

0.00

5.11

0.00

0.00

0.00

0.00

0.00

0.00

0.52

61.1

80.

0033

.18

3-4

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.56

64.5

30.

0034

.91

4-4

0.00

0.00

0.00

0.00

1.45

0.00

0.00

0.00

0.00

0.00

0.00

0.55

63.5

90.

0034

.41

4-5

0.00

0.00

0.00

0.00

10.2

00.

000.

000.

000.

000.

000.

000.

4957

.36

0.00

31.9

6

t=5×

105

year

s

1-4

0.00

0.00

0.00

0.00

26.7

20.

000.

000.

001.

300.

060.

170.

3845

.45

0.00

25.9

1

2-4

0.00

0.00

0.00

0.00

36.4

50.

000.

000.

001.

740.

080.

280.

3238

.23

0.00

22.8

9

3-4

0.00

0.00

0.00

0.00

22.4

10.

000.

000.

000.

740.

030.

100.

4148

.85

0.00

27.4

6

4-4

0.00

0.00

0.00

0.00

18.0

30.

000.

000.

000.

680.

030.

170.

4351

.36

0.00

29.3

0

4-5

0.00

1.91

0.00

3.61

63.6

22.

121.

370.

002.

560.

480.

240.

1013

.29

1.10

9.58

Con

tinue

don

next

page

346Ta

ble

E.8

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=1×

106

year

s

1-4

0.00

5.82

6.83

2.40

52.7

32.

131.

250.

002.

260.

450.

210.

0912

.58

0.61

12.6

3

2-4

0.00

10.5

016

.25

1.43

36.8

01.

591.

050.

001.

890.

390.

180.

0812

.94

0.26

16.6

4

3-4

0.00

4.17

4.28

2.70

57.3

22.

481.

130.

002.

560.

460.

250.

1014

.69

0.78

9.09

4-4

0.00

8.21

11.8

51.

9544

.00

1.88

1.01

0.00

2.06

0.40

0.20

0.08

12.3

90.

5015

.46

4-5

0.00

14.2

223

.99

0.32

24.8

81.

170.

780.

341.

400.

300.

130.

0511

.67

0.01

20.7

3

t=1.

5×10

6ye

ars

1-4

0.00

13.2

623

.45

0.64

25.5

61.

210.

800.

131.

440.

310.

140.

0511

.93

0.01

21.0

7

2-4

0.00

13.9

024

.01

0.52

25.3

11.

190.

790.

321.

430.

300.

130.

0511

.87

0.01

20.1

6

3-4

0.00

13.7

422

.89

0.66

26.2

01.

240.

820.

081.

480.

310.

140.

0611

.43

0.01

20.9

4

4-4

0.00

13.8

323

.48

0.47

25.6

71.

210.

800.

231.

450.

310.

140.

0511

.64

0.01

20.7

2

4-5

0.00

15.4

226

.40

3.52

26.9

51.

270.

840.

461.

520.

320.

140.

0612

.62

0.00

10.4

7

Con

tinue

don

next

page

347Ta

ble

E.8

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=2×

106

year

s

1-4

0.00

14.4

224

.42

0.84

25.1

71.

190.

790.

421.

420.

300.

130.

0511

.81

0.00

19.0

3

2-4

0.00

15.1

225

.77

2.41

26.3

71.

250.

830.

451.

490.

320.

140.

0612

.38

0.00

13.4

2

3-4

0.00

14.3

324

.23

0.37

25.0

51.

180.

780.

371.

410.

300.

130.

0511

.75

0.01

20.0

1

4-4

0.00

14.6

124

.82

1.61

25.5

11.

210.

800.

411.

440.

310.

140.

0511

.97

0.00

17.1

3

4-5

0.00

14.4

524

.83

5.21

25.2

01.

190.

790.

431.

420.

300.

130.

0611

.83

0.00

14.1

6

t=2.

5×10

6ye

ars

1-4

0.00

15.3

726

.30

2.62

26.8

01.

270.

840.

461.

510.

320.

140.

0612

.58

0.00

11.7

2

2-4

0.00

15.1

826

.01

4.09

26.4

71.

250.

830.

461.

490.

320.

140.

0612

.43

0.00

11.2

7

3-4

0.00

14.9

025

.46

1.87

26.0

01.

230.

810.

451.

470.

310.

140.

0612

.19

0.00

15.1

3

4-4

0.00

15.4

226

.40

3.29

26.8

91.

270.

840.

461.

520.

320.

140.

0612

.62

0.00

10.7

6

4-5

0.00

16.7

528

.86

6.55

29.1

31.

380.

910.

501.

640.

350.

150.

0713

.70

0.00

0.00

Con

tinue

don

next

page

348Ta

ble

E.8

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=3×

106

year

s

1-4

0.00

15.5

126

.60

4.59

27.0

81.

280.

890.

471.

530.

320.

160.

0612

.70

0.00

8.81

2-4

0.00

15.8

527

.26

5.53

27.6

31.

300.

900.

471.

560.

330.

160.

0612

.97

0.00

5.97

3-4

0.00

16.0

127

.46

4.35

27.9

21.

320.

870.

481.

580.

330.

150.

0613

.10

0.00

6.36

4-4

0.00

15.3

526

.36

4.83

26.7

81.

260.

870.

461.

510.

320.

160.

0612

.56

0.00

9.48

4-5

0.00

16.7

328

.83

6.63

29.1

11.

380.

910.

501.

640.

350.

150.

0713

.69

0.00

0.00

349Ta

ble

E.9

:Pre

dict

edbu

lkel

emen

talp

lane

tary

abun

danc

esfo

rHD

4203

.All

valu

esar

ein

wt%

.

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

wt%

t=2.

5×10

5ye

ars

1-3

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.27

44.4

60.

0055

.27

2-3

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.27

44.4

90.

0055

.24

3-3

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.27

44.4

00.

0055

.33

4-3

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.27

44.4

90.

0055

.25

t=5×

105

year

s

1-3

0.00

0.00

0.00

0.00

4.04

0.00

0.00

0.00

0.00

0.00

0.26

0.25

42.5

20.

0052

.93

2-3

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.26

44.4

20.

0055

.31

3-3

0.00

0.00

0.00

0.00

1.45

0.00

0.00

0.00

0.00

0.00

0.19

0.26

43.7

10.

0054

.39

4-3

0.00

0.00

0.00

0.00

8.64

0.00

0.00

0.00

0.00

0.00

0.52

0.24

40.3

20.

0050

.28

Con

tinue

don

next

page

350Ta

ble

E.9

–co

ntin

ued

from

prev

ious

page

Sim

ulat

ion

HM

gO

SFe

Al

Ca

Na

Ni

Cr

PTi

SiN

C

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