DOI: 10.1126/science.1099050, 989 (2004);305 Science

et al.John D. AndersonDiscovery of Mass Anomalies on Ganymede

This copy is for your personal, non-commercial use only.

clicking here.colleagues, clients, or customers by , you can order high-quality copies for yourIf you wish to distribute this article to others

  here.following the guidelines

can be obtained byPermission to republish or repurpose articles or portions of articles

  ): October 18, 2014 www.sciencemag.org (this information is current as of

The following resources related to this article are available online at

http://www.sciencemag.org/content/305/5686/989.full.htmlversion of this article at:

including high-resolution figures, can be found in the onlineUpdated information and services,

http://www.sciencemag.org/content/305/5686/989.full.html#ref-list-1, 1 of which can be accessed free:cites 3 articlesThis article

7 article(s) on the ISI Web of Sciencecited by This article has been

registered trademark of AAAS. is aScience2004 by the American Association for the Advancement of Science; all rights reserved. The title

CopyrightAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by theScience

on

Oct

ober

18,

201

4w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

o

n O

ctob

er 1

8, 2

014

ww

w.s

cien

cem

ag.o

rgD

ownl

oade

d fr

om

on

Oct

ober

18,

201

4w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

o

n O

ctob

er 1

8, 2

014

ww

w.s

cien

cem

ag.o

rgD

ownl

oade

d fr

om

sample become smaller than a few tens ofmicrometers, the basic processes of plasticdeformation are affected; thus, it may not bepossible to define the strength of a givenmaterial in the absence of physical conditionsthat are completely specified. The resultsshow that such influences occur at muchlarger dimensions than are classically under-stood for metal whisker-like behavior (6).Emerging strain-gradient–based continuumtheories of deformation (that is, models thatincorporate a physical length scale into theconstitutive relations for the mechanical re-sponse of materials) must carefully accountfor these fundamental changes of deforma-tion mechanisms that extend beyond thegradient-induced storage of defects.

References and Notes1. E. O. Hall, Proc. Phys. Soc. London B 64, 747 (1951).2. N. J. Petch, J. Iron Steel Inst. 174, 25 (1953).3. S. Yip, Nature 391, 532 (1998).4. S. S. Brenner, J. Appl. Phys. 27, 1484 (1956).5. S. S. Brenner, J. Appl. Phys. 28, 1023 (1957).6. S. S. Brenner, in Growth and Perfection of Crystals,

R. H. Doremus, B. W. Roberts, D. Turnbull, Eds. (Wiley,New York, 1959), pp. 157–190.

7. H. Suzuki, S. Ikeda, S. Takeuchi, J. Phys. Soc. Jpn. 11,382 (1956).

8. J. T. Fourie, Philos. Mag. 17, 735 (1968).9. S. J. Bazinski, Z. S. Bazinski, in Dislocations in Solids,

F. R. N. Nabarro, Ed. (North Holland, Amsterdam,1979), vol. 4, pp. 261–362.

10. G. Sevillano, in Materials Science and Technology,Vol. 6 Plastic Deformation and Fracture of Materials,H. Mughrabi, Ed. (VCH, Weinheim, Germany, 1993),vol. 6, pp. 19–88.

11. N. A. Fleck, G. M. Muller, M. F. Ashby, J. W. Hutchin-son, Acta Metall. Mater. 42, 475 (1994).

12. Q. Ma, D. R. Clarke, J. Mater. Res. 10, 853 (1995).13. W. D. Nix, H. Gao, J. Mech. Phys. Solids 46, 411 (1998).14. J. S. Stolken, A. G. Evans, Acta Mater. 46, 5109 (1998).15. J. F. Nye, Acta Metall. 1, 153 (1953).16. M. F. Ashby, Philos. Mag. 21, 399 (1970).17. M. D. Uchic, D. M. Dimiduk, J. N. Florando, W. D. Nix, in

Materials Research Society Symposium Proceedings, E. P.George et al., Eds. (Materials Research Society, Pittsburgh,PA, 2003), vol. 753, pp. BB1.4.1–BB1.4.6.

18. W. N. Sharpe, K. M. Jackson, K. J. Hemker, Z. Xie, J.MEMS Syst. 10, 317 (2001).

19. M. A. Haque, M. T. A. Saif, Sensors Actuators A 97-98,239 (2002).

20. H. D. Espinosa, B. C. Prorok, M. Fischer, J. Mech. Phys.Solids 51, 47 (2003).

21. H. D. Espinosa, B. C. Prorok, B. Peng, J. Mater. Res. 52,667 (2004).

22. M. Mills, N. Baluc, H. P. Karnthaler, in Materials Re-search Society Symposium Proceedings, C. T. Liu etal., Eds. (Materials Research Society, Pittsburgh, PA,1989), vol. 133, pp. 203–208.

