(received; accepted) to appear in pasp - yale exoplanetsexoplanets.astro.yale.edu/eprv.pdf · to...

1

to appear in PASPPreprint typeset using LATEX style emulateapj v. 01/23/15

STATE OF THE FIELD: EXTREME PRECISION RADIAL VELOCITIES

Debra A. Fischer2, Guillem Anglada-Escude3, 4, Pamela Arriagada5, Roman V. Baluev6,7, Jacob L.Bean8, Francois Bouchy9, Lars A. Buchhave10, Thorsten Carroll11, Abhijit Chakraborty12, Justin R.

Crepp13, Rebekah I. Dawson14,15, Scott A. Diddams16, 17, Xavier Dumusque18, Jason D. Eastman19,Michael Endl20, Pedro Figueira21, Eric B. Ford14, 15, Daniel Foreman-Mackey22, 23, Paul Fournier24,

Gabor Furesz25, B. Scott Gaudi26, Philip C. Gregory27, Frank Grundahl28, Artie P. Hatzes29,Guillaume Hebrard30, 31, Enrique Herrero32, David W. Hogg22, 33, Andrew W. Howard34, John A.Johnson19, Paul Jorden35, Colby A. Jurgenson2, David W. Latham19, Greg Laughlin36, Thomas J.

Loredo37, Christophe Lovis18, Suvrath Mahadevan14, 15, 38, Tyler M. McCracken2, Francesco Pepe18,Mario Perez39, David F. Phillips19, Peter P. Plavchan40, Lisa Prato41, Andreas Quirrenbach42,

Ansgar Reiners43, Paul Robertson14, 15, Nuno C. Santos21, 44, David Sawyer2, Damien Segransan18,Alessandro Sozzetti45, Tilo Steinmetz46, Andrew Szentgyorgyi19, Stephane Udry18, Jeff A. Valenti47,

Sharon X. Wang14, 15, Robert A. Wittenmyer48, 49, Jason T. Wright14, 15, 38

(Received; Accepted)to appear in PASP

ABSTRACT

The Second Workshop on Extreme Precision Radial Velocities defined circa 2015 the state ofthe art Doppler precision and identified the critical path challenges for reaching 10 cm s−1

measurement precision. The presentations and discussion of key issues for instrumentationand data analysis and the workshop recommendations for achieving this bold precision aresummarized here.Beginning with the HARPS spectrograph, technological advances for precision radial ve-locity measurements have focused on building extremely stable instruments. To reach stillhigher precision, future spectrometers will need to improve upon the state of the art, pro-ducing even higher fidelity spectra. This should be possible with improved environmentalcontrol, greater stability in the illumination of the spectrometer optics, better detectors,more precise wavelength calibration, and broader bandwidth spectra. Key data analysischallenges for the precision radial velocity community include distinguishing center of massKeplerian motion from photospheric velocities (time correlated noise) and the proper treat-ment of telluric contamination. Success here is coupled to the instrument design, but alsorequires the implementation of robust statistical and modeling techniques. Center of massvelocities produce Doppler shifts that affect every line identically, while photospheric veloc-ities produce line profile asymmetries with wavelength and temporal dependencies that aredifferent from Keplerian signals.Exoplanets are an important subfield of astronomy and there has been an impressive rate ofdiscovery over the past two decades. However, higher precision radial velocity measurementsare required to serve as a discovery technique for potentially habitable worlds, to confirmand characterize detections from transit missions, and to provide mass measurements forother space-based missions. The future of exoplanet science has very different trajectoriesdepending on the precision that can ultimately be achieved with Doppler measurements.Keywords: instrumentation: spectrographs - methods: observational - methods: statistical

technique : radial velocities - techniques: spectroscopic

[email protected] The content of this publication emerged from pre-

sentations and discussion by the 150 participants in theSecond Workshop on Extreme Precision Radial Velocities,held at Yale University. The talks and posters from thismeeting are archived at http://eprv.astro.yale.edu

2 Department of Astronomy, Yale University, NewHaven, CT 06511 USA

3 Centre for Astrophysics Research, Science and Tech-nology Research Institute, University of Hertfordshire,College Lane, Hatfield AL10 9AB, UK

4 School of Physics and Astronomy, Queen Mary Uni-versity of London, 327 Mile End Road, London E1 4NS,UK

5 Department of Terrestrial Magnetism, Carnegie Insti-tute of Washington, Washington, DC 20015, USA

6 Central Astronomical Observatory at Pulkovo ofRussian Academy of Sciences, Pulkovskoje shosse 65, St

Petersburg 196140, Russia7 Sobolev Astronomical Institute, St Petersburg State

University, Universitetskij prospekt 28, Petrodvorets, StPetersburg 198504, Russia

8 Department of Astronomy and Astrophysics, Univer-sity of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637,USA

9 Aix Marseille Universite, CNRS, LAM (Laboratoired’Astrophysique de Marseille) UMR 7326, 13388 Marseille,France

10 Centre for Star and Planet Formation, NaturalHistory Museum of Denmark & Niels Bohr Institute,University of Copenhagen, Øster Voldgade 5-7, DK-1350Copenhagen K, Denmark

11 Leibniz-Institut fur Astrophysik Potsdam, An derSternwarte 16, 14482 Potsdam, Germany

12 Astronomy and Astrophysics Division, PhysicalResearch Laboratory (PRL), Ahmedabad 380009, India

2 Fischer et al.

1. INTRODUCTION

The past two decades have been a golden era forthe discovery of exoplanets — thousands of exo-planets have been detected using Doppler measure-ments, transit photometry, microlensing, and directimaging. Pioneering technology has driven remark-able acceleration in the rate of detections — of spe-cial note: the clever use of an iodine reference cell

13 Department of Physics, University of Notre Dame,South Bend, IN, USA

14 Department of Astronomy and Astrophysics, ThePennsylvania State University, 525 Davey Laboratory,University Park, PA 16802, USA

15 Center for Exoplanets and Habitable Worlds, ThePennsylvania State University, University Park, PA 16802,USA

16 National Institute of Standards and Technology, 325Broadway, Boulder, CO 80305, USA

17 Department of Physics, University of Colorado, 2000Colorado Ave, Boulder, CO, 80309, USA

18 Observatoire Astronomique de l’Universite deGeneve, 51 chemin des Maillettes, CH-1290 Versoix,Switzerland

19 Harvard-Smithsonian Center for Astrophysics, Cam-bridge, MA 02138, USA

20 The University of Texas at Austin and Department ofAstronomy and McDonald Observatory, 2515 Speedway,C1400, Austin, TX 78712, USA

21 Instituto de Astrofısica e Ciencias do Espaco, Uni-versidade do Porto, CAUP, Rua das Estrelas, 4150-762Porto, Portugal

22 Center for Cosmology and Particle Physics, Depart-ment of Physics, New York University, USA

23 Astronomy Department, University of Washington,Box 951580, Seattle, WA 98195, USA

24 Fibertech Optica Inc., Canada25 MIT Kavli Institute for Astrophysics and Space

Research 77 Mass Ave 37-515, Cambridge, MA, 02139,USA

26 Department of Astronomy, Ohio State University,140 W. 18th Ave., Columbus, OH 43210, USA

27 Physics and Astronomy, University of BritishColumbia, 6244 Agricultural Rd, British Columbia,Canada V6T 1Z1

28 Stellar Astrophysics Centre, Department of Physicsand Astronomy, Aarhus University, Ny Munkegade 120,DK-8000 Aarhus C, Denmark

29 Thuringer Landessternwarte, Sternwarte 5, Tauten-burg 5, 07778 Tautenburg, Germany

30 Institut d’Astrophysique de Paris, UMR7095 CNRS,Universite Pierre & Marie Curie, 98bis boulevard Arago,F-75014 Paris, France

31 Observatoire de Haute-Provence, Universite d’Aix-Marseille & CNRS, F-04870 Saint Michel lObservatoire,France

32 Institut de Ciencies de lEspai (CSICIEEC), CampusUAB, Facultat de Ciencies, Torre C5 parell, 2a pl, 08193Bellaterra, Spain

33 Center for Data Science, New York University, USA34 Institute for Astronomy, University of Hawaii, Hon-

olulu, HI 96822, USA35 e2v Technologies, 106 Waterhouse Lane, Chelmsford,

Essex, UK36 UCO Lick Observatory, Department of Astronomy

and Astrophysics, University of California at Santa Cruz,Santa Cruz, CA 95064, USA

37 Center for Radiophysics and Space Research, SpaceSciences Building, Cornell University Ithaca, NY 14853-6801, USA

38 Penn State Astrobiology Research Center, ThePennsylvania State University, University Park, PA 16802,USA

39 NASA Headquarters, Washington D.C., USA40 Department of Physics, Astronomy and Material

Science, 901 S National Avenue, Missouri State University,Springfield, MO 65897, USA

for wavelength calibration and modeling of the in-strumental profile to achieve radial velocity (RV)precisions of a few meters per second using generalpurpose spectrometers (Butler et al. 1996; Marcy &Butler 1992); the stabilized HARPS spectrometer,which set a new standard in RV precision (Mayoret al. 2003; Pepe et al. 2002); ground-based tran-sit surveys that evolved rapidly from demonstratingthe existence of transiting extrasolar planets (Henryet al. 2000; Charbonneau et al. 2000) to achiev-ing 1-mmag photometric precision (Johnson et al.2009); and the Kepler space mission with a dra-matic improvement over the precision of ground-based photometry. The Kepler mission confirmedearlier suggestions (Mayor & Udry 2008) that mostof the stars in our galaxy have planetary systemsand that small planets are ubiquitous (Howard et al.2012; Fressin et al. 2013; Buchhave et al. 2014).However, while ever smaller and lower mass planetshave been detected in the past few years, all cur-rent techniques fall just short of detecting so-calledexo-Earths (planets that are nearly the mass of theEarth, orbiting at habitable zone distances) aroundnearby stars.

A generation of students has grown up thinkingof exoplanet science as a booming field where therate of discovery and characterization has a steepand positive trajectory. However, the key to growthin this field has been the sequential improvementsin technology and measurement precision and thisis also a fundamental requirement for the future ofthe field. If we keep making the same observationswith the same instruments, we will improve the SNRand population size, but we will basically have thesame results and the field will stagnate; advances instrategy, analysis and instrumentation are requiredto reach higher RV precision and to push into newparameter space.

New space missions including the Transiting Ex-oplanet Survey Satellite (TESS; Ricker et al. 2014),the CHaracterizing ExOPlanet Satellite (CHEOPS;Fortier et al. 2014) and PLAnetary Transits and Os-cillation of stars (PLATO; Rauer et al. 2014) willhave the precision to detect transiting planets withsmall radii and will observe bright nearby stars.

41 Lowell Observatory, 1400 West Mars Hill, Road,Flagstaff, AZ 86001, USA

42 Landessternwarte, Zentrum fur Astronomie derUniversitat Heidelberg, Konigstuhl 12, 69117 Heidelberg,Germany

43 Institut fur Astrophysik, Georg-August-Universita,Friedrich-Hund-Platz 1, 37077 Gottingen, Germany

44 Departamento de Fısica e Astronomia, Faculdade deCiencias, Universidade do Porto, Rua do Campo Alegre,4169-007 Porto, Portugal

45 INAF-Osservatorio Astrofisico di Torino, Via Osser-vatorio 20, I-10025 Pino Torinese, Italy

46 Menlo Systems GmbH, Am Klopferspitz 19a, 82152Martinsried, Germany

47 Space Telescope Science Institute, 3700 San MartinDr., Baltimore, MD 21218, USA

48 School of Physics and Australian Centre for Astro-biology, University of New South Wales, Sydney, NSW2052, Australia

49 Computational Engineering and Science ResearchCentre, University of Southern Queensland, Toowoomba,Queensland 4350, Australia

State of the Field: EPRV 3

Doppler observations will provide critical supportfor these missions and will remain a key asset inthe search for exo-Earths (Mayor et al. 2014). If wecan improve our current instrumental precision andif we can distinguish stellar photospheric velocitiesfrom Keplerian motion, then we have a chance of de-tecting, confirming and characterizing a bounty ofexoplanets in new mass and period regimes aroundnearby stars.

In July 2015, we held the Second Workshop forExtreme Precision Radial Velocities (EPRVs) atYale University with three goals: to examine thecurrent state of the Doppler precision, to discussrecent advances, and to chart a course for eliminat-ing the remaining obstacles on the road towards 10cm s−1. We discussed the future game-changers andthe current bottlenecks. This paper summarizes thepresentations and discussions from this workshop.Section ?? presents the state of the art for fourteendifferent RV surveys highlighted at the workshopand compares some of the key attributes correlatedwith high Doppler precision. In Section ??, we dis-cuss instrumentation challenges and solutions. InSection ?? we discuss the challenges to high pre-cision that are not instrumental in nature, suchas stellar atmospheric velocities and telluric linesin the Earth’s atmosphere and capture the discus-sion about statistical analysis techniques that showpromise in distinguishing stellar photospheric sig-nals from Keplerian motion.

2. STATE OF THE ART

It is important to first clarify what we mean byDoppler precision. Radial velocity measurementsare currently carried out by one of two methods:the iodine technique or the cross correlation tech-nique (Lovis & Fischer 2010). The estimated singlemeasurement precision (or averaged nightly veloc-ity precision) is a good indication of the photon-limited “on sky” precision. The long-term velocityrms (several days to years) is yet another indicator,exposing both systematic instrumental errors andthe limitations in analysis techniques for treatingvariability from the stellar photosphere (so-calledstellar jitter).

Participants at the workshop discussed theDoppler precision for current radial velocity planetsearch programs. In standardized formats, presen-ters were asked to show the dependence of singlemeasurement precision (SMP) on the signal to noiseratio (SNR) for the equivalent of a 3 km s−1 pixelbin at 550 nm and to provide the radial velocityrms of their program stars without removing trendsor Keplerian signals. This is the first side-by-sidecomparison that has ever been made for Dopplerplanet search programs and we owe a great debtof gratitude to the teams that contributed data forthis comparison50. Their generosity in sharing ac-cumulated data allows the community to considerthe possible relative importance of environmentalstability, spectral resolution, wavelength coverage,

50 Additional current or planned PRV spectrographs canbe found in Tables 2 and 3 of Plavchan et al. (2015)

calibration techniques and observing cadence. Nocomparison metric is perfect and there will still bediscrepancies that arise because of differences in thestellar samples and the scientific goals of the pro-grams.

Table 1 lists the key parameters for key Dopplersurveys. The programs are sorted by the demon-strated single measurement precision. We summa-rize some of the fundamental parameters for theprograms, including whether the coupling of lightis accomplished with a slit or fiber, whether thereis any environmental control (however, the extentof environmental control varies widely), the spectralresolution, wavelength range, method of wavelengthcalibration, single measurement precision for SNRof 200 (at 550 nm), the number of stars on the pro-gram and the time baseline of the program. Fiberfed, stable instruments with high spectral resolutionrepresent the state of the art circa 2015. Future in-struments will require even more stringent specifica-tions in order to gain another order of magnitude inRV precision. High resolution and broad bandwidthmay end up being critical parameters for fitting outperturbing signals from stellar photospheres and tel-luric contamination.

The Doppler programs listed in Table 1 are dis-cussed in more detail below in order of the date thateach planet survey began.

2.1. 3-m Lick Hamilton, 1987 - 2011

The Hamilton spectrograph (Vogt 1987) at LickObservatory51 was used to search for exoplanets be-tween 1987 and 2011 (Fischer et al. 2014; Butler& Marcy 1997). The program effectively ended in2011 when insulating material on the cell burnedand changed the iodine spectrum of the cell. TheHamilton echelle spectrograph is a general purposeinstrument that can be fed with either the 0.6-mCoude Auxiliary Telescope or the 3-m Shane tele-scope. The wavelength range can be selected to in-clude wavelengths from 390 - 900 nm in a singleobservation. The instrumental resolution dependson the selected slit width, varying from 30,000 -115,000, but the typical resolution used for Dopplerplanet hunting was R ∼ 50, 000. The instrument islocated in a coude room and experiences diurnal andseasonal temperature swings of several degrees. Onepioneering aspect of this program was the use of aniodine reference cell for the wavelength calibrationand modeling the line spread function (Butler et al.1996; Marcy & Butler 1992) to reach a measurementprecision of 3 m s−1. The use of a reference cell isideal for general-purpose instruments because theforward modeling of iodine accounts for variationsin the SLSF and instrumental drifts. The iodineabsorption lines only span a wavelength range from510 to 620 nm; this limits the Doppler analysis toabout 110 nm of the spectrum and high SNR is re-quired in order to model the multi-parameter SLSF.