23. P. Veyssiere, G. Saada, in Dislocations in Solids,F. R. N. Nabarro, M. S. Duesbery, Eds. (North Holland,Amsterdam, 1996), vol. 10, pp. 253–440.

24. P. B. Hirsch, Philos. Mag. A 65, 569 (1992).25. X. Shi, G. Saada, P. Veyssiere, Philos.Mag. Lett.71, 1 (1995).26. Supported by the Air Force Office of Scientific Re-

search and the Accelerated Insertion of Materialsprogram of the Defense Advanced Research ProjectsAgency (M.D.U. and D.M.D.) under the direction of C.Hartley and L. Christodoulou, respectively, and by theU.S. Department of Energy and NSF (J.N.F. andW.D.N.). The Ni superalloy single crystal and corre-sponding bulk mechanical test data were provided byT. Pollock of the University of Michigan. We grate-fully acknowledge useful discussions with T. A.Parthasarathy, K. Hemker, and R. LeSar. We alsoacknowledge H. Fraser, whose efforts enabled manyaspects of the instruments used in this work.

9 April 2004; accepted 21 July 2004

Discovery of Mass Anomalieson Ganymede

John D. Anderson,1* Gerald Schubert,2,3 Robert A. Jacobson,1

Eunice L. Lau,1 William B. Moore,2 Jennifer L. Palguta2

We present the discovery of mass anomalies on Ganymede, Jupiter’s third andlargest Galilean satellite. This discovery is surprising for such a large icy satellite.We used the radio Doppler data generated with the Galileo spacecraft duringits second encounter with Ganymede on 6 September 1996 to model the massanomalies. Two surface mass anomalies, one a positive mass at high latitudeand the other a negative mass at low latitude, can explain the data. There areno obvious geological features that can be identified with the anomalies.

Jupiter’s four Galilean satellites can be ap-proximated by fluid bodies that are distortedby rotational flattening and by a static tideraised by Jupiter. All four satellites are insynchronous rotation with their orbital peri-ods, and all four are in nearly circular orbitsin Jupiter’s equatorial plane (1). Previouslywe reported on the interior structure of thefour Galilean satellites as inferred from theirmean densities and second-degree (quadru-pole) gravity moments (2). The inner threesatellites, Io, Europa, and Ganymede, havedifferentiated into an inner metallic core andan outer rocky mantle. In addition, Europaand Ganymede have deep icy shells on top oftheir rocky mantles. The outermost satellite,Callisto, is an exception. It has no metalliccore, and rock (plus metal) and ice are mixedthroughout most if not all of its deep interior.

These interior models are consistent withthe satellites’ external gravitational fields, asinferred from radio Doppler data from closespacecraft flybys, with one exception. It isimpossible to obtain a satisfactory fit to theDoppler data from the second Ganymedeflyby (G2) without including all gravity mo-ments to the fourth degree and order in thefitting model. The required truncated spheri-cal harmonic expansion for Ganymede’sgravitational potential function V takes theform (3)

V�r,�,�� �

GM

r �1��n�2

4 �m�0

n �R

r� n

�Cnm cos m� �

Snm sin m�� Pnm(sin�)� (1)

The spherical coordinates (r, �, �) are re-ferred to the center of mass, with r the radialdistance, � the latitude, and � the longitudeon the equator. Pnm is the associated Legendrepolynomial of degree n and order m, and Cnm

and Snm are the corresponding harmonic co-efficients, determined from the Doppler databy least squares analysis.

By taking the satellite’s center of massat the origin, its first degree coefficients arezero by definition, although all harmonicsof degree greater than one can be nonzero(3). The gravity parameters needed to fitthe G2 Doppler data to the noise level areGM, where M is the mass of the satelliteand G is the gravitational constant; fivesecond-degree coefficients; seven third-degree coefficients; and nine fourth-degreecoefficients, for a total of 22 gravity param-eters. With only two flybys and no globalcoverage of Ganymede’s gravitational po-tential, the truncated harmonic expansion isnot unique. Consequently, the 22 gravityparameters have little physical meaning.