The search for exoplanets at Lick Observatory be-gan with a sample of 109 stars and the program was

51 Presentation by Debra Fischer

4 Fischer et al.

Table 1Current Doppler Planet Search Programs

Spectrograph slit or Temp Spectral Wavelength Wavelength SMP [m s−1] Number Durationfiber Control Resolution range [nm] calibrator SNR = 200 of stars of program

HARPS f Y 115,000 380 – 690 ThAr 0.8 2000 2003 –HARPS-N f Y 115,000 380 – 690 ThAr 0.8 500 2012 –PARAS f Y 67,000 380 – 690 ThAr 1.0 27 2012 –CHIRON f Y 90,000 440 – 650 Iodine 1.0 35 2011 –SOPHIE f Y 75,000 387 – 694 ThAr 1.1 190 2011 –PFS s Y 76,000 390 – 670 Iodine 1.2 530 2010 –HIRES s Y 55,000 364 – 800 Iodine 1.5 4000 1996 –Levy (LCPS) s Y 110,000 376 – 970 Iodine 1.5 100 2013 –Levy (CPS) s Y 100,000 376 – 940 Iodine 2.0 300 2013 –SONG s N 90,000 440 – 690 Iodine 2.0 12 2014 –HRS s Y 60,000 408 – 784 Iodine 3.0 100 2001 – 2013Hamilton s N 50,000 390 – 800 Iodine 3.0 350 1987 - 2011UCLES s N 45,000 478 – 871 Iodine 3.0 240 1998 –Tull s N 60,000 345 – 980 Iodine 5.0 200 1998 –

allocated roughly 25 nights per year; that alloca-tion was augmented with as many as 50 additionalnights per year on the smaller Coude Auxiliary Tele-scope. The first assessment of the occurrence rateof exoplanets (Cumming et al. 1999) and the firstassessment of the impact of the impact of photo-spheric magnetic activity on radial velocity preci-sion (Saar et al. 1998) was made using data fromthe Lick planet search program. The sample sizewas increased (Fischer et al. 1999) to include an ad-ditional ∼ 300 stars, with a focus on a subset ofmetal-rich stars. Johnson et al. (2007) carried out asearch for planets orbiting subgiants. The Hamiltonspectrograph was also used to study the impact ofoptical scrambling on radial velocity measurements(Spronck et al. 2010, 2012a,b, 2013).

With the iodine modeling technique for the LickHamilton and CTIO CHIRON programs, the spec-trum is divided into many small chunks, typically2 or 3 A wide, and the wavelength solution, thespectral line spread function, and the Doppler shiftare modeled for every chunk. Each spectral chunkprovides an independent estimate of the relativeDoppler shift that is good to about 30 – 50 m s−1

and 3σ outliers are rejected. Then, a weighted un-certainty is calculated for each chunk as follows.First, the difference, di, between the velocity foreach ith chunk and the median velocity of all chunksin a given observation is calculated:

di = veli −median(vel) (1)

The uncertainty in the measurement for each chunk,σi, reflects the ability of that chunk to consistentlyreport a Doppler shift and it is determined over sev-eral observations as the standard deviation of di forn observations:

σi = stddev(di[1], ..., di[nobs]) (2)

Thus, di for a particular chunk may be large (orsmall) with many observations, but as long as it isconsistently large (or small), σi for the chunk will besmall. This allows for offsets between chunks (e.g.,that might occur because of stitching errors in the

CCD or other instrumental issues). Chunks withvalues of di that are erratic from one observation tothe next will have a large uncertainty, σi. A subtlecorollary is that the sigma for a given chunk is betterdetermined as more observations are accumulated,i.e., the uncertainty for a specific observation canchange slightly as future observations are analyzed.

The single measurement precision (SMP) at Lickwas limited by instrumental errors, rather than pho-ton statistics. The Hamilton spectrograph was nota stabilized instrument and this set the floor for theSMP of Doppler measurements to about 3 m s−1

(Butler et al. 1996) with rms velocities greater than5 m s−1. Figure 1 (left) shows the dependence ofestimated internal errors on the SNR of the observa-tions. The different families of errors (depicted withdifferent plot symbols) correspond to eras wherethe CCD detectors were changed on the Hamiltonspectrograph. In particular, the worst radial veloc-ity precision for the Lick program occurred when athinned CCD (dewar 6) was used; this device suf-fered from charge diffusion that broadened the SLSFand yielded a significantly degraded velocity preci-sion. Figure 1 (right) is a histogram of the rms ofthe velocities. No trends or Keplerian signals werefitted out and most stars have rms velocities thatwere greater than the 10 m s−1 boundary of theplot.

The Lick planet search program demonstrates theimportance of using a stable, special-purpose instru-ment. Several different detectors were used over thecourse of the 25 year program and each of thesechanges to the instrument introduced systematicoffsets in the time series radial velocity data. Im-proving the instrument stability was difficult in thelarge coude room where large seasonal temperaturewere observed. The Lick planet search program wasretired as the new Automated Planet Finder wasbeing brought online.

2.2. 10-m Keck-1 with HIRES spectrograph, 1996 –

In the early days of radial velocity planet searches,HIRES (Vogt et al. 1994) on the Keck 10-m tele-


Figure 1. Single measurement precision as a function of SNR (left) for dewar 13 (blue triangles) used from 1994 - 1997, dewar6 (green diamonds) from 1998 - 2000, and dewar 8 (red circles) from 2001 - 2011. The radial velocity rms scatter (right) isplotted for data from the Hamilton spectrograph at Lick Observatory; most stars have rms scatter greater than the 10 m s−1

cutoff (Figures provided by Debra Fischer).

scope52 was one of the instruments that made highimpact contributions to exoplanet detections. Theprogram began in 1996 and has continued opera-tions to this day. The spectrometer was designed asa slit-fed instrument and originally configured fora Doppler planet search with a wavelength rangeof 389 – 618 nm and a 0 .′′8 slit that provides amoderate resolution of about 55,000 (higher resolu-tion can be achieve by narrowing the slit with anaccompanying loss of light). In 2004, the detectorwas upgraded to a mosaic of three CCDs, provid-ing wavelength coverage of 364 – 479 nm, 498 – 642nm, and 655 – 797 nm for each detector respec-tively. The wavelength calibration is achieved withan iodine reference cell and the Doppler analysis istherefore restricted to wavelengths between 510 –620 nm. Although HIRES is not in a vacuum en-closure, the temperature is a fairly stable (1◦ ± 1◦

C) in the instrument room.The primary science goals are planet detection

and characterization for a broad range of stellarpopulations (Vogt et al. 2010a,b). A hallmark ofthe Keck program is the collaborative integrationof projects from several principal investigators, us-ing a time-sharing scheme that pools 40 – 60 nightsper year. This strategy improves the observing ca-dence for several programs, including the CaliforniaPlanet Search (CPS; Howard et al. 2010), the N2K(“next 2000”) search for gas giant planets aroundmetal rich stars (Fischer et al. 2005), a search forplanets orbiting subgiants (Johnson et al. 2007) andthe “Eta-Earth” program to systematically searchfor low mass planets (3 − −30M⊕) orbiting in

52 Presentation by Andrew Howard

the habitable zone of the nearest 230 GKM stars(Howard et al. 2009). Keck HIRES programs alsofollow up transiting planets (e.g., Kepler , K2, HAT-NET) to determine masses (Marcy et al. 2014b;Weiss & Marcy 2014; Marcy et al. 2014a) and tomeasure the Rossiter-McLaughlin effect (Sanchis-Ojeda et al. 2015; Winn et al. 2011b,a, 2010). Keckdata have been used to derive planet occurrencerates (Cumming et al. 2008; Howard et al. 2012)and spectra have been used for characterization ofhost star metallicity and activity (Fischer & Valenti2005; Valenti & Fischer 2005; Isaacson & Fischer2010). Collectively, more than 4000 stars have beenobserved and analyzed from Keck-HIRES.

Before the HIRES detector upgrade, a numberof detector-related noise sources produced flux de-pendent errors. After correcting for this effect, theSMP was 3 m s−1. When the detector was up-graded in August 2004, the SMP improved to about1.5 m s−1 for a SNR of 200 and reached a floor ofabout 1 m s−1 for SNRs approaching 500. The ra-dial velocity rms is typically greater than 2 m s−1

because of instrumental errors, limitations of theiodine technique (Isaacson & Fischer 2010; Sproncket al. 2015), and the impact of stellar photosphericvelocities, or stellar “jitter.” Figure 2 (left) showsthe dependence of estimated internal errors for CPSobservations as a function of the SNR of the obser-vations. Figure 2 (right) is a histogram of the rmsof the velocities (without attempting to remove anytrends or Keplerian signals).

Although the iodine technique enables the useof general purpose instruments for precise Dopplermeasurements, this method requires high SNR(about 200 per pixel) for the forward modeling pro-

6 Fischer et al.

0 2 4 6 8 10RMS of RVs (m/s)

0

20

40

60

80

Num

ber o

f Sta

rs

Figure 2. Radial velocity precision (left) and rms velocity scatter for Doppler measurements by the California Planet Searchteam using the HIRES at Keck. (Courtesy of Andrew Howard)

cess. The variable SLSF contributes to increasedscatter in the radial velocity measurements and lim-its the ability to take advantage of the exceptionalsignal to noise that is possible with a 10-m tele-scope. The CPS team is now designing SHREK, anew stabilized instrument for the Keck II telescope.

2.3. 2.7 McDonald and Tull Coude spectrograph,1998 –

The Tull spectrograph (Tull et al. 1995) has beenused at the 2.7-m Harlan J. Smith telescope at Mc-Donald Observatory53 for exoplanet searches since1998 and more than 10,000 RV measurements havebeen made over the past 15 years. The observingtime is scheduled roughly once per month. Thespectral resolution is 60,000 and the wavelengthrange is 345 – 1000 nm. The spectrometer is notenvironmentally stabilized and it is slit-fed; wave-length calibration is carried out with an iodine ref-erence cell, restricting Doppler analysis to the wave-length range of 510 – 620 nm.

As shown in Figure 3 there are about 200 stars onthe exoplanet survey with the Tull spectrograph; 82of these stars have an extensive baseline of observa-tions. The primary science goal of this program isthe detection of Jupiter analogs at 4 – 5 AU.

The internal errors represent the formal uncer-tainty of the weighted mean of the individual RVsthat are modeled for small spectral chunks. Thesechunks are typically 2 – 3 A wide and the internal er-ror depends on the overall width of the distributionof the accepted chunks (extreme deviating chunkRVs are rejected) and their total number. A de-tailed description can be found in (Endl et al. 2000).The mean SMP errors peak at about 5 m s−1 andthe velocity rms scatter peaks at about 6 – 7 m s−1.When observing the sun through a solar port wherethere is a more homogeneous illumination of the slit,the RV data routinely improves to a precision of 2 –3 m s−1 demonstrating the importance of uniformillumination of the spectrometer optics.

The most important weaknesses of this programare that this is a large multi-setup, multi-user in-

53 Presentation by Michael Endl

strument with complex, large optics, relatively poortelescope image stability and guiding and a 2-pixelsampling of the instrumental profile. The detectoris a Tektronix CCD (circa 1990). The project couldlikely be improved with a new 15-micron CCD, oc-tagonal fiber link, wavefront sensor for focus, andfast tip/tilt for image stabilization.

2.4. 3.9-m AAT and UCLES Coude spectrograph,1998 –

The Anglo-Australian Planet Search (AAPS) hasbeen in continuous operation since 1998, usingthe University College London Echelle Spectro-graph (UCLES) at the 3.9-m Anglo-Australian Tele-scope54. The 1 arcsecond slit is used for the AAPSand corresponds to a resolution of 45,000. Theinstrument wavelength range extends from 4780 –8415 A and the instrument employs an iodine ref-erence cell for wavelength calibration. For flexiblescheduling, the program uses an automated queue-based observing system, which controls instrumentconfiguration, removes operator error, and imple-ments parallel detector readout and telescope slew-ing.

UCLES on the AAT has concentrated on the samesample of 240 stars from 1998 to 2012, detectingmore than 45 new planets orbiting these stars (But-ler et al. 2001; Carter et al. 2003; Bailey et al. 2009;O’Toole et al. 2009; Tinney et al. 2011; Wittenmyeret al. 2014). The AAPS has entered its final phase ofoperations and is concentrating on the key sciencequestion: What is the occurrence rate of Jupiter-analogs, gas giant planets still orbiting beyond thefrost line with no inner gas giant planets? Owingto the legacy of the 17-year continuously-observedsample, the AAPS remains a leader in the detectionof long-period planets.

Although UCLES is a non-stabilized spectro-graph, the AAPS has achieved a velocity precisionof ∼3 m s−1 per epoch at a signal-to-noise of 200per pixel and a resolution of 45,000. The quotedvelocity uncertainties from the AAPS include theeffects of photon-counting uncertainties, residual er-

54 Information provided by Rob Wittenmyer


Figure 3. (left) Estimated single measurement precision as a function of SNR using the Tull spectrograph on the 2.7-m HarlanSmith Telescope at McDonald Observatory. Different color plot symbols are for different stars. (right) Radial velocity scatter(right) for the stars observed with this same spectrograph at McDonald Observatory. (Courtesy of Michael Endl)

Figure 4. Radial velocity scatter (right) for UCLES. (Cour-tesy of Robert Wittenmyer)

rors in the spectrograph PSF model, and variationbetween the underlying iodine-free template spec-trum and spectra observed through the iodine cell.The spectrum is broken up into several hundred 2 Achunks and velocities are derived from each chunk(Butler et al. 1996). The final radial velocity mea-surement is determined as the mean of the chunks,and the quoted internal uncertainties are estimatedfrom the scatter of the individual chunks (Butleret al. 1996). Figure 4 is a histogram of the rms ofthe velocities (without attempting to remove anytrends or Keplerian signals).

Over the lifetime of the AAPS, the team hasworked to improve the stability and precision ofthe radial velocity measurements. In 2005 the pro-gram began using longer integrations, which aver-aged over stellar oscillation noise (O’Toole et al.2008) and delivered higher SNR (typically 400). Asa result, the systematic and stellar uncertaintieswere reduced below 2 m s−1 as demonstrated for

the bright triple-planet-hosting star 61 Vir (Vogtet al. 2010b). This long-term stability is reflectedin the number of long-period systems detected byAAPS; the majority of AAPS planets (62±13%)have periods longer than one year.

To advance the precision at the AAT, a next-generation spectrograph, Veloce, is being builtas a replacement for UCLES, with commission-ing planned in late 2016. Veloce is an asymmet-ric white-pupil echelle spectrograph that employsthe innovations used by other PRV instruments(e.g. G-CLEF, SALT-HRS, and KiwiSpec) to maxi-mize velocity stability: dual-shell thermal enclosure,vacuum-enclosed echelle grating, octagonal fibres,an innovative ball-lens double scrambler, and wave-length calibration with an ultra-stablized pulsed-laser frequency comb (Murphy et al. 2007). Thiscalibration source will be injected into the simulta-neous calibration fiber feed to achieve a wavelengthcalibration better than 20 cm s−1.

2.5. 9.2-m Hobby-Eberly telescope and HRSspectrometer, 2001 –

The High Resolution Spectrograph (HRS; Tull1998) was commissioned at the 9.2-m Hobby-EberlyTelescope (HET) at McDonald Observatory55 in2001 and carried out a search for exoplanets through2013. The instrument and telescope are currentlyclosed for the HET upgrade project, but will berecommissioned in 2016. The wavelength range ofHRS is 408 – 784 nm and the spectral resolution isR=60,000. An iodine reference cell is used for wave-length calibration. The instrument is not stabilizedfor temperature or pressure. Observations are car-ried out in queue mode scheduling and stars areobserved between 1 and 5 times per month. Overthe past 10 years, more than 1600 RV measurementshave been obtained.

The primary targets on the HRS program are 41faint stars; these are typically M dwarfs with ap-parent magnitudes of 10 < V < 12. There is also aprogram to carry out follow-up of Kepler transiting

55 Presentation by Michael Endl

8 Fischer et al.

planet candidates for mass determination.There are about 65% slit losses with the HRS.

This occurs because the slit must be narrowed toreach a resolution of 60,000. As a result, the HRSobservations have a SNR that is typically around100; this reduces the Doppler precision when mod-eling with the iodine technique and yields estimatedSMP errors that range from 4 to 8 m s−1 with along term velocity rms that is greater than 6 m s−1

(Figure 5).The instrument does not have an exposure me-

ter; this is particularly critical for HET because thetelescope design produces variable illumination atthe telescope pupil. The HRS-upgrade project isnow underway with plans to provide image slicersfor an increase in resolution to 70,000, a new effi-cient cross disperser, octagonal fiber feeds to pro-vide some scrambling, and an exposure meter. Theimproved efficiency should allow for observations ofstars that are about two magnitudes fainter with thesame SNR. The team notes that the last twelve RVmeasurements of sigma Draconis show a low rms of1 m s−1. These observations were taken when theouter ring of the HET mirror segments were alreadytaken off, pointing to a possible problem with theoptical quality of the camera that was improved bystopping down the pupil to stabilize the PSF.

2.6. 3.6-m ESO telescope and HARPS, 2003 –

The High Accuracy Radial Velocity PlanetSearcher (HARPS) spectrometer was commissionedin 2003 (Mayor et al. 2003; Pepe et al. 2002) on the3.6-m telescope at La Silla56 in Chile and was thefirst spectrograph to be specifically designed for aDoppler exoplanet survey. The instrument operatesin a vacuum enclosure with a stable temperature of17◦±0.01◦ C and the operating pressure is kept sta-ble to better than 0.01 mbar since pressure changeswill introduce drifts in the spectrum at the levelof about 100 m s−1 per mbar. The fiber-fed instru-ment has a resolution of 115,000 and the calibrationof the entire wavelength range from 380 nm to 690nm is achieved with simultaneous reference from aThorium-Argon lamp with a second fiber to trackinstrumental drifts during the night. Doppler mea-surements are obtained by cross-correlating eachspectrum with a template mask. HARPS uses afiber double scrambler (Avila & Singh 2008) to in-vert the near and far fields producing a scramblinggain of about 10,000 for consistent illumination ofthe optics. HARPS ushered in a new era for radialvelocity measurements, and was the first instrumentto deliver better than 1 m s−1 RV measurement pre-cision.

Several exoplanet programs are carried out withHARPS, including a search of metal-rich and metal-poor stars (Santos et al. 2014), an M dwarf exo-planet search (Bonfils et al. 2013), and a search forsuper-Earth and Neptune mass planets around FGKstars (Pepe et al. 2011). The particular HARPSprogram that was highlighted at the EPRV work-shop was the high precision program that focuses

56 Presentation by Christophe Lovis

on detection of the lowest mass exoplanets to revealpopulation statistics around FGK type stars.

HARPS and HARPS-N both use the cross corre-lation technique (Baranne et al. 1996; Pepe et al.2002). The internal uncertainties are calculated asthe quadratic sum of three different contributions:1) photon and readout noise, 2) wavelength cali-bration error, and 3) instrumental drift error. Theradial velocity (RV) uncertainty caused by photonand readout noise is obtained by propagating er-ror bars from the spectrum to the weighted CCF(Pepe et al. 2002), and computing the fundamentalRV uncertainty on the CCF using the formula inBouchy et al. (2001). A global uncertainty on thewavelength calibration is estimated from the rmsdispersion of Thorium Argon (ThAr) lines aroundthe wavelength solutions, as well as the total num-ber of fitted ThAr lines. Finally, a drift uncertaintyis also computed as the fundamental RV uncertaintyon the simultaneous reference fiber. Combined to-gether, these error sources provide a lower bound tothe true error bars on the RVs. Additional contri-butions from stellar photospheric velocities, back-ground contamination, and other instrumental ef-fects should also be added in quadrature to the in-ternal errors (Dıaz et al. 2016; Santerne et al. 2015).

It is worth noting that HARPS was a significantfinancial investment for the European Southern Ob-servatories (ESO), reflecting a strong vision and po-litical commitment to the improvement of spectrom-eters for exoplanet detection. As Figure 6 (left)shows, a velocity precision of 0.8 m s−1 is achievedwith SNR of 200. Higher SNR improves the sin-gle measurement precision to better than 0.5 m s−1.The long term velocity rms scatter shown in Figure6 (right) is also significantly lower than the velocityscatter with the iodine technique; many stars showan rms that is less than 2 m s−1. HARPS pushedthe instrumental errors lower by a factor of two rel-ative to the general-purpose spectrometers with io-dine reference cells for wavelength calibration.

Importantly, the team sees evidence for photo-spheric activity that is imprinted in the stellarspectrum by using several indicators: line bisectorshapes and variations in the full width half max forthe CCF, and emission in the cores of Ca II H & Klines (Queloz et al. 2001; Figueira et al. 2013; Gomesda Silva et al. 2012) The precision on HARPS is af-fected by guiding errors and variations in the focus,both of which lead to variable illumination of thespectrometer optics and instabilities in the SLSFLast summer, the team implemented new octago-nal fibers to produce a higher scrambling gain forthe light injected into the spectrograph. The instru-ment is also now equipped with a laser frequencycomb (LFC) for a better wavelength calibration.The commissioning tests with the LFC demonstratea dramatic improvement in precision and also iden-tified stitching errors in the pixel format of the CCD(discussed in Section 3.1).

An important lesson learned from HARPS is thathigher SNR, higher resolution, and higher fidelityspectra are needed to make significant progress on


Figure 5. Radial velocity precision as a function of SNR (left) and radial velocity scatter (right) for HRS. (Courtesy of MichaelEndl)

Figure 6. Single measurement precision as a function of SNR (left) and radial velocity scatter (right) at HARPS for the targetsample of FGK dwarfs to search for super Earth and Neptune mass exoplanets with HARPS. (Courtesy of Christophe Lovis)

disentangling stellar activity from the center of massvelocities for chromospherically quiet stars. In re-sponse to this, the team is building ESPRESSO onthe Very Large Telescope (VLT) at Paranal in Chile.

2.7. Haute Provence 1.93-m telescope andSOPHIE spectrometer, 2006 –

The ELODIE spectrograph (Baranne et al. 1996)that was used to discover 51 Peg b (Mayor & Queloz1995) and other exoplanets with the 1.93-m tele-scope at Observatoire de Haute-Provence was re-placed by the SOPHIE57 spectrograph in 2006 (Per-ruchot et al. 2008). That instrument has a resolu-tion of 75,000 with spectral sampling of two pixelsFWHM. The wavelength range is 387 – 694 nm andwavelength calibration is carried out with thoriumargon injected in a second fiber for simultaneouswavelength calibration. In 2011, a significant up-grade was made to the spectrometer, and an octag-onal fiber was added to provide better scramblingand to improve the precision (Bouchy et al. 2013).

Among the different SOPHIE planet surveys, thehigh-precision program focuses on 190 G & K dwarfsusing ∼ 16% of the telescope time distributed in

57 Presentation by Francois Bouchy

fractional nightly allocations. The primary sciencegoal is to search for Super-Earth and Neptune massplanets. There are also follow up programs for tran-sit candidates and plans for future TESS follow-up.

As illustrated in Figure 7 (left) the estimatedSMP errors are about 1 m s−1 for SNR of 200. ThisSNR is reached in about fifteen minutes on V=7.5stars. This exposure time is adequate to averageover p-mode oscillations in solar type stars. Thereare 49 stars with more than 20 measurements andFigure 7 (right) shows that the velocity rms peaksat ∼ 3 m s−1.

One challenge with SOPHIE is the thermal cou-pling between the spectrograph and the telescopepillar, which introduces annual uncontrolled tem-perature variations. There are plans to improve thethermal control. The ThAr wavelength calibrationis one of the current limiting factors in the RV pre-cision and there are plans to implement a Fabry-Perot etalon for simultaneous drift and wavelengthcalibration. A new data reduction package is alsobeing installed with all of the improvements fromthe most recent HARPS pipeline.

One lesson from SOPHIE is that the charge trans-fer inefficiency of the CCD is a critical parameter.

10 Fischer et al.

Figure 7. Theoretical uncertainty based on SNR and radial velocity scatter for the SOPHIE spectrograph. (Courtesy ofFrancois Bouchy)

In addition, scrambling of both the near and far fieldof the fiber output beam is important; the octagonalfiber was critical for helping to keep the RV preci-sion of SOPHIE competitive. Finally, all availablespectroscopic indicators (e.g., line bisectors, FWHMof the cross correlation function, Ca II H & K linecore emission) should be used to help interpret anysignals in the radial velocity measurements.

2.8. 6-m Magellan telescope with the PFSspectrometer, 2010 –

The Planet Finder Spectrograph (PFS; Craneet al. 2006) was commissioned at the 6.5-m Magel-lan telescope58 in 2010 and continues to be used tosearch for exoplanets. About 30 nights are allocatedin 10-day runs each semester. The echelle gratingis in a vacuum enclosure and the instrument hasactive thermal control. This slit-fed spectrographhas a resolution of 76,000 with a 0.5 arc second slit.The wavelength range extends from 390 to 670 nmand an iodine cell is used to calibrate the spectrumbetween 510 and 620 nm for Doppler measurements.

There are about 530 stars on the Magellan PFSDoppler survey. The primary goal of this program isthe detection of low mass companions around starsthat are closer than 50 parsecs. There is also a col-laborative program to obtain Rossiter-McLaughlinmeasurements to determine the coplanarity of tran-siting exoplanet orbits and follow-up programs forthe Hungarian Automated Telescope - South (HAT-S) and the Kepler “K2” mission.

Figure 8 (left) shows that the internal SMP forPFS is about 1.2 m s−1 at a SNR level of 200, withan rms floor (Figure 8, right) that typically rangesbetween 2 – 4 m s−1. The typical SNR is about 300for most Magellan PFS observations.

There are plans to refine the optical alignmentof the spectrograph to achieve better image qual-ity. Additional upgrades are being implemented thisyear, including replacing the CCD system with a de-vice that has smaller pixels, better electronics andfaster readout. A pupil slicer is planned that willfeed six optical fibers to increase the resolving power

58 Presentation by Pamela Arriagada

and to introduce some scrambling.The team is also improving the analysis to reduce

the number of free parameters in the forward mod-eling of the iodine spectra. The higher resolutiontemplate spectra provide higher precision especiallyfor late-type stars. High cadence observations arean advantage for detecting short-period planets dur-ing the 10-day observing runs. However, the gaps inthese data sets also cause statistical sampling prob-lems for detecting lower amplitude systems wherethe prospective Keplerian velocity amplitudes arecomparable to the photospheric velocity jitter.

2.9. 1.5-m CTIO telescope with the CHIRONspectrometer, 2011 –

The CHIRON spectrometer (Tokovinin et al.2013) was commissioned at the SMARTS 1.5-mCTIO telescope59 in 2011 and is still being used forexoplanet searches. The instrument was upgradedand recommissioned in 2012 with a new echelle grat-ing in a vacuum enclosure, two stages of thermalcontrol (the spectrograph enclosure and an outerroom maintain temperature stability to ±1C), anexposure meter for calculating the observation mid-points for barycentric velocity corrections, an oc-tagonal fiber feed for better scrambling, and a newCCD controller for faster readouts. The wavelengthrange of CHIRON extends from 440 to 650 nm withpartial orders from 620 – 870 nm. Wavelength cali-bration is accomplished with an iodine cell, limitingthe Doppler information to the wavelength subin-terval from 510 – 620 nm. The bare fiber producesa spectral resolution of 28,000. An image slicerwas built to increase the resolution to 90,000 andmaximize throughput; however, the Doppler preci-sion with the slicer was limited to a few meters persecond, probably because of unstable illuminationof the slicer and imperfect flat-fielding through thefiber slicer. Instead, a slit mask in front of the fiberis used for the high precision mode. This increasesthe resolution to either R = 90, 000 or R = 140, 000,albeit at the cost of lost light.

The primary goal of the CHIRON program was

59 Presentation by Debra Fischer


Figure 8. Estimated single measurement precision as a function of SNR (left) and radial velocity scatter for PFS. (Courtesyof Pamela Arriadada)

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the search for planets around alpha Centauri A andB and the program also included 35 bright stars.The low throughput associated with a high resolu-tion spectrograph on a small telescope required twohour exposures on stars fainter than V = 5. This ul-timately lead to a program re-scope to concentrateon the brightest stars with the goal of understand-ing the limitations of radial velocity precision fordetection of lower mass planets. The program usesqueue scheduling (Brewer et al. 2014) and this en-ables observations of a few bright stars on virtuallyevery clear night.

The radial velocities and uncertainties are cal-culated as described in Section 2.1. At a SNR of200, the SMP errors for CHIRON are 1 m s−1 and

the SMP improves to 0.5 m s−1 as the SNR ap-proaches 500. Figure 9 (left) shows the dependenceof estimated internal errors on the SNR of the ob-servations. Figure 9 (right) is a histogram of therms of the velocities (no trends or Keplerian signalswere removed) with a minimum rms of 2 m s−1.The fairly narrow range in rms velocities occurs be-cause the program concentrated on chromospheri-cally quiet stars.

The alpha Cen survey suffered from increasingcontamination as the separation of the two binarystars decreased from 6 arcseconds in 2011 to 4 arc-seconds in 2013 (when the project was put on hold).The contamination was significant with 2.′′7 fiber,selected to accommodate the frequent poor seeing

12 Fischer et al.

at the observatory. A technique was developed tofit for scaled flux contamination when modeling theradial velocity of each star, however this only pro-vided a precision of 3 m s−1.

CHIRON demonstrated the advantage of a fiber-fed instrument and very high cadence Doppler ob-servations. The biggest challenge with CHIRON isthe struggle to obtain the high SNR needed for 1m s−1 precision with the iodine technique; this isdifficult on a small aperture telescope and therewere additional challenges with poor guiding andtelescope control system failures. As a result, theprogram goals shifted to understanding the limita-tions of radial velocity precision by focusing on asmall subset of the very brightest stars.

Perhaps the most important lesson from CHIRONis that even with a more stable instrument, parame-ter degeneracies in forward modeling were identifiedthat ultimately limit the RV precision (in additionto stellar jitter) with the iodine technique (Sproncket al. 2015). While a more precise wavelength cal-ibrator that spans a broader wavelength range onCHIRON is desirable, the instrument is not in avacuum enclosure and CHIRON was not designedto be stable enough for simultaneous thorium ar-gon or laser frequency combs. The lesson here isthat a change in wavelength calibration is not al-ways an easy retrofit; it is something that needs tobe designed into the instrument from the start. Theteam is now building on lessons learned with CHI-RON in the design of a new spectrometer, the EX-treme PREcision Spectrograph (EXPRES) for the4.3-m Discovery Channel Telescope (commissioningis planned for summer 2017). This vacuum-enclosedwhite pupil design spectrometer will have a resolu-tion of R=150,000, a broad wavelength range, andcalibration with a laser frequency comb.

2.10. PARAS

PARAS (PRL Advanced Radial-velocity Abu-skySearch) is currently India’s only exoplanet searchand characterization program60 and started sci-ence observations in 2012 (Chakraborty et al. 2010,2014). PARAS obtains a single-shot spectral cover-age of 3800 – 9500A at a resolution of 67,000 with4-pixel sampling. Radial velocity measurements arecalculated using simultaneous wavelength calibra-tion with a Thorium-Argon (ThAr) hollow cathodelamp. The spectrograph is maintained under stabletemperature conditions and enclosed in a vacuumvessel. The enclosure has active temperature con-trol to correct for thermal conduction through theconcrete pier under the spectrograph; temperatureis monitored both inside the vacuum chamber andin the room, and corrections for the heat loss or gainare applied by changing the heater power. This pro-vides an rms thermal stability of 25 ± 0.009C dur-ing the night. The typical vacuum stability is about0.05 millibar during a night of observations. An e2vdeep depletion 4kx4k CCD is used for imaging thespectra along with the ARC Inc., Leach Controller

60 Presentation by Abhijit Chakraborty

for CCD electronics and interface with Computer.Simultaneous ThAr exposure along with a ThAr ex-posure immediately after the observation is used tocorrect for instrument drifts with an rms error of 90cm s−1 or better (Chakraborty et al. 2014).

The blaze peak efficiency of the spectrograph be-tween 5000 A and 6500A, including the detector,is about 30%; and about 25% including the fibertransmission. The total efficiency, including spec-trograph, fiber transmission, focal ratio degradation(FRD), and telescope (with 81% reflectivity consid-ering primary and secondary mirrors) is ∼ 7% inthis same wavelength region.