The reference radius R for the potentialfunction is set equal to the best determinationof Ganymede’s physical radius from space-craft images, 2631.2 � 1.7 km (4). With thisradius, Ganymede is the largest satellite in thesolar system, larger than Saturn’s satelliteTitan and even larger than the planet Mercu-ry. Its GM value, as determined by four fly-bys (G1, G2, G7, G29), is 9887.83 � 0.03km3 s�2 (4), which yields a mean density of1941.6 � 3.8 kg m�3, consistent with adifferentiated metal-rock interior and an icyshell about 800 km deep (2). Ganymede’stotal mass is (1.48150 � 0.00022) 1023 kg,where the error is dominated by the uncer-tainty in G (5), not the uncertainty in GM.

The higher degree coefficients required tofit the Ganymede G2 data must be a reflectionof some other, and more localized, distortion ofthe gravitational field. In order to describe thismore localized field, we first obtained a best fitto Ganymede’s global field with just the param-eters GM and the five second-degree gravitycoefficients. Using this field, we calculatedDoppler residuals about the best fit. Before any

1Jet Propulsion Laboratory, California Institute ofTechnology, Pasadena, CA 91109–8099, USA. 2De-partment of Earth and Space Sciences, University ofCalifornia, Los Angeles, CA 90095–1567, USA. 3Insti-tute of Geophysics and Planetary Physics, Los Ange-les, CA 90095–1567, USA.

*To whom correspondence should be addressed; E-mail: john.d.anderson@jpl.nasa.gov

R E P O R T S

www.sciencemag.org SCIENCE VOL 305 13 AUGUST 2004 989

fitting model was applied, the structure of theDoppler data was dominated by the GM term(Fig. 1). After removal of the best-fit model forGM and the second-degree field, the residualswere dominated by the localized gravity anom-aly or anomalies (Fig. 2). These residuals werenumerically differentiated by the cubic-splinetechnique developed for lunar mascons (6),thereby yielding acceleration data along the lineof sight (Fig. 3).

Mass points were moved around on thesurface until the acceleration data were fit withan inverse square Newtonian acceleration onthe spacecraft in free fall (Gm/d2), with m themass of a mass point fixed in the body ofGanymede and d its distance from the space-craft as a function of time. This Newtonianacceleration was then projected on the line ofsight in order to produce a model for the ob-served acceleration. Nonlinear least squaresanalysis was used to find the best fit for themasses and for the locations of the mass points.

A reasonably good fit to the accelerationdata can be achieved with just two masses,although a better fit is achieved with threemasses (Table 1 and Fig. 3). This suggeststhat there are at least two distinct gravityanomalies on Ganymede. The first can berepresented by a positive mass of about 2.6 10�6 the mass of Ganymede on the surface athigh latitude near the closest approach point,and the second by a negative mass of about5.1 10�6 times the mass of Ganymede atlow latitude. The first mass is needed to fitthe positive peak in the acceleration data atclosest approach. The second mass fits thepeak after closest approach and fills in thelarge depression in the acceleration data,thereby providing a better overall fit. A third,smaller positive mass of about 8.2 10�7 themass of Ganymede improves the overall fitand produces a better fit to the accelerationdata just before closest approach (Table 1 andFig. 3). Because these results and standarderrors are obtained by formal nonlinear leastsquares analysis, the results are model depen-dent with three independent variables (mass,latitude, longitude) for each anomaly. The re-sults do not necessarily imply that the physicalanomalies are known to a similar accuracy.

The results of Table 1 indicate that thefirst two larger masses are stable againstchanges to the fitting procedure, but that theirlocations can change appreciably. This can bedemonstrated by changing the starting condi-tions for the fit from mass values near the twosolutions of Table 1 to mass values of zero.The least-squares procedure converges to thesame solutions regardless of the starting val-ues for the masses. This suggests that thesolutions represent the best global fit to thedata, at least for small masses placed on thesurface. The values of the masses are stable towithin a standard deviation, although the lo-cations can change by tens of a standard

deviation. There are no obvious geologicalstructures at the locations of the mass anom-alies on Ganymede’s surface that could beidentified as the sources of the anomalies.

There may be additional gravity anomalieson Ganymede, but they are undetectable with

only the two close flybys available. There mayalso be gravity anomalies on other Galilean sat-ellites, especially on Europa, which has a differ-entiated structure similar to that of Ganymede.The only Europa flyby suitable for anomalydetection is the one on the 12th orbital revolution

400

200

0

-200

-400

-600

-800

Do

pp

ler

velo

city

(m

s-1)

Time from Ganymede closest approach (s)