The PARAS data analysis pipeline (Chakrabortyet al. 2014) is custom-designed and based on theREDUCE routines of Piskunov & Valenti (2002).The pipeline performs the routine tasks of cosmicray correction, dark subtraction, order tracing, andorder extraction. A thorium line list is used to cre-ate a weighted mask which calculates the overallinstrument drift, based on the simultaneous ThArexposures.

RVs are derived by cross-correlating the targetspectra with a suitable numerical stellar templatemask. The stellar mask is created from a syn-thetic spectrum of the star, and contains the ma-jority of deep photospheric absorption lines (Pepeet al. 2002, and references therein). RV measure-ment errors include photon noise errors (Bouchyet al. 2001) and other errors like those associatedwith fitting the cross correlation function. Typi-cally, two to three RV points are used to calculatethe nightly mean velocity. Chakraborty et al. (2014)demonstrate a mean nightly rms scatter of 1.2 m s−1

for the star Sigma Draconis over a period of sevenmonths and 1 m s−1 for HD 9407 over ∼ 30 days.Additional velocities now show 1.4 m s−1 over twoyears for Sigma Draconis and 1 m s−1 for tau Cetiover a period of 40 days.

Figure 10 shows the estimated measurement pre-cision of PARAS for 27 bright stars since the be-ginning of observations in 2012. These sources haveat least 10 epochs of observations spanning morethan 30 days. On a clear photometric night with90% reflectivity on the telescope primary and sec-ondary mirrors, a SNR of 200 per 3km s−1 RV binis reached in about 15 minutes on a 6.5-magnitudestar.

The small telescope aperture of 1.2-m with itslarge tracking errors (of the order of 1 to 1.5 arc-seconds) is one of the greatest short comings of theproject. A combination of octagonal and circularfibers (without a double scrambler) helps to stabi-lize illumination of the spectrograph optics. Insteadof a pinhole at the telescope focal plane, a focal re-ducer is used to focus the F/4.5 beam on the octag-onal fiber. The image of the star slightly overfillsthe fiber which is about 2 arcsecs on the sky. Thishelps to take care of telescope tracking and atmo-spheric scintillation issues at the cost of some lightloss.

The team plans to move PARAS to a new 2.5-mtelescope in late 2019 or early 2020 with a fast tip-


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Figure 10. Precision and radial velocity scatter for PARAS. (Courtesy of Abhijit Chakraborty) The plot on the left showsthe nightly RV scatter as a function of SNR in 3 km s−1 bins and the plot on the right is a histogram of the long term rmsscatter for 27 bright stars.

tilt image stabilizer and an ADC at the Cassegrainfocus for proper injection of light into the fiber. Thenew telescope will have rms tracking and jitter er-rors of less than 0.1 arcsecsonds. The temperaturecontrol and spectrograph room will be redesigned toalleviate the present deficiencies like the heat con-duction issues from the pier and to achieve thermalstability of 25±0.001C. This will eliminate the needfor taking large number of ThAr calibrations duringthe night, providing additional time for more stellarobservations.

2.11. 3.5-m TNG telescope with the HARPS-Nspectrometer, 2012 –

In 2012, a near twin of HARPS was commissionedat the Telescopio Nazionale Galileo (TNG) observa-tory61. The vacuum enclosed instrument, HARPS-N, has temperature and pressure stabilization, a res-olution of 115,000 and wavelength range from 383to 693 nm. HARPS-N was initially commissionedwith Thorium Argon simultaneous calibration, witha planned upgrade to an optical frequency comb.The instrument is fed by a combination of octag-onal fiber and double scrambler, which inverts thenear and far fields. A failure of the CCD delayedthe debut of this instrument, but regular operationsare now underway.

HARPS-N is being used for several collabora-tive exoplanet detection programs (Cosentino et al.2014), including the Global Architecture of Plane-tary Systems (GAPS; Covino et al. 2013) program.In summer 2015, a novel program was started tocarry out solar observations with the goal of reach-ing sufficient measurement precision to detect Venus(Dumusque et al. 2015b). The solar observations areone example of a project that is not photon starved,and uses high cadence (5-minutes) for about 4 hourseach day, using a compact solar telescope to feed theHARPS-N spectrograph. When using the HARPS-N LFC, the error from the wavelength calibrationis only 6 cm s−1 and the estimated precision is afew meters per second over the course of a week.

61 Presentations by David Phillips and Lars Buchhave

The project uses a photometric F − F ′ correction(Aigrain et al. 2012; Dumusque et al. 2015b) fromthe Solar Dynamo Observatory (SDO) images to re-duce this to 1 m s−1.

The velocities and uncertainties are calculated asdescribed in Section 2.6. Figure 11 shows that themeasurement precision at HARPS-N is similar toHARPS. The estimated SMP for SNR of 200 is be-tween 0.5 – 1 m s−1. The rms velocity scatter peaksat about 2 m s−1.

RePack is the name of a Doppler pipeline forHARPS-N, written by Lars Buchhave. Here, theinternal uncertainties are calculated by cross cor-relating either a high SNR observed spectrum ora co-added combined spectrum (i.e., a template)against the observed spectra. Typically, a deltafunction template is used. This template consistsof weighted delta functions based on the measuredline centers of known absorption lines, so that eachline can contribute to the CCF with some weight.Individual lines have a relatively poor wavelengthdetermination, often with several hundreds of me-ters per second uncertainties. The final RV of eachorder can thus be several hundreds of meters per sec-ond offset compared to the other orders because ofthe (combined) uncertainties in the position (wave-lengths) of the delta function lines. The offset is theaverage offset between the weighted delta functionlines compared to the actual stellar spectrum. Thiscan create problems when the spectrum is shiftedaround by the barycentric correction, because lineswill move from higher to lower and lower to higherSNR regions on the detector (because of the blazefunction). In other words, the combined RV offsetof the order can change because e.g. a strong linemight move towards lower SNR if it moves towardsthe edge of the order.

In contrast, an observed template will yield RVsfor the individual orders that are more realisticallyscattered around the RV shift between template andobservation. With RePack, a radial velocity mea-surement is determined for each individual orderusing a CCF and the internal uncertainty is cal-culated as the photon weighted rms of the RVs for

14 Fischer et al.

Figure 11. Histograms of the estimated SMP and radial velocity scatter for stars with more than 10 observations at HARPS-N.(Courtesy of Lars Buchhave)

each order, divided by the square root of the totalnumber of orders used. The final RV is measuredby co-adding the CCFs for each order and then de-termining the position of the co-added CCF peak.

The precision of HARPS-N allows for the detec-tion of additional errors that are normally maskedby poorer precision data. A three-minute thermalcycle on the cold plate in the CCD cryostat atHARPS-N was identified and the thermal cyclingis believed to produce an expansion-contraction cy-cle that slightly shifts the position of the CCD. Thetemperature variations from the cold plate probecorrelate directly with wavelength (velocity) shiftsin the thorium argon calibration lines for short 20-second exposures. The stability of the wavelengthsolution was restored by taking 5-minute thorium-argon observations to average over the cold-plate jit-ter cycle. Two different data analysis pipelines havebeen tested at HARPS-N; this was a useful exercisethat helped to identify new areas for improving theRV precision.

2.12. 2.4-m APF with the Levy spectrometer, 2013–

The 2.4-m Automated Planet Finder (APF;Radovan et al. 2010; Vogt et al. 2014) is locatedat Lick Observatory62 and the Levy spectrographwas commissioned at the APF in 2013. The instru-ment uses a narrow slit to reach resolutions up to150,000. Like Keck-HIRES, the wavelength calibra-tion is carried out with an iodine cell and thereforethe wavelength range used to derive Doppler veloci-ties is limited to 510 – 620 nm. However, the spectraspan from 374 – 950 nm, enabling the use of chro-mospheric diagnostics like the Ca II H & K lines.

The telescope time on the APF is divided be-tween two groups; the Lick-Carnegie Planet Search(LCPS) team at UC Santa Cruz observes about 100stars and the California Planet Search (CPS) teamat UC Berkeley and the University of Hawaii ob-serves a few hundred stars. The science goals ofboth teams include detection and characterizationof low mass exoplanet systems and follow-up obser-

62 Presentations by Greg Laughlin and Andrew Howard

vations to better resolve components of multi-planetsystems. In the future, the APF will provide sup-port for the NASA TESS mission. A big advantageof the APF is that it is a robotic instrument andthe observing scripts can be launched from remotesites (Burt et al. 2015). The unique combination oflarge telescope time allocation and small user groupallows the facility to obtain very high cadence mea-surements.

The CPS team aims for a fixed target SNR of200 per observation; this yields estimated internalerrors of about 2 m s−1. Typically many observa-tions are taken for each star during a given nightand the velocity is averaged to give better preci-sion. Because the CPS team is observing stars withlow chromospheric activity and a known legacy ofDoppler velocities from Keck HIRES, the rms of thevelocities is a tighter distribution than Keck HIRES,centered on 3 – 4 m s−1. Figure 12 (left) shows thedependence of estimated internal errors on the SNRof the observations. Figure 12 (right) is a histogramof the rms of the velocities (without attempting toremove any trends or Keplerian signals).

The Lick Carnegie team has estimated errors ofabout 1.5 m s−1 per observation at a SNR of 200and 1 m s−1 at SNR of 400 and the velocity rms istypically greater than 2.5 m s−1. Figure 13 (left)shows the dependence of estimated internal errorson the SNR of the observations. Figure 13 (right) isa histogram of the rms of the velocities (no trendsor Keplerian signals were removed).

The precision of the Levy spectrometer is limitedto about 1 m s−1 by the iodine reference cell. Al-though the flexible scheduling has been critical forthis program, only a relatively small number of ob-servations can be taken each night because of themodest 2.4-m telescope aperture.

2.13. Hertzprung 1-m telescope with the SONGspectrometer, 2014 –

The SONG spectrometer (Grundahl et al. 2011)was commissioned in mid-2014 at the Mount TeideObservatory in Tenerife63. The instrument has a

63 Presentation by Frank Grundahl


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Figure 13. Radial velocity precision as a function of SNR (left) and velocity rms (right) for the Lick Planet Search team withthe Levy Spectrograph at the Automated Planet Finder. (Courtesy of Greg Laughlin)

series of slits and is operated with a spectral res-olution of 90,000 and an optical wavelength rangeof 440 – 690 nm. The instrument is not in a stabi-lized vacuum enclosure so an iodine reference cell isused to measure Doppler shifts between 510 – 620nm. The detector is a 2k by 2k Andor device with2-second readout, suitable for measuring the oscilla-tion periods of stars. There is a fast tip/tilt systemto help stabilize the slit illumination.

The science program focuses on a relatively smallsample of twelve stars with the goal of obtaining as-teroseismology data, reaching a better understand-ing of stellar physics and detecting exoplanets. Ex-cept for time lost to weather, this is a dedicatedfacility that obtains very high cadence observationsevery night. The telescope will be part of a networkthat spans the globe for nearly continuous obser-vations of stars. The estimated SMP error (Figure14) is about 2 – 4 m s−1 with an rms of about 4m s−1. The best precision is obtained for K dwarfs,but there is still large scatter in the RV errors.

SONG is optimal for bright targets. However,the program is new, so the data analysis pipelinesare still being developed. The iodine cell is in acollimated beam and demonstrated fringing; this

cell has just been replaced with a cell that haswedged optical windows that are counter-rotated.The small 1-m telescope aperture means that thestars must be brighter than V of 6.5 for reasonableexposure times and high SNR.

2.14. Future RV Programs

In addition to these ongoing Doppler planetsearches, there are several funded new spectrome-ters that will come online in the few years, includ-ing the first node of Network of Robotic EchelleSpectrographs (NRES) on the LCOGT telescopesin 2015 with a target RV precision of 3 m s−1 (East-man et al. 2014), CARMENES in 2015 at the 3.5-mCalar Alto Observatory (Quirrenbach et al. 2014),HPF in 2016 on the 9-m HET (Mahadevan et al.2012), MINERVA 1-m telescope array in 2016 atMt. Hopkins (Swift et al. 2015), Veloce in 2016at the AAT; ESPRESSO in 2017 at the 8-m VLT(Pepe et al. 2013), EXPRES in 2017 on the 4.3-mDiscovery Channel Telescope at Lowell Observatory,SPIRou in 2017 at the 3.6-m CFHT (Artigau et al.2014a), the NNEXPLORE spectrograph at the 3.5-m WIYN telescope in 2018, iLOCATOR at the 8.4-m Large Binocular Telescope in 2018 (Bechter et al.

16 Fischer et al.

Figure 14. Radial velocity precision as a function of SNR for SONG and the histogram of nightly errors for 12 stars. Onestar has internal nightly errors that are greater than 10 m s−1. (Courtesy of Frank Grundahl)

2015) and G-CLEF in 2020 at the GMT (Szentgy-orgyi et al. 2012). For a more comprehensive list offuture instruments, see Tables 2 and 3 in Plavchanet al. (2015).

3. INSTRUMENTATION CHALLENGES

Efforts to identify confusing sources of velocityscatter from stellar photospheres will be more ef-fective if the instrumental precision is securely be-low the target RV precision for the stars64. Theserequirements set the top level specifications for ob-serving cadence and spectral resolution, which inturn dictates the wavelength bandpass, type ofwavelength calibration, signal-to-noise ratio (SNR),precision for the barycentric correction, and re-quired stability for the spectral line spread function(Connes 1985; Bouchy et al. 2001; Podgorski et al.2014).

Asymmetric white pupil spectrograph designs of-fer several advantages for PRV spectrometers. Theoverall size of the optics and the instrument is re-duced, and vignetting and aberrations are reduced.The white pupil design offers higher efficiency andbetter image quality than conventional designs withthe same resolution. White pupil designs have in-trinsic cylindrical field curvature that is tradition-ally mitigated with a toroidal (cylindrical) field flat-tener that must be placed very close to the detector.A curved CCD would be an ideal solution, but these

64 Presentations by Andrew Szentgyorgyi and Suvrath Ma-hadevan

are not commercially available. Instead a Manginmirror can be used in place of the folding trans-fer mirror to compensate for cylindrical field errors.However, care must be taken since the Mangin mir-ror can produce significant ghosts if it is not wedged.

High velocity precision requires high SNR andbroad wavelength bandpass, so a telescope of atleast a modest aperture is required for all exceptthe brightest stars. The size of spectrometer op-tics increases with the size of the telescope unlessclever designs are implemented (e.g., the anamor-phic design of ESPRESSO or single mode fibers be-hind adaptive optics systems). The need for bothhigh resolution and broad bandwidth often impliesthat two (or more) cameras will be required, eachwith its own challenges. Often, the efficiency for theblue arm of the instrument is challenging because ofthe lower transmission of optical glasses below 420nm and the fibers must be kept short to minimizeattenuation of light. Spectra obtained from the redarm of the spectrometer have telluric contaminationthat shift across the rest frame of the stellar spectrabecause of the barycentric velocity of the Earth.

Camera designs for spectrometers fall into oneof two categories. Standard designs have 7-9lenses that are independently testable. Fabricationand alignment of these (mostly spherical) optics isstraightforward; however, there can be a significanthit in terms of efficiency, ghosting and scatteredlight. New high-dispersion glasses are now available(Ohara and Nikon i-Line) that can reduce the num-


ber of optical elements needed for standard cameradesigns. The second type of camera is a pupil-foldedcamera that uses aspheric components. These arenot independently testable and carry some risk inmanufacturing and alignment; however, the opticsare very efficient with few ghosting and scatteredlight problems.

The need to precisely centroid spectral lines andto track line profile variations from stellar pho-tospheres (granulation, spots, plage, variations inlong-term magnetic fields) sets top-level require-ments for environmental stability. The solutionfrom HARPS was to put the instrument in a vac-uum chamber with vibration isolation. Tempera-ture and pressure in vacuum enclosures are rou-tinely controlled at the level of 10 mK and 10−2

Torr respectively; at this level, refractive index vari-ations are no longer a problem. However, temper-ature stability below 1 mK and pressure stabilitybelow 10−7 Torr is desirable because this will stopmolecular transfer, providing a system that is al-most completely radiatively coupled. This is thestate of the art for infrared instruments with liquidnitrogen tanks and charcoal or zeolite getters forcryo-pumping.

The ease of environmentally stabilizing a spec-trometer is inversely proportional to the size of thevacuum enclosure. Most enclosures are high gradesteel, which is easy to weld, or aluminum, which ismore difficult to weld. Optical benches have beenmade out of aluminum (NRES, KiwiSpec, HPF),mild steel (HARPS, ESPRESSO), invar and com-posite material. All have virtues and drawbacks.Aluminum is light weight, low cost, and low tech-nical risk, but may pose a high performance riskfor radial velocity precision because of the thermalproperties that must be carefully controlled. Steelis heavy, but easy to process, with high thermalinertia and low cost. Invar is heavy with high ther-mal inertia; it is difficult to manufacture, posing amoderate technical and RV performance risk. Thedesign trade study for G-CLEF found that carbonfiber epoxy met the systems engineering require-ment with excellent conductivity and low thermalinertia. There is some technical risk since this is anew material and it is known to outgas water. How-ever, in a vacuum, outgassing will decrease over timeto acceptable levels (may need to pump for about ayear).

As the spectrometers become more complex, ahigher level of systems engineering is required withwell-considered budgets for throughput, radial ve-locity precision, sequencing, timing, and delivery(e.g., Podgorski et al. 2014). New software pro-grams are being developed to integrate these errorbudgets and to track compliance; this makes it eas-ier to understand the design impact if, for example,a vendor delivers a component that does not meetthe specification (many components are still con-tracted to vendors with a best effort commitment).The error budget should distinguish between errorsources that can be calibrated out and those thatcannot. In their error budget for G-CLEF, Pod-gorski et al. (2014) describe error sources that affect

the calibration and observations equally and there-fore can be calibrated out with an extremely stableinstrument. These include:

• Thermal stability: thermo-elastic distortionsof the spectrograph can shift the spectra andaffect focus. For G-CLEF temperature loadsof 0.001C were applied in the FEA model (us-ing the Smithsonian Astrophysical Observa-tory Bisens software) and a lateral motion of110 (55 cm/s) was identified; the solution wasto adopt lower CTE materials and improvethermal control.

• Mechanical stability: the spectrometer is af-fected by changes in atmospheric pressure out-side the enclosure that result in deformationof the spectrograph causing lateral shifts andfocus errors; vibrations can also cause lat-eral shifts, focus errors, and PSF broadening;instability of materials can occur; for exam-ple from moisture desorption of the compositebench with G-CLEF.

• Pressure changes: because the wavelength cal-ibrator follows the same path and column den-sity as the program observations this can becalibrated out if the drift is slow compared tothe observation times.

• CCD stitching errors: the lithographic processfor making CCDs steps the mask in discretesteps, leaving positional errors after blocks of512 pixels. As Doppler shifts or barycentricmotion causes the spectral line to cross one ofthese regions, a spurious wavelength shift willbe measured (Dumusque et al. 2015a). Ac-cording to Paul Jorden, the stitching errorshave been reduced by a factor of three withthe current e2v devices.

Other error sources that cannot be calibrated out(Podgorski et al. 2014), include:

• Barycentric errors: current state of the artalgorithms, when combined with precise ex-posure meters, provide corrections good to 2cm s−1.

• Software fitting errors: affect both the cali-brator and extraction of the science spectra.

• Micro-vibration: it is possible to obtain ∼ 1mg vibration control, but smaller vibrationscan be coupled to the detector and wouldbroaden the lines.

• Detector errors: including controller read-out errors, intra-pixel QE variations, non-identical pixel sizes, detector heating on read-out, dependence of CTE on amount of carriedcharge.

• Stray light: to minimize this, use baffling andghost or scattered light analysis in the instru-ment design and keep the echelle orders well-separated.

18 Fischer et al.

• Tracking: this includes both telescope and on-instrument tracking. For negligible contribu-tion to the RV error, displacements should beless than a quarter of the fiber diameter witha scrambling gain of 10,000. This is possiblewith octagonal fibers and a double scramblerto invert the near and far field.

• Telescope focus errors and variable seeing con-ditions will lead to variable instrument illumi-nation, though translating this variation intan RV error is difficult.

• Imperfect atmospheric dispersion compen-sator: will vary the spatial illumination of theoptics in a wavelength dependent manner.

Imperfect atmospheric dispersion compensationcan potentially introduce systematic effects in themeasurements. For example, for fiber-fed spectrom-eters, the photocenter of the image might not fall atthe center of the fiber at all the wavelengths. Thiscould change the measured spectral energy distri-bution, introducing time-correlated changes in theslopes of the echelle orders. Data reduction andextraction should account for this, and algorithmsmust be tested against the range of changing condi-tions during commissioning. A second effect is thatchromatic dependence in the fiber illumination maycouple with scrambling efficiency and produce vari-ations in the spatial illumination of the optics in awavelength dependent manner.

3.1. Detector Technology

Charge-coupled devices (CCDs) are the detectorof choice for optical spectrographs due to their highquantum efficiency (QE), low noise, large dynamicranges, excellent linearity, and large pixel formatsubstrates65. CCD detector technology continuesto provide a steady improvement in performancealong with new and innovative features, which helpto make extreme precision RV measurements pos-sible. This section summarizes the current stateof the art for CCD technology and highlights someof their limitations in optical spectrograph perfor-mance.

CCDs are sensitive over a broad wavelength rangefrom 350 – 950 nm, but require anti-reflection (AR)coatings to achieve high QE. Simple coatings mustbe optimized for specific wavelength ranges andthus are not ideal for the broad wavelength rangesof some spectrographs. More sophisticated gradedcoatings are available, which have spatial gradientsin the AR coating to match the spectrograph band-pass. The spatial pattern of the AR coating canbe customized for the spectrograph design — op-timized spectral response is ideal for fixed formatspectrographs. In addition to improving the QE,the AR coatings will minimize reflections and thusminimize ghosts and fringes.

Inherent to CCD fabrication there are slight vari-ations in the pixel spacing and geometry that can

65 Presentations by Andy Szentgyorgyi and Suvrath Ma-hadevan

Figure 15. Example of the pixel image blocks required tocreate a 2k x 2k pixel CCD with exaggerated random positionerrors relative to the reference frame (image credit to e2vtechnologies).

introduce errors in extreme precision RV measure-ments. Construction of the CCDs manufactured bye2V66 starts with a metal mask with a pattern ofamplifiers, registers and image region that definesthe structure of the device. The image area of theCCD is fabricated with a photolithography processby projecting a block of 512 x 512 pixels onto thesilicon image region. The number of pixels in ablock is limited by the field flatness of the camera.To produce CCDs larger than 512 x 512 pixels re-quires that the block mask be stepped and reimaged(stitched) multiple times to form larger area devices.A stepper motor moves the camera to position forprojecting the adjacent block images and each blockhas a random alignment error relative to the stepperreference frame as illustrated in Figure 15.

Two machines are used by e2V for the stitchingprocess. The Ultratech stepper will lay down up totwo blocks in x and multiple blocks in y with analignment precision of 250 nm. The stitching errorsfor these devices can be seen by eye where the adja-cent blocks overlap. The newer Nikon stepper willlay down multiple blocks in x and y with a stepperalignment precision of 90 nm. While each stitchedblock is the same by design, there will be alignmentdifferences between the blocks. Even with perfectalignment at the edges of the blocks, there can be ameasurable boundary effect because of overlappingof the masks. Both pixel size variations and stitch-ing errors can be calibrated with a laser frequencycomb or laser metrology (Shao et al. 2013).

Pixels on either side of the boundary can haveslightly different dimensions. There are magnifica-tion and distortion errors in the photolithographyprocess that can influence alignment. The pixelsizes have random uncertainties of ±150 nm (or 1%for a 15-micron pixel) from the tolerances of thelithographic process.

CCDs and complementary metal-oxide-

66 Presentation by Paul Jorden


semiconductor (CMOS) chips exhibit patternnoise caused by QE variations, multiple output am-plifiers, surface defects, and process variations. Thepattern noise is small in modern detectors and fixedstructure can be removed with calibration images.CCD output amplifiers can be manufactured withlow read noise (<2 e- rms) and consistent electricalgain so that multiple outputs do not contributesignificantly to pattern noise. Process variations indetector fabrication, such as pixel size, thin filmthickness, doping, metallization, and impuritiescause a pixel response non-uniformity (PRNU).The pixel response uniformity in back-thinnedCCDs is best at 650 nm, with the non-uniformitiesincreasing at UV wavelengths from laser annealingprocess and at red wavelengths due to fringing.The PRNU can be improved with a good ARcoating and thick silicon devices.

To improve the QE response in the red and nearIR, deep depletion CCDs are fabricated with high-resistivity silicon material (high ρ) and have less sili-con removed during the thinning process to producethick (50-200 micron) devices. This results in thepixel sky scraper effect where the height of the pixelis very large compared to its width: for example, theLSST chips are 100 microns thick with 10-micronpixels. The high ρ silicon allows a greater depletionlayer within the tall pixel that minimizes the field-free region near the surface and allows electrons pro-duced there to be more readily captured and col-lected within the pixel. This minimizes charge dif-fusion effects — electrons wandering into neighbor-ing pixels — and improves the modulation transferfunction (MTF), which is a measure of the resolu-tion capabilities of the CCD. Conversely, the highρ silicon also introduces electrostatic fields in theCCD that could adversely affect charge collection:when one pixel fills up with signal charge it can in-fluence the collection of charge in neighboring pix-els because of these electrostatic effects (Weatherillet al. 2014). In other words, the high ρ silicon im-proves the MTF, but subtle variations in the MTFare possible as pixels fill up with charge and changethe electric field lines in surrounding pixels. Deepdepletion devices are also available and can exhibittree ring patterns from resistivity variations in sili-con boule (Plazas et al. 2014).

Charge transfer inefficiency (CTI) is a measureof charge transfer across each pixel and is typicallybetween 0.0010% and 0.0001%. CTI losses occur intraps that collect and hold some number of electronsbefore releasing them at a later time. For a 10,000e- signal, a CTI of 0.001% corresponds to a loss of100 electrons per 1000 pixel transfers. This gen-erally results from 100 single electron traps withina 1000-pixel row or column. CTI is an average ofcharge trapping events over the whole detector ar-ray. CTI is a function of temperature and trans-fer frequency (clocking) as well as the signal levelper pixel (Bouchy et al. 2009). Higher clock volt-ages can improve CTI but also introduce the risk ofclock-induced charge (CIC) trapping, although tri-level clocking will reduce CIC. On the larger formatdevices that are required for high-resolution spec-

trometers, the process of transferring charge can dis-sipate power in the silicon chip and cause warpingthat can affect the measured radial velocity. TheESPRESSO team estimates that 2 nm rms stabilityis required for 10 cm s−1 RV precision.

Charge traps occur in discrete locations and arestable so that it is possible to identify and char-acterize them using the pocket-pumping technique(Wood et al. 2014). Because radiation in space pro-duces ongoing deterioration of the detector by cre-ating traps, EUCLID plans to use pocket-pumpingto identify the charge traps and then apply postprocessing corrections. Detectors used for ground-based facilities will not suffer from ongoing degra-dation and can probably be characterized in the labprior to installation in the instrument; the measure-ment of charge traps would allow a correction to beapplied to correct for CTI.

Silicon has a thermal coefficient of expansion of2.6×10−6/C and thus contracts on cooling; a 4k 15-micron thick sensor will shrink by 12 microns whencooled. For large format CCDs it is very importantthat the silicon is bonded to a package with a similarexpansion rate to prevent stresses from building upas the devices are cooled. Silicon carbide (SiC) isan ideal material for CCD packages because it hasa high thermal conductivity and low density withhigh strength, and a coefficient of expansion (4.0×10−6/C) that is well matched to the silicon CCD.Both e2V and STA offer SiC packages for their largeformat CCDs.

The detector technology described in this sum-mary was focused on specific detectors currently inuse in precision optical RV spectrographs. It is byno means an exhaustive analysis of all detector op-tions and features available today. This summaryinstead highlights some of the important types ofconsiderations that need to be made when usingCCD detectors in extreme precision RV spectro-graphs. Through a combination of advancementsin detector technology and better calibration tech-niques, the detector performance required to achieve10 cm s−1precision is within reach.

3.2. Wavelength calibration

Historically, wavelength calibration for astronom-ical observations has been carried out with emis-sion lamps or absorption cells. These wavelengthcalibrators have a price performance that is hardto beat67. A crisis has been precipitated by a de-cision by all suppliers, globally, of hollow cathodelamps to cease the manufacture of Thorium-Argon(ThAr) hollow cathode lamps with metallic cath-odes. All ThAr lamps are now made with thoriumoxide, which introduces impurities into the cathode.These impurities produce undesirable spectral fea-tures — sometime referred to as “grass” — whichquantifiably compromise wavelength calibration ofcross dispersed echelle spectrographs68. These tra-

67 Presentation by Suvrath Mahadevan68 Abhijit Chakraborty has a program to develop ThAr

lamps for astronomers in collaboration with Indias atomicenergy program

20 Fischer et al.

ditional calibrators have inherent limitations thatpreclude a Doppler precision of better than about1 m s−1. The ThAr spectrum changes as the lampages and the emission lines are broad, saturated andirregularly spaced. If the ThAr spectrum passesthrough a fiber that is adjacent to the science fiber,the calibration is made for pixels that are offset fromthe science spectrum and an ultra-stable spectrom-eter is required for a reliable interpolation. Further-more, there is no conventional lamp that providesadequate calibration in the near infrared; chargefrom argon lines diffuses into neighboring pixels andthe thorium lines do not have adequate density.

The iodine reference cell technique is ideal for anunstabilized or general-purpose spectrograph, be-cause the forward modeling technique accounts forvariations in the spectral line spread function andmodeling of the wavelength and dispersion with ev-ery observation. However, the iodine technique hasa precision that is limited to ∼ 1 m s−1 for sev-eral reasons. First, the wavelength region is limitedto 510 – 620 nm, where the molecular iodine linesform, and there are light losses of about 25% fromthe iodine cell. The superimposed absorption spec-trum also masks line profile variations that mightbe diagnostic of stellar activity. In addition, theintrinsic iodine spectrum is required for the for-ward modeling process; at the level required forsub-meter per second precision, the PSF of the high-resolution, high-SNR Fourier transform spectrome-ter (FTS) scans cannot be precisely deconvolved.Furthermore, there are degeneracies between pa-rameters used in the forward modeling (Sproncket al. 2015) to measure Doppler shifts. Even ifthe spectrometer SLSF is stabilized, the Levenberg-Marquardt algorithm used to model shifts in thestellar lines is driven by chi-squared minimizationand will fit out weak telluric contamination or someof the photospheric noise; this adds scatter to themeasurement of the center of mass velocity of thestar.

Both the absolute wavelength of the calibratorand the spectrometer wavelength dispersion mustbe known with incredible precision if instrumentsare to achieve the precision necessary to detectEarth analogs. The reflex velocity induced by theEarth on the Sun is 9 cm s−1, or equivalently, a100 kHz shift in frequency over one year. The idealwavelength calibrator for the detection of Earthanalogs must have a single measurement precision ofabout 1 cm s−1 and must be stable for the expectedduration of the observations (years).

Ideally, light from the calibrator would follow thesame light path through the spectrometer as thestarlight. However, because a superimposed wave-length calibrator will obscure the stellar spectrumand make it more difficult to extract astrophysicalDoppler signals, the calibration source must be spa-tially offset or temporally interleaved with the stel-lar observations. The ideal calibrator would havespectral features that are uniformly spaced (to max-imize information content), unresolved (making ituseful for caliibrating instrumental errors and theinstrumental profile), well separated (ensuring fea-

tures can be cleanly resolved by a high-resolutionspectrometer), and robust to ensure long-term ac-curacy is maintained.

3.2.1. High Precision Wavelength Calibrators

To improve the wavelength calibration precisionfrom lamps or reference cells, several photonicsources, including laser frequency combs, stabilizedetalons, line-referenced electro-optical combs, tun-able Fabry-Perots, and chip-scale microcombs arebeing studied for precision radial velocity spectrom-eters.69 These methods are summarized in Figure16.

LFCs can meet the requirements of an ideal wave-length calibrator. LFCs use femtosecond mode-locked lasers to produce extremely narrow emissionlines (Murphy et al. 2007; Li et al. 2008; Ostermanet al. 2007; Steinmetz et al. 2008). The LFC hasperfectly uniform spacing of its individual emissionline modes; this has been tested to 20 digits of pre-cision (Ma et al. 2004). Moreover, LFCs with broadoctave-spanning spectra can employ self-referencingto measure the carrier envelope offset, which pro-vides a straightforward means to stabilize the ab-solute optical frequency of every comb element, inaddition to the mode spacing. This creates an op-tical synthesizer where the frequency of every combtooth is known with the same precision as the mi-crowave standard (such as cesium clocks or GPSsignals) that provide the reference signal for theLFC. And because such microwave standards canbe traced to the internationally defined SI second,the absolute frequencies of the comb are stable fordecades. For example, when referenced to the freeand wide-spread signals from the GPS (global posi-tioning system) clocks, the long-term absolute fre-quency of the comb could be stable to better than10−11 (i.e., < 0.3 cm/s) (Quinlan et al. 2010; Lom-bardi 2008), meeting or exceeding the precision andstability required for RV planet searches. The ad-vantage of the self-referenced LFC is significant, inthat it directly ties the comb frequencies to interna-tional standards (not artifacts or secondary refer-ences) and leverages the tremendous technologicalinfrastructure of GPS and other global navigationsatellite systems (GNSS).

Among the challenges for LFCs is the innatelyclose mode spacing of typically 0.1 – 1 GHz, whichrequires spectral filtering of ∼ 98% of the modeswith one or more Fabry-Perot (FP) cavities to pro-duce a calibration grid with 10 – 40 GHz spacing(commensurate with the resolving power of a high-resolution spectrometer). Although filtered, the un-wanted modes do not completely go away (Sizer1989; Osterman et al. 2007; Braje et al. 2008; Quin-lan et al. 2010; Ycas et al. 2012). More importantthan the fact that residual side modes remain, isthat the suppressed remnants can be asymmetricand thus potentially shift the line center as seen bythe spectrograph. Careful attention to this matter isrequired in order to provide a comb with sufficientside mode suppression and symmetry such that it

69 Presentation by Scott Diddams


A. Cavity filtering of low-‐rep-‐rate comb

B. Electro-‐op:c modula:on comb

fm

Electro-‐op:c Modulator

no

Comb Output Input

no ± nfm

C. Broadband Fabry-‐Perot cavi:es

•  Most mature technology •  Commercialized and field tested •  S:ll rela:vely complicated •  Requires suppression of un-‐wanted

side modes

•  10+ GHz rates straighNorward •  Presently works best at 1550 nm •  Decoherence at broadest

bandwidths must be considered •  Requires long-‐term stability of

reference laser or self-‐referencing

•  Simple and robust •  10+ GHz rates straighNorward •  Broad bandwidths with flat spectral

envelope •  Demonstrated in the field •  Long-‐term stability is the main

poten:al drawback

E. Direct comb genera:on at 10+ GHz

8 mm

D. Micro-‐resonator combs

•  Op:cal synthesis on a chip •  10-‐1000 GHz are natural spacings •  Presently works best in near IR •  Revolu:onary technology that is

maturing rapidly

•  Direct mode-‐locked laser genera:on at 10+ GHz spacing

•  Systems being explored at 800 nm (Ti:Sapphire), 1000 nm (Yb), and 1550 nm (Er)

•  10 GHz Ti:sapphire technology recently commericialized

Figure 16. Overview of various photonic sources that have been employed, or are being studied, as calibration sources forprecision radial velocity spectroscopy. Frames (A), (C), (D), and (E) are adapted with permission from Osterman et al. (2007);Halverson et al. (2014); Bartels et al. (2009); Li et al. (2012), respectively.

22 Fischer et al.

does not affect the calibration at the level of desiredRV performance (Probst et al. 2014).

Another challenge with LFCs is that spectralbroadening with nonlinear optics is required to gen-erate a comb that spans a broad bandwidth or oper-ates at optical wavelengths. This is straightforwardat the native mode spacing of 0.1-1 GHz, but dueto a corresponding reduction in pulse peak power,significant broadening is more challenging at 10+GHz mode spacing. A complication of this is thatthe side modes that one would like to suppress canbe parametrically amplified during nonlinear spec-tral broadening and can even overtake the principalcomb line (Chang et al. 2010). In some systems,this problem has been overcome by using up to 3concatenated filter cavities in order to provide suf-ficient suppression of unwanted side modes (Probstet al. 2014). Another approach to dealing with para-metric sidemode reamplification is to first spectrallybroaden at the native repetition rate, and then spec-trally filter the broadened comb with a purely linearFabry-Perot filter cavity. This approach has beenundertaken by the teams providing LFC calibratorsfor HARPS-N (Li et al. 2015) and the Penn StateHabitable zone Planet Finder (HPF). For example,with the HPF instrument the original 250 MHz laserat 1550 nm is broadened into the Y and J band witha highly nonlinear fiber (HNLF) at the native repe-tition rate to avoid parametric amplification of theside modes; the signal is then filtered using cavi-ties with low dispersion mirrors. While sidemodesmay still exist, their impact on the spectral calibra-tion can be calculated from simple linear optics andmeasured in-situ (Li et al. 2008).

As an example of how far the LFC technology hasmatured in the past few years, Menlo Systems70

now offers a commercial GPS-locked LFC that isdesigned to reach an accuracy of 4 mm/s at op-tical wavelengths (Probst et al. 2014). The sys-tem uses an state of the art IR fiber laser as a ro-bust seed source. The low repetition rate (corre-sponds to a small mode spacing) of the fundamen-tal femptosecond-laser is increased by mode filteringthrough three FP cavities with finesse of about 3000.Any mode spacing between 1GHz and 25GHz - inmultiple integers of 250MHz - can thus be choosento best fit the spectrographs resolving power. Thefilter narrowband IR spectrum is then amplified inan fiber amplifier and subsequently broadened in aspecially designed photonic crystal fiber (PCF).

The system uses an IR fiber laser with mode fil-tering through three FP combs, signal amplificationand spectral broadening. The use of FP cavitieswith a high finesse of 3000 significantly reduces thesidemodes and thereby minimizes their reamplifica-tion during spectral broadening. The spectrum isflattened to better than a few dB by using a liquidcrystal display with active feedback loop, and theline intensities have low fluctuations over a broadoptical wavelength band of 400 – 700 nm with 15 to25 GHz mode spacing.

Two Menlo system LFCs (with mode spacings of

70 Presentation by Tilo Steinmetz

18 GHz and 25 GHz) were tested during a cam-paign at HARPS from April 8 – 18, 2015. Thecomb illuminated 48 echelle orders with 12,000 linesper channel. The HARPS pipeline produces 1-d ex-tracted spectra for every order and a Gaussian wasused to fit the LFC line centers. Modal noise in thefibers changes the intensity profile of the comb linerecorded on the detector. Fiber agitation is requiredto ensure each comb mode has a smooth, stableSLSF that is not dominated by the speckle inter-ference pattern associated with multimode fibers il-luminated by coherent sources. The wavelength so-lution was determined with an accuracy of 5 cm s−1

after binning 5 exposures, and improved to betterthan 1 cm s−1 by binning 20 exposures.

The Menlo LFC systems have been developed forlong term fail-safe turnkey operation. The systemtakes 10 minutes to change from the off state (laseramplifiers off) to standby mode with the laser on,locks enabled, and high power amplifier off. Fromthe standby mode, it only takes 10 seconds to switchto full operation. There are some expected main-tenance costs: the broadening fiber needs to bechanged once per year and the pump diodes canfail every year or two. These components are builtin as modules that can be easily replaced at a costof a few thousand dollars.

3.2.2. Line-referenced electro-optical frequency combs(LR-EOFC)

In contrast to the mode-locked laser at the heartof the LFC, the LR-EOFC provides a spectrumof lines generated by electro-optic modulation. Apump laser is locked to an atomic or molecular tran-sition and is then phase modulated and amplifiedto produce tunable sidebands with a spacing setby the modulation frequency (Ishizawa et al. 2011).Yi et al. (2015) have demonstrated a stability of< 200 kHz (∼ 0.3 m s−1) with a LR-EOFC at H-band wavelengths. The advantage of this techniqueis that there are no side modes; the system onlygenerates the carrier with frequency sidebands thatcan be referenced to a microwave standard. Combgeneration makes use of commercial off the shelftelecommunication components, but has currentlybeen operated in wavelength bands where opticalamplifiers and phase modulators are available (1-2µm) from the telecom industry.

There is still technology development needed tocreate EOFC broadband combs with constant powerper comb mode, but the same techniques employedby (Probst et al. 2014) should be adaptable to suchcombs. Another challenge is that although the linespacing of the LR-EOFC is fixed to a microwavereference, the seed laser for the comb needs to belocked to prevent wavelength drifts. In presentsystems, this has been provided by a laser thathas its frequency locked to transitions in hydrogencyanide or acetylene (Yi et al. 2015). While thisis straightforward, robust and commercially avail-able, the long-term stability (e.g. months to years)of such molecularly-stabilized lasers is not known.Alternative atomic references for such LR-EOFCscould include narrower saturated absorption tran-


sitions in acetylene (Edwards et al. 2004) or thewell-studied rubidium D1 and D2 lines. The spec-tral broadening is also more difficult at the highmode spacing of the EOFC due to the commensu-rate reduction in pulse energy. However, very re-cently a 10 GHz EOFC centered at 1550 nm hasbeen broadened to octave span and self-referencedsuch that the frequency of its seed laser can alsobe referenced to a microwave standard, and therebyinherit the stability advantages similar to the LFCdescribed above (Beha et al. 2015).

3.2.3. Micro-combs

One of the most exciting developments in laserfrequency comb technology is a new approach togenerate broad bandwidth combs in chip-scale de-vices. Such microcombs use the nonlinear Kerr ef-fect in a dielectric micro-ring to produce a combwith line spacing that can be tuned between 10 and800 GHz without the need for filtering (Del’Hayeet al. 2007, 2008; Kippenberg et al. 2011; Jung et al.2014). While still at a relatively early stage oftechnical development, such microcombs hold thepromise of frequency comb stability and accuracyin a very robust, compact, and potentially inexpen-sive silicon chip package. At present, the main chal-lenges associated with microcombs are related to de-terministic low-noise operation and increased spec-tral span, as required for self-referencing. Addition-ally, the broadest bandwidth microcombs presentlyoperate with mode spacing of 200 GHz, which maytoo high for many high-resolution spectrographs(Brasch et al. 2014), although microcomb technolo-gies exist down to mode spacings of a few GHz (Liet al. 2012). Finally, microcombs generally havenative wavelengths in the near IR (1550 nm) butdoubled or tripled frequencies can shift the combto red and green wavelengths and self-referencingto microwave standards can be used for 2/3 or fulloctave-spanning combs (Jost et al. 2015; Del’Hayeet al. 2015) . The development of microcombs isprogressing rapidly, and it is likely that in the nearfuture this new integrated technology could offer anattractive alternative for precision RV applications.

3.2.4. Fabry-Perot Interferometers

Fabry-Perot interferometers provide a dense gridof lines with a technological approach that is simplerand a price tag that is lower than laser frequencycombs71. However, the systems need to be refer-enced to LFCs, lamps or atomic features (Baueret al. 2015; McCracken et al. 2014; Reiners et al.2014; Schwab et al. 2015; Halverson et al. 2014).Precise vacuum and temperature controls are gen-erally required to stabilize the devices and it is im-portant to track and correct for drifts in the disper-sion.

Etalons are fixed length Fabry Perot interferome-ters that produce broadband optical combs whenilluminated with a broad bandwidth white lightsource. The HARPS etalon has Zerodur spacers to

71 Presentation by Ansgar Reiners

control the index of refraction, scrambled uniformillumination, and stringent temperature and pres-sure control (Wildi et al. 2012). These broadbandsources have adjustable mode spacing, simplicityand good short-term stability. The night-to-nightdrift of the etalon lines is about 10 cm s−1and thestability over 60 days is about 1 m s−1 (Wildi et al.2012). Near-IR fiber etalons have achieved betterthan 1 m s−1 stability over 12 hour timescales. Inmost cases, the frequency drift is not directly mea-sured or corrected. Reiners et al. (2014) have sug-gested including a gas cell (e.g., Rb) stabilized laserto track frequency drifts and to derive wavelengthoffset corrections.

Tunable FPIs that are white-light illuminated alsoproduce a broadband comb of lines like the etalon,however they employ feedback to stabilize the wave-length zero point of the comb with locking to opticalatomic standards like the rubidium D2 line at 780nm. In order to provide sufficient precision, the FPcavity finesse needs to be high (at least 50 – 100)at the wavelength of the laser lock, while the finessecan be decreased via engineering of the coatings toprovide broad bandwidth coverage at other wave-lengths.

Reaching 1 cm s−1 wavelength calibration preci-sion is a grand challenge. By way of comparison, theRamsey fringe of the cesium clock has a line widthof about 1 Hz and a microwave oscillator can belocked to the central fringe with a precision of 10−13

in one second; and with averaging one can achieve afractional measurement uncertainty of about 10−16

(Heavner et al. 2014). In terms of splitting the line,this is the most precise spectroscopy that has everbeen done and allows the line centroid to be de-termined to one part in 1,000,000. However, thismeasurement is carried out in the lab with state-of-the-art microwave sources and laser-cooled cesiumatoms. By comparison, astronomers who aim toreach 1 cm s−1 precision (equivalent to 15 kHz res-olution in the visible) are using stellar spectral fea-tures that are many GHz wide. If successful, thisgrand challenge would rival the line-splitting preci-sion of work done by the AMO physicists; however,with the additional challenges of the accurate collec-tion, dispersion and recording (at the photon count-ing level) of the relatively broad and faint spectralabsorption lines.

3.3. Fibers and scrambling

The spectrograph projects the image of the en-trance slit onto the detector as a function of wave-length. Images of the telescope pupil (far field) alsoilluminate the echelle and other optics; alt-az tele-scopes that employ image derotators can end upwith rotating spider mounts on the echelle. Anyvariability in the illumination of the spectrographoptics (say, because of guiding errors or changesin seeing) manifests as variability in the spectrum.This is a severe limitation for precise radial velocitymeasurements. Optical fibers provide an importantbenefit; not only do they offer a flexible way to cou-

24 Fischer et al.

ple light from the telescope into a spectrograph72,they also offer the additional advantage of providinga more stable input illumination (Heacox 1986).

However, light will exhibit modal noise when trav-eling through a multi-mode fiber; this is particularlyimportant for coherent light sources like lasers orlaser frequency combs. Modal “noise” is a manifes-tation of mode coupling that produces an irregularintensity distribution emerging from a fiber (Bau-drand & Walker 2001). When a laser is coupled intoa multi-mode fiber, the light travels in many modesalong the fiber; these modes are out of phase witheach other, resulting in the complicated speckle in-terference pattern that illuminates the spectrographoptics. If nothing moves, the spatial speckle patternis time invariant. However, stresses or motion of thefiber cause temporal shifts in the speckle pattern.When multi-mode fibers are used, some effort is re-quired to scramble, or mix the modes. This can bedone by shaking or agitating the fiber (Lemke et al.2011; McCoy et al. 2012; Plavchan et al. 2013b).

When multi-mode fibers are used, some effort isrequired to scramble, or mix the modes. Many ex-periments have been carried out showing that whenlight is injected into a multi-mode fiber with a cir-cular cross-section, the output intensity distribu-tion is not completely independent of the input il-lumination. Circular fibers have reasonably goodazimuthal scrambling, but poor radial scrambling.This results in variable illumination of the slit andspectrograph optics, and these undesired perturba-tions are imprinted in the spectrum, adding noiseto the data.

The ideal optical fiber has high throughput anda well-scrambled output that is independent of theway that light enters the fiber. To achieve hightransmission, the fiber length should be minimized;AR coatings can be applied to the fiber faces, andthe focal ratio degradation (FRD) can be minimizedby controlling the light injection cone to match thenumerical aperture or acceptance angle of the fiber.Some FRD will still occur during the fiber fabrica-tion and mounting process, from micro-roughnessand micro-bending, subsurface damage and otherinduced stress in the fiber (Ramsey 1988; Carrasco& Parry 1994; Avila 1998). The use of connectorscan also be a significant source of FRD and soft, lowshrinkage glue must be used to avoid strains. Fibermanufacturers do not typically measure FRD.

The use of fibers with non-circular cross-sections(octagonal, square or rectangular) break the sym-metry of the wave guide and provide an easy way toscramble modes (Chazelas et al. 2010; Avila 2012;Spronck et al. 2012a). Scrambling performance isimproved by exchanging the in-focus near field (theimage) and the out of focus far field (pupil illumina-tion) between two fibers (Hunter & Ramsey 1992).Variations in the fiber near field directly lead to fluc-tuations in recorded spectral features while varia-tions in the far field change the illumination of spec-trometer optics, leading to distortions in the PSF.

72 Presentations by Paul Fournier and Suvrath Mahadevanand breakout session led by Gabor Furesz and Paul Fournier

Both effects lead to spurious velocity shifts and aredetrimental to extreme precisoin measurements.

Far-‐field Output

ΔdNF

Near-‐field Output Input

Δdin

Outpu

t barycen

ter

Input barycenter Δdin

Δdout Le5

Right

ΔdFF

Figure 17. Cartoon illustrating measurement of scramblinggain by translating the test fiber across a fixed illuminationspot and recording the output at each position. Measure-ments are made for the fiber near field and far field. (Cour-tesy of Sam Halverson)

As shown in Figure 17, the scrambling gain ofa system — for the near field — can be measuredby taking the ratio of the displacement of the lightsource at the entrance of the fiber to the residualshift in the center of mass intensity distributionof the fiber output (Avila & Singh 2008). Scram-bling gains of up to a few hundred are achieved forpure circular fibers; octagonal core geometry yieldsa scrambling gain of up to about 1000, while octago-nal fibers with double scramblers exhibit ∼ 10−20kscrambling gain (Feger et al. 2012). Effects of in-adequate scrambling in the far field can only beevaluated, by modeling how the observed pupil illu-mination irregularity propagates through an opticalsystem (Sturmer et al. 2014). This can be done byray-tracing through the instrument optical model,which leads to an estimate of the RV measurementsensitivity to far field variations. It has to be noted,though, that predicting the exact behavior and ef-fects of the far field for an as-built instrument isalmost impossible. It is because the as-built aber-rations can significantly effect how the far field prop-agates through an optical system. Eliminating sen-sitivity of the as-built spectrographs, or variationsin the far field of fiber systems, is key to furtherimprove PRV performance.

Single mode fibers (SMFs) offer an interesting al-ternative to multi-mode fibers (Crepp 2014). Trueto their name, SMFs propagate a single mode (actu-ally, two polarization modes are possible) of light; asa result, the fibers deliver a uniform intensity distri-bution to the spectrometer — the SLSF has unpar-alleled stability — and there is no modal noise fromthe fiber. The challenge is coupling light into thesmall 5µm diameters of the SMF, however, extremeadaptive optics systems with high strehl ratios likethe Subaru Coronagraphic Extreme Adaptive Op-tics (SCExAO) have reached fiber coupling efficien-cies of 68% with an 8µm fiber core (Jovanovic et al.2014).

4. EXTRACTING KEPLERIAN SIGNALS


Once the Doppler shift has been measured in aspectrum, the time series velocities are analyzedfor Keplerian signals. At this point, there are sys-tematic error sources that add to the formal errorsto obscure the detection of low amplitude systems.Telluric lines (from the Earth’s atmosphere), stellaroscillations, sunspots, plage, granulation and merid-ional flows, all modify the shape of spectral lines asa function of time, and produce obscuring velocitysignals.

In many cases, astronomers have not been ableto physically distinguish between stellar jitter andcenter of mass velocity with activity diagnostics;instead, some magnitude of the jitter is added inquadrature when using chi-squared minimization forfitting for Keplerian signals in radial velocity timeseries data. Regardless of whether the magnitudeis assumed (e.g., based on spectral type) or inferredfrom the data, this approach is clearly insufficient;it implicitly assumes that jitter can be representedas a white noise source and does not leverage in-formation about the time-coherence in the stellaractivity signal.

Another approach for mitigating stellar activity isto first measure apparent radial velocity shifts (ne-glecting activity) and then apply a bandpass filterin the Fourier (frequency) domain with the aim ofremoving signals due to stellar activity. This ap-proach has been used with some success (Howardet al. 2011, 2013; Fulton et al. 2015). However, theFourier components are fixed; since the underlyingnoise sources change in time, the extracted signalwill be distorted. In the best case, this introducessmall systematic errors in the orbital parameters. Inthe worst case, true planetary signals are attributedto stellar activity or the analysis process introducesspurious coherent velocity variations that are mis-taken for planets.

The following cases offer a representative sampleof putative planetary systems that have been de-bated, and the different approaches applied by thecommunity:

• GJ 581, with emphasis in the case of GJ 581dplanet candidate initially described Mayoret al. (2009). Subsequent arguments relat-ing the signal to stellar rotation, activity andthe statistical treatment of the problem can befound in Robertson et al. (2014), and Hatzes(2015).

• α Cen Bb, which corresponds of a signal of∼ 0.5 m s−1 on a time-series strongly dom-inated by noise with structure. The initialclaim was made in Dumusque et al. (2012),and some doubts on the series whitening ap-proach and caveats about statistical signifi-cance can be found in Hatzes (2013) and Ra-jpaul et al. (2016).

• HD 41248b & c. These two Doppler signalswere initially attributed to a pair of resonantplanets in Jenkins et al. (2013). Argumentsin favor and against of activity induced vari-

ability were given in Santos et al. (2014) andJenkins & Tuomi (2014).

4.1. Statistical Analysis Techniques

The interpretation of radial velocity data increas-ingly relies upon statistical analysis techniques73.In medical fields, there has been a near crisis in theability to replicate the statistical analysis of scien-tific results (Ioannidis 2005). This is in part becausescientists often know what results they expect andthis can influence their interpretation, but it is alsobecause of the misuse of null hypothesis tests, suchas false alarm probability (FAP) and Kolmogorov-Smirnoff analysis. The repercussions can include fi-nancial cost, wasted time re-assessing false discover-ies, and public mistrust of science. Our communityseems to appreciate the importance of reaching outto statisticians and developing more sophisticatedapproaches to data analysis.

The FAP test is a common tool for testing thereality of a Keplerian signal in radial velocity data(Marcy et al. 2005). This statistical test is usuallycarried out with a bootstrap Monte Carlo simula-tion. A Keplerian fit to the initial prospective sig-nal is made and the χ2

ν value is saved. The velocitydata are then scrambled, while retaining the timesof the observations and the errors; for each realiza-tion, a blind search is made for the best Keplerianvalue and the resulting χ2

ν is recorded. If a signalwas really contained in the original velocities, thenthe subsequent scrambled data are likely to havepoorer χ2

ν values. This approach has the advantageof characterizing the impact of non-Gaussian sys-tematic errors in a data set. The reported FAP isthe fraction of Monte Carlo realizations that yieldedχ2ν values lower than the original set. As noted by

Marcy et al. (2005), the FAP test specifies the prob-ability that incoherent noise could have yielded asuperior Keplerian fit by chance. It does not neces-sarily show that the planet interpretation is correct— the signal could arise from window functions orstellar activity or systematic instrumental errors.

Statisticians prefer to call this a p-value becausethe language “false alarm probability” seems tocarry an implication about the reality of the signalor the planet interpretation. The p-value tells usabout the probability of obtaining a particular sig-nal given the null hypothesis (i.e., given the assump-tion that the data are merely incoherent noise).

4.1.1. Bayesian Analysis

The field of radial velocity exoplanet detectionhas undergone a dramatic shift over the past twodecades74. For many early years, “discovering aplanet meant that astronomers had: 1) identifieda possible model to explain a series of Dopplerobservations as due to a planet and measurementnoise, and 2) rejected the null hypothesis that asimpler model without the planet could reasonablyexplain the data. This approach worked well forplanet surveys that focused on well-characterized

73 Presentation by Tom Loredo74 Presentation by Eric Ford

26 Fischer et al.

and quiet FGK dwarf stars with radial velocityamplitudes that were much larger than individualDoppler errors and plausible stellar activity signals.Astronomers did not want to risk incorrect detec-tions near the threshold of their errors. When indoubt, the solution was to collect more observations.

More recently, astronomers have begun adoptinga Bayesian framework for characterizing the massesand orbits of exoplanets, as well as performing rigor-ous model comparison to quantify the evidence forplanet detections. In this framework, the criteriafor detecting a planet is that the model including aplanet has a higher posterior probability than themodel or models without a planet.

The paradigm shift to adopt Bayesian inferencehas been fueled by the appreciation for greater sta-tistical rigor, more accurate estimates of parameteruncertainties, and the greater sensitivity possiblewith a rigorous statistical analysis. Perhaps mostimportantly, a Bayesian approach allows us to quan-titatively answer questions that we actually want toask. For example, we can quantify the evidence forthere actually being N planets, rather than just re-jecting the null hypothesis. Many statisticians liketo think of Bayesian model comparison as a quan-titative ”Occam’s razor” for comparing competingmodels. Others prefer to make principle decisionsusing a utility function after after marginalizing overuncertainty in models and parameters.

Of course, simply switching to a Bayesian frame-work does not solve all our problems. One barrierto widespread adoption of Bayesian method is thenecessity of computing multidimensional integrals.This can be computationally expensive, particularlyfor models with many parameters and when com-paring the evidence for multiple competing models.This barrier has been largely overcome for parame-ter estimation applied to Doppler surveys thanks toincreased computational power and improved sam-pling algorithms. A second barrier is the intellectualinvestment required to understand the underlyingalgorithms. For example, the choice of the proposaldistribution in Metropolis-Hastings Markov chainMonte Carlo (MCMC) algorithms often makes thedifference between fast and extremely slow conver-gence. Therefore, one should always check multipleconvergence diagnostics to identify any signs of non-convergence. Bayesian model comparison is partic-ularly computationally expensive, so it is temptingto use short-cuts, such as the Bayesian InformationCriterion (BIC). The BIC was designed to identifythe most probable model in abundant data settings,but its approximations are not sound for quantifyingmodel uncertainty in small or modest data settings,as arise in Doppler planet hunting. Fortunately, theexoplanet community is gradually gaining experi-ence with successful application of Bayesian meth-ods to interpret observations.

A third barrier is the misperception that the needto explicitly choose priors is an inherent weakness ofthe Bayesian approach. If anything, it is a featurethat the Bayesian framework clarifies the assump-tions before entering into an analysis and providesa straightforward path for testing the sensitivity of

conclusions to those assumptions. Of course, it isuseful to choose priors wisely. Often physical in-tuition, such as symmetries, or knowledge of previ-ously identified planetary systems, can inform thechoice of priors. A general principle is to err onthe side of overly broad priors. When in doubt,one should perform a sensitivity analysis to quantifywhether key results would change for different rea-sonable choices of priors (Tuomi & Anglada-Escude2013).

For complex models it is also wise to verify thatone’s model works well on simulated data to ensurethat the chosen priors are appropriate for a givenapplication. For model checking refer to Gelmanet al. (2013). Too often people using Bayesian meth-ods ignore model checking, because it doesn’t havea neat and tidy formal expression in the Bayesianapproach. But it is no less necessary to do goodness-of-fit type checks for a Bayesian analysis than it isfor a frequentist analysis.

A more fundamental challenge is that one mustidentify an appropriate model for interpreting ob-servations, regardless of whether using a frequentistor Bayesian approach. Analysis is straightforwardwhen the physical model is known, but inference ismuch more challenging when the model is physicallyincomplete. Early searches for giant planets appro-priately considered only Keplers laws, but modernsearches for low mass planets are significantly af-fected by stellar activity, especially when surveysinclude active stars. Unfortunately, we do not cur-rently have a practical model of stellar activity, noreven a clear path to such a model. Activity indica-tors sometimes correlate with velocities, but this isnot always the case.

The problem of model incompleteness has beenone cause for apparent contradictory results con-cerning signals that seem to be highly significant butare close to the measurement uncertainty level. Forexample, a discontinuity of a few m s−1 (eg. from achange of the gas cell or Th Ar lamp) will typicallybe much better fit by a sinusoid than a model withwhite noise only. If the model could account for realdiscontinuities, it would be clear that the additionof a sinusoid yielded a poorer match to the data. Ina Bayesian context, this leads to an overestimationof the evidence because the sum over the modelsis only done for a subset of them. Thus, evidenceratios should not be interpreted as definitive prooffor detections. This issue affects the model prob-abilities even if the multidimensional integrals areexecuted exactly. It is also related to the discussionabout prior choices, in the sense that zero probabil-ity is implicitly assigned to a large number of alter-native models. One way to mitigate this confusionis to secure minimal evidence ratio thresholds basedon simulated data that is as close as possible to thereal data. A more informative, but more resourceintensive approach, is to confirm or refute signals forthe same star using different instruments or tech-niques. For example, highly significant candidatesignals were spotted in UVES data, but could notbe confirmed with HARPS measurements (Tuomiet al. 2014). When applied to a large enough sample


of objects, it is possible to construct more completemodels or design a properly calibrated probabilitythreshold system to identify reliable exoplanet sig-nals.

It is useful to keep in mind that “All modelsare wrong; some models are useful” (attributed toGeorge Box 1979). Even after one verifies that amodel and algorithm perform well when analyzingsimulated data, one must still verify that they areuseful for actual astronomical observations. Thiswill require extensive astronomical observations, ex-tracting additional information from each spectrumto probe stellar activity, new models for joint radialvelocity and activity data, and improved samplingalgorithms. Therefore, future Doppler detectionsof low-mass planets will require very large amountstelescope time. In an effort to make efficient useof precious astronomical resources, it is natural toseek out the most powerful statistical methods toincrease the sensitivity to low-mass planets and sci-entific impact of Doppler surveys. Our commu-nity must identify realistic science goals, design ob-serving strategies optimized to match those goals,and persuade time allocation committees to allo-cate sufficient time to characterize long-term andshort-term stellar variability and systems of multi-ple planets.

We will likely be forced to learn to live with un-certainty. Given our upcoming requests for largeinvestments of astronomical observatories, we willneed to publish observations of both strong andmarginal detections and learn to responsibly con-vey the limitations of our studies to other scientistsand the public. This greater cultural shift towardsemphasizing reproducible research is essential to thecredibility of planet detections, astronomy and sci-ence in general.

4.1.2. Gaussian processes

A Gaussian process regression is a powerful statis-tical analysis technique (beyond simply minimizingchi-squared in our models) that can be applied tothe detection of weak signals in the presence of rednoise75. Both the systematic and correlated noisesources can be included in the model and should befit simultaneously with the signal (not sequentially)and marginalized out to correctly remove or mini-mize the parameters that are not of interest and tothereby avoid distorting the underlying signals.

Chi-squared is defined as the sum of the squareddifferences between the data points, yi, and themodel (mi are theoretical points for a Keplerian sig-nal), divided by the independent uncertainties σi

2,as shown in Equation 3. It is also possible to switchfrom summation to vector notation and to relatechi-squared to the natural log of a Gaussian likeli-hood function, L, by writing the difference of thedata76 and model as a vector difference with thenoise represented as a diagonal co-variance (V ) ma-trix (Equation 4).

75 presentation by David Hogg76 Also see the presentation by Guillam Anglada-Escude

χ2 ≡∑i

[yi −mi]2

σi2(3)

χ2 = [y −m]T · V −1 · [y −m]

V = C

Cij = σi2δij

−2 lnL = [y −m]T · V −1 · [y −m] + ln detV +N(4)

If there are multiple components to the (Gaus-sian) noise, their covariances add in the noise co-variance tensor, V . For example, if a second noisesource is added through the covariance tensor, Q,the variance tensor becomes V = C + Q as shownin Equation 5. This approach is straight forwardand allows for the analysis of very high dimensionalspaces and high fidelity signal recovery.

−2 lnL = [y −m]T · V −1 · [y −m] + ln detV +N

V = C +Q

Cij = σi2δij

(5)

Systematic sources of error can be modeled as thesum of M basis vectors with off-diagonal terms. Ifa Gaussian prior can be placed on the linear am-plitudes, the systematic noise can be representedby a rank-M covariance matrix and marginalizedto obtain a best fit. For example, in the case ofKepler photometric time-series data, the systematicnoise sources (e.g. from the spacecraft jitter) can bemodeled as the sum of M basis vectors; in this case,the basis vectors might contain information aboutthe behavior of other stars.

−2 lnL = [y −m]T · V −1 · [y −m] + ln detV +N

V = C +B · Λ ·BT

B = block of M basis vectors

Λ = M ×M prior variance(6)

The noise tensor, V , encodes beliefs about thecontaminating Gaussian noise and it can be de-signed to include a component for complex system-atic noise. The models may be enormous, but it isimportant to fit for all of the nuisance parameters.For expressions like V in Equation 6, it is numeri-cally safer to factorize the matrix than to computeinverse matrices or determinants directly.77

Baluev (2013) treated time-correlated red noisesources as a Gaussian random process with an ex-ponentially decaying correlation function and foundthat some of the announced planets around GJ 581were illusions of red noise78. Good statistical meth-ods for handling red noise sources from stellar pho-

77 In the python numpy package, never use inv, alwaysuse solve; never use det, always use slogdet.

78 Presentation by Roman Baluev

28 Fischer et al.

tospheres and instrumental errors are needed beforewe can determine the ultimate limitation to Dopplerprecision from stellar noise (Baluev 2015). In recentyears, Bayesian inference has become a central toolfor the study of planetary or stellar signals in anyRV dataset (e.g., Faria et al. 2016).

4.2. Photospheric velocities: stellar jitter

The contributions to radial velocity measure-ments that arise from photospheric motions are gen-erally termed “stellar jitter” and are currently anobfuscating source of time-correlated noise for RVmeasurements that aim to detect weak Kepleriansignals. The typical magnitude of stellar jitter is1 – 3 m s−1 for chromospherically quiet stars (Du-musque et al. 2011). Stellar jitter is caused by a va-riety of physical processes79. Unfortunately, thereis no general analytical model for photospheric sig-nals. Activity signals manifest as both incoherentand quasi-periodic variability.

Stars that are quiet can rather suddenly becomemore active (Santos et al. 2014). For example Fig-ure 18 shows radial velocity measurements of themoderately active star, Epsilon Eridani. Velocitieswere obtained with the CHIRON spectrograph andare shown for two different epochs. In 2012, a 50 daytime series of radial velocities (from JD 2456200 toJD 2456250) has an rms of 13.6 m s−1 and showsperiodogram power that peaks at 11.18 days, con-sistent with the 11.35 and 11.55-day spot rotationalperiod observed in 2005 using the Microvariabilityand Oscillations of STars (MOST) satellite (Crollet al. 2006). The 11 day radial velocity signal in Ep-silon Eridani has been shown to correlate with pho-tometric variability using MOST satellite and con-current radial velocity measurements with the CH-IRON spectrograph in 2014 (Giguere et al. 2016).This signal weakens over time with the rms drop-ping to a 3.37 m s−1 and is not seen in the peri-odogram of velocities obtained in 2014 (from JD2456980 to JD 2457030).

Cool stars have convective envelopes that supportacoustic modes (p-modes) with velocity variationsat the level of a meter per second on timescales ofseveral minutes (Kjeldsen & Bedding 1995). Gran-ulation in the photosphere is a manifestation ofthousands of rising warm gas cells surrounded bya network of descending cool gas (Del Moro 2004);kilometer-per-second velocities average out to someextent, leading to a net blueshift of a few meters persecond in Sun-like stars (Gray 2009) and operate ontimescales from hours to a few days. The granula-tion blueshift depends on stellar properties and fora given star varies as photospheric magnetic fieldsevolve (Dumusque et al. 2011).

Active regions on stars arise from magnetic fieldsthat thread the photosphere. Magnetic fields coa-lesce into flux tubes, producing faculae (plage is thechromospheric counterpart) that are bright whensmall and dark when large (spots). The typical ac-tive structure that is observed on the Sun is com-

79 Presentation by Damien Segransan

posed of a dark spot in the center with strong mag-netic fields and large flux tubes, surrounded by fac-ulae. On average the faculae region is ten timeslarger than the dark spot region (Chapman et al.2001). Magnetic fields act locally to inhibit convec-tion, which suppresses the net convective blueshiftinduced by convection (Dravins 1982). A dark spotand a faculae are therefore redshifted regions rela-tive to the quiet photosphere (Cavallini et al. 1985).

Magnetic flux tubes form and decay on timescalescomparable to the stellar rotation period, typicallyseveral days to a few months. Dark cool spots man-ifest as missing flux at the position of the spots.This breaks the symmetry of a rotationally broad-ened line, producing an east-west line asymmetry asa function of the rotational phase. This producesa net velocity shift and also changes the FWHMof all the spectral lines, and therefore the FWHMof the spectral CCF profile. As dark spots andbright plage evolve and rotate across the visiblehemisphere, they alter the weighting of projectedvelocities (Dumusque et al. 2014; Saar & Donahue1997).

Long term magnetic cycles change the convectionpatterns (e.g. inhibiting convection), thus changingline-bisectors and line-shifts (Dravins 1982). Thesecycles have timescales from a few hundred days toseveral years (Meunier & Lagrange 2013; Santoset al. 2010), comparable to the orbital periods ofreal Jupiter like planets.

It is easier to obtain high precision on very shorttimescales where the changes in the photosphericvelocities that imprint variability in the spectralline profile are minimized. Bourrier & Hebrard(2014) devised an empirical correction for an ob-served wavelength dependent velocity trend and ob-tained residual velocity rms of 30 cm s−1 when fit-ting the Rossiter-McLaughin effect for 55 Cancrie80. Long term precision is more difficult to main-tain because the many sources of stellar jitter addspurious temporally correlated scatter to the centerof mass Doppler velocities. These noise signals are afunction of spectral type (lowest jitter for K dwarfsand larger for warmer stars) and evolutionary stateof the stars (higher for subgiants or more evolvedstars). Fortunately, stellar jitter has two importantproperties that can be exploited:

• it is not a persistent Keplerian signal; it waxesand wanes, it is not perfectly coherent, andit varies on timescales that are different fromcenter of mass (COM) radial velocities

• the underlying physical phenomena thatspawn jitter have detailed spectroscopic, pho-tometric, wavelength dependent, and polar-ization signatures that are in principle distin-guishable from simple wavelength shifts dueto Keplerian Doppler shifts.

Figure 19 compares the full disk solar spectrumat times of low and high activity, overplotting the

80 Presentation by Guillaume Hebrard


Figure 18. Radial velocity measurements of Epsilon Eridani using the CHIRON spectrometer at CTIO have internal errorsof 1 m s−1. In 2012 (top panel) a clear 11.4-day periodicity is seen, which matches the rotation of the star. The rms variability

is 13.6 m s−1This signal attenuates over time and in 2014 (bottom panel) was not detectable. (Courtesy of Debra Fischer)

30 Fischer et al.

magnified difference spectrum (red) on the averagesolar spectrum (black). Individual lines repond dif-ferently to changes in photospheric activity and pro-vide a way to distinguish surface phenomena fromKeplerian velocities.

5377 5378 5379 5380 5381 5382 5383

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Figure 19. Full disk solar spectrum and the magnified dif-ference between active and inactive states. Individual linesrespond differently to activity changes, providing a way tohelp distinguish surface phenomena from Keplerian velocityshifts (Courtesy of Jeff Valenti).

4.2.1. Spectral Diagnostics of Jitter

Astronomers have used diagnostics of stellar ac-tivity to decorrelate photospheric signals and radialvelocities81. These diagnostics include measure-ments of emission in the cores of Ca II H&K spectrallines, changes in the spectral line bisector, or vari-ability in the full width half maximum (FWHM) ofthe spectral cross correlation function (CCF; Du-musque et al. 2014). Emission in the cores of H α,the Na-D lines, or the sodium doublet at about 819nm (Schlieder et al. 2012) provides more informa-tion about stellar activity for M dwarfs, which donot have much flux at the Ca H&K wavelengths82.

The variations in the line bisector and FWHMare induced by active regions and are increasinglypronounced with stellar rotation. However, whenlooking at slow rotators like the Sun, it is more dif-ficult to resolve the tiny variations in the bisectorand FWHM, making these ineffective diagnostics ofstellar activity (Desort et al. 2007; Dumusque et al.2014; Santos et al. 2014). Observing with higherspectral resolution and with high sampling shouldhelp and additional spectroscopic diagnostics mustbe found. Currently, if significant signals can be de-tected in activity diagnostics, it is at least a warningthat prospective Doppler signals may be spurious(Queloz et al. 2001).

Two important upgrades were made to theHARPS pipeline that improved the precision ofspectroscopic activity diagnostics. First, it wasfound that subtraction of scattered light (especiallyfrom the ThAr calibration fiber) near the Ca II

81 Presentation by Nuno Santos82 Presentation by Paul Robertson

H&K lines improved the logR′HK measurements(Lovis et al. 2011). Second, the blue-to-red flux ra-tio varies because of weather conditions; imposinga fixed spectral energy distribution to the star be-fore calculating the CCF vastly improved the CCFbisector and FWHM diagnostics83 (Cosentino et al.2014). The very stable spectral line spread functionhas been a decisive advantage for high-fidelity spec-trographs like HARPS that allows for recovery ofspectroscopic activity indicators, even for chromo-spherically quiet stars.

A caveat is that the activity indicators can beaffected by instrumental effects and should not beused blindly. Over the past decade, there has beena small focus drift in HARPS that might have beenmis-interpreted as a drift in FWHM from instrinsicstellar variability. Because this was seen for manystars, it is clearly an instrumental effect and wasfitted out. In another example, low frequency mod-ulation in the radial velocities was observed as afunction of air mass in the star 18 Sco (and hasalso been seen in other stars). The source of thisvariation is ambiguous; is this granulation? seeing?SNR?

The stellar spectrum contains a wealth of infor-mation that remains to be explored. The physicsof stellar atmospheres should guide us in devisingclever spectroscopic diagnostics and different starsmay require different approaches. Regions of faculaeand spots in the Sun have been modeled and demon-strate unequivocally that these features produce ve-locity variations of a few meters per second over oneactivity cycle (Lagrange et al. 2010; Meunier et al.2010; Borgniet et al. 2015). Similarly, Haywood etal. (2015; poster at the EPRV meeting) shows corre-lations for simultaneous Solar Dynamic Observatorydata and HARPS velocity measurements. Otheruseful approaches might include Zeeman modelingof the magnetic field strength (Reiners et al. 2013)and magneto-hydrodynamic simulations to betterunderstand the effect of granulation on line forma-tion (Cegla et al. 2015). The HARPS-N solar tele-scope will provide excellent data to understand fur-ther the effect of stellar activity on radial velocitymeasurements (Dumusque et al. 2015b). Studieslike these associate physical phenomena with radialvelocity variations and offer an important meansfor disentangling photospheric signals from centerof mass velocities.

4.2.2. Identifying Jitter with Doppler Imaging

Stellar astronomers carry out Doppler imaging onrapidly rotating stars by inverting time series spec-tral line profile information84. Conventional wisdomsuggests that it is not possible to carry out Dopplerimaging on slowly rotating stars, but progress hasrecently been made by employing principal compo-nent analysis of the CCF for time series radial ve-locity data from HARPS.

To motivate this analysis, solar synoptic mag-netograms from June 2012 were used as a model

83 Presentation by Christophe Lovis84 Presentation by Thorsten Carroll


for the magnetic field on the surface of the Sun.Magneto-convection simulations were then used tosimulate the temperature and velocity structurewith one degree spatial resolution using the MU-RaM code (Vogler et al. 2005) and a radiative trans-fer code was used to produce composite spectra for156 absorption lines at each of 40 rotation phases.A singlular value decomposition (SVD; analogousto the CCF) of the time series spectra revealed anapparent radial velocity variation (induced by thephotospheric surface phenomena) with the same pe-riod as the stellar rotation and an amplitude of∼ 1.5 m s−1. Contributions to the simulated photo-spheric velocity variations came from the magneticfield (from Zeeman splitting; < 1% effect), spots(<10% effect) and plage (∼ 90% effect). The 40time series CCF profiles were then inverted to pro-duce a reasonably realistic reconstruction of the sur-face features that were initially used to generate thespectra.

In his workshop presentation, Thorsten Carrollreported promising progress using principal compo-nent analysis (PCA) on the CCF of HARPS spectrafor the slowly rotating star HD 41248 (rotation pe-riod of 25 days). This star is particularly interest-ing because of confusion about whether radial ve-locities are Keplerian signals or a red noise sourcefrom photospheric signals (Jenkins et al. 2013; San-tos et al. 2014; Jenkins & Tuomi 2014). Carrollfound that the first PCA eigenvector contains al-most the entire radial velocity signal. The spectrallines from HD 41248 were then divided according tolow (< 1.25eV) and high (> 2.5eV) excitation po-tential (EP). The CCF of both sets of lines showedessentially the same phase-folded periodicity in theradial velocity; however, an offset in the velocityzero point was observed. Velocities derived fromthe CCF for the high EP lines were blue-shifted byabout 150 m s−1 relative to the low EP lines be-cause they form deeper in the stellar atmosphereand where the convective velocities are higher. Theeigenfunctions of the CCF contained additional in-teresting information; the first eigenfunction for thehigh EP lines showed an asymmetry (a broadeningeffect), while the first eigenfunction for the CCF oflow EP lines was symmetrical. Thus, the spectralline shape varied with depth in the stellar atmo-sphere in a way that is consistent with the radialvelocity signature — this is an impressive demon-stration that the CCF velocity signature here comesfrom convection, not from a center of mass velocityof the star. Thus, radiative transfer with magneto-convection simulations may ultimately offer an im-portant foundation for understanding photosphericvelocities as we move toward 10 cm s−1.

4.3. Near Infrared Radial Velocities

For sunlike stars with spots, there may be an ad-vantage to observing at near infrared wavelengths85.The temperature of a spot can be 500 to 1500Kcooler than the surrounding photosphere. If weadopt a toy model of two blackbodies with tem-

85 Presentation by Lisa Prato

peratures representing the spot and the stellar pho-tosphere, the contrast between the emitted lightis much higher at blue wavelengths than at redwavelengths. As a result, the radial velocity mod-ulation for spotted stars has larger amplitudes inthe optical, compared to near infrared wavelengths,an effect that has been well-studied in young ac-tive stars (Mahmud et al. 2011; Prato et al. 2008).Because of the importance and potential of RVmeasurements at NIR wavelengths, many futureinstruments, including CARMENES (Quirrenbachet al. 2014), the Infrared Doppler (IRD) spectro-graph for high-precision radial velocity measure-ments (Tamura et al. 2012), SPIRou (Artigau et al.2014a), and HPF (Mahadevan et al. 2012), are be-ing designed to operate in the NIR.

Most of the activity indicators that are used to-day are simply not as precise or as efficient as weneed them to be86. There is not a single activity in-dicator that is 100% efficient and it is unrealistic toassume that all signals without activity correlationsare correct. One way to confirm the planet interpre-tation is to measure Doppler velocities in the nearinfrared; the precision for the NIR radial velocitiesis now at the level of about 2 m s−1 (Figueira et al.2010b; Crockett et al. 2012).

Huelamo et al. (2008) showed that the radial ve-locity variations using optical spectroscopy of a starin the TW Hydra association disappeared whenobserved with CRIRES using near infrared wave-lengths. Infrared CRIRES data were also used toconfirm that variations in several K giants werecaused by planetary companions (Trifonov et al.2015). Bean et al. (2010) used an ammonia gas cellfor wavelength calibration on CRIRES to achievea Doppler measurement precision of 5 m s−1 onM dwarf stars87. They found that the noise floorfor NIR precision was set by telluric contamination;there was no NIR wavelength region in the CRIRESbandpass that was free of telluric lines at the levelneeded to detect habitable planets, even around Mdwarfs.

CRIRES is fed with light from an AO system,which helps to stabilize the slit illumination. Whilethe slit fed spectrograph is ideal for backgroundsky subtraction, intensity scrambling is not possi-ble, so the spectrograph has variable illuminationof the optics. The spectrograph is cryo-cooled, how-ever, it is not a stabilized instrument. Bean et al.(2010) found that the use of an ammonia gas cellcalibration for the K-band (2.3 µm) required manyfree parameters to forward model the instrumentalpoint spread function and the system was less effi-cient because the K-band was not at the peak of thespectral energy distribution of their early M dwarfstars. However, the NIR spectral range does containsignificant Doppler information for mid to late Mdwarfs (Figueira et al. 2016; Beatty & Gaudi 2015)and advantages of working at NIR wavelengths tomitigate activity signals make it worthwhile to con-tinued efforts to improve precision in the NIR.

86 Presentation by Pedro Figueira87 Presentation by Jacob Bean

32 Fischer et al.

With faculae or plage, the associated magneticfields suppress convection and this perturbs thespectral line profile and produces photosphericDoppler shifts. Although there is only a small tem-perature difference between faculae and the pho-tosphere; Marchwinski et al. (2015) used the FF’technique (Aigrain et al. 2012) on photometry fromthe SORCE spacecraft to show that the plage-dominated activity in the Sun exhibits smaller ra-dial velocity