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000

Fig. 1. Radio Dopplerresiduals before the ap-plication of any fittingmodel. The time tags forthe rawDoppler data arein seconds from J2000(JD 2451545.0 UTC) asmeasured by the stationclock. The time tags forthe plot are referencedto the G2 closest ap-proach time of 6 Sep-tember 1996, 19:38:34UTC, ground receivetime. The gap in the plotbefore closest approachis a result of a failure ofthe spacecraft receiverto phase lock to the up-link radio carrier wave. Areference frequency of 2.296268568 GHz has been subtracted from the raw data, and the result has beenconverted to Doppler velocity by the unit conversion factor Hz � 0.065278 m s�1. The data are generatedby sending a radio wave to the spacecraft, which returns it to the station by means of a radio transponder(two-way Doppler). Therefore the frequency reference for the Doppler shift is a hydrogen maser at thestation, not the spacecraft’s crystal oscillator. The sample interval for the data is 10 s.

Do

pp

ler

velo

city

(m

m s

-1)

Time from Ganymede closest approach (s)3000200010000-1000-2000

-2

-1

0

1

2 Fig. 2. Doppler resid-uals of Fig. 1, afterthe application of afitting model that in-cludes Ganymede’smass (GM) and itssecond degree andorder gravity field.The remaining resid-uals are evidence ofone or more gravityanomalies near the Ga-lileo trajectory track.

Fig. 3. Acceleration datain units ofmgal (10�5ms�2) as derived from theDoppler residuals of Fig.2. The best-fit accelera-tion model for two sur-face masses is shown inred. The best-fit modelfor three surface massesis in green.

R E P O R T S

13 AUGUST 2004 VOL 305 SCIENCE www.sciencemag.org990

(E12) at an altitude of 201 km. The E12 closestapproach point is near the equator at a latitude of�8.7° and a west longitude of 225.7°. However,unlike G2 at an altitude of 264 km, Doppler datafrom E12, as well as three other more distantflybys (E4 at 692 km, E6 at 586 km, and E11 at2043 km), can be fit to the noise level withsecond-degree harmonics. The two Callisto fly-bys that yield gravity information are more dis-tant (C10 at 535 km and C21 at 1048 km). Noanomalies are required to fit data from four Ioflybys (I24 at 611 km, I25 at 300 km, I27 at 198km, and I33 at 102 km). A satisfactory fit can beachieved with a second degree and order har-monic expansion for all the satellite flybys ex-cept G2, and for that one flyby even a thirddegree and order expansion leaves systematicDoppler residuals. The G2 flyby is unique.

The surface mass-point model provides asimple approach to fitting the data. Furtheranalysis will be required to determine if othermass anomalies at different locations anddepths below the surface might also yieldacceptable fits to the Doppler residuals. Ourfitting model of point masses does not allowspecification of the horizontal dimensionsover which the density heterogeneities ex-tend, although these are likely to be hundredsof kilometers, comparable to the distancesfrom the anomalies to the spacecraft. Withadditional study of the point-mass model andincorporation of more realistic anomalyshapes (disks, spheres) into the analysis, itmay be possible to identify the physicalsources of the anomalies. If the anomalies areat the surface, or near to it, then they could besupported for a lengthy period of geologicaltime by the cold and stiff outer layers ofGanymede’s ice shell.

References and Notes1. A compilation of satellite data can be found in D. J.

Tholen, V. G. Tejfel, A. N. Cox, Allen’s AstrophysicalQuantities, A. N. Cox, Ed. (Springer-Verlag, New York,ed. 4, 2000), pp. 302–310.

2. The interior composition, structure, and dynamics ofthe four Galilean satellites have been summarized,along with a bibliography, by G. Schubert, J. D. Ander-son, T. Spohn, W. B. McKinnon, in Jupiter, F. Bagenal,

T. E. Dowling, W. B. McKinnon, Eds. (Cambridge Univ.Press, New York, 2004), chap. 13.

3. W. M. Kaula, Theory of Satellite Geodesy (Blaisdell,Waltham, MA, 1966).

4. J. D. Anderson et al., Galileo Gravity Science Team,

Bull. Am. Astron. Soc. 33, 1101 (2001). This referenceincludes the best determination of Ganymede’s radi-us currently available.

5. P. J. Mohr, B. N. Taylor, Phys. Today 55, BG6 (2002).Because of recent determinations, the adopted valueof G has fluctuated over the past few years. We usethe current (2002) value recommended by the Com-mittee on Data for Science and Technology(CODATA), G � 6.6742 10�11 m3 kg�1 s�2, witha relative standard uncertainty of 1.5 10�4.

6. P. M. Muller, W. L. Sjogren, Science 161, 680(1968).

7. We acknowledge the work of O. Olsen for finding fitsto the fourth-degree gravitational field. We thank W.L. Sjogren, A. S. Konopliv, and D.-N. Yuan for theirassistance, especially for providing us with a recom-piled version of their gravity-anomaly software Grav-ity Tools. We also thank D. Sandwell for helpfuldiscussions about the nature of Ganymede’s gravityanomalies, and S. Asmar, G. Giampieri, and D.Johnston for helpful discussions. This work was per-formed at the Jet Propulsion Laboratory, CaliforniaInstitute of Technology, under contract withNASA. G.S., W.B.M., and J.L.P. acknowledge supportby grants from NASA through the Planetary Geologyand Geophysics program.

12 April 2004; accepted 8 July 2004

Probing the AccumulationHistory of the Voluminous

Toba MagmaJorge A. Vazquez1*† and Mary R. Reid1,2

The age and compositional zonation in crystals from the Youngest Toba Tuff recordtheprelude to Earth’s largestQuaternary eruption.Weused allanite crystals to dateand decipher this zoning and found that the crystals retain a record of at least150,000 years of magma storage and evolution. The dominant subvolcanicmagma was relatively homogeneous and thermally stagnant for 110,000years. In the 35,000 years before eruption, the diversity of melts increasedsubstantially as the system grew in size before erupting 75,000 years ago.

Toba caldera, a continental arc volcano inSumatra, Indonesia, produced Earth’s largestQuaternary eruption, ejecting �3000 km3 ofmagma 73,000 � 4000 years ago (1). Atmo-spheric loading by aerosols and ash from theToba eruption may have accelerated coolingof Earth’s climate (2) and resulted in near-extinction of humans (3). How quickly thisand other huge volumes of magma can amassis unclear, especially because large volumesof eruptible magma have not been detectedbeneath areas of active and/or long-livedmagmatism (4, 5). The rate of magma accu-mulation can dictate whether reservoirs ofmagma simply cool and solidify or persist at

magmatic conditions (6, 7), and may influ-ence the probability of volcanic eruption andthe characteristics of associated plutonic in-trusions (8, 9). A detailed record of magmaticevolution is that retained by the composition-al zoning of major minerals (10, 11), and thismight reveal how magma chambers accumu-late and change (12, 13). However, currentanalytical techniques are not sufficiently sen-sitive to put the chemical zoning in majorminerals into an absolute time frame. Hence,it is impossible to relate the zoning stratigra-phy of one crystal to another or evaluate theage of magma associated with crystallization.Here we use a combination of in situ compo-sitional and isotopic analyses on single crys-tals of a less abundant mineral, the epidote-group mineral allanite, to date and quantifycompositional zoning within and betweencrystals in the Youngest Toba Tuff (YTT)and to establish how this voluminous magmaevolved before eruption.

Allanite is a common accessory mineral inrhyodacitic and rhyolitic magmas and may haveconsiderable compositional zoning in major and

1Department of Earth and Space Sciences, Univer-sity of California, Los Angeles, CA 90095–1567,USA. 2Department of Geology, Northern ArizonaUniversity, Flagstaff, AZ 86011, USA.

*To whom correspondence should be addressed. E-mail: jvazquez@ess.ucla.edu†Present address: Department of Geological Sciences,California State University, Northridge, CA 91330–8266,USA.

Table 1. Least-squares fits to the acceleration data for two masses on Ganymede’s surface and also forthree masses on the surface. The three independent variables in the fitting model for each mass are Gm,and the geographic coordinates latitude and west longitude. For reference, the closest approach locationis at latitude 79.3° and west longitude 123.7° at an altitude of 264 km. The measure of goodness of fitis given by the variance �2 for the acceleration residuals. A qualitative measure of the goodness of fit isgiven by Fig. 3.

Six-parameter fit for two masses (�2 � 0.0244 mgal2)First mass Second mass Third mass

Gm (km3 s�2) 0.0237 � 0.0056 �0.0558 � 0.0084 �Latitude (°) 58.9 � 1.5 24.2 � 5.5 �Longitude W (°) 65.2 � 1.6 61.8 � 5.4 �

Nine-parameter fit for three masses (�2 � 0.0192 mgal2)First mass Second mass Third mass

Gm (km3 s�2) 0.0256 � 0.0038 �0.0500 � 0.0058 0.0081 � 0.0021Latitude (°) 77.7 � 1.0 39.9 � 2.6 53.6 � 2.3Longitude W (°) 337.3 � 5.1 355.6 � 4.6 140.1 � 4.8

R E P O R T S

www.sciencemag.org SCIENCE VOL 305 13 AUGUST 2004 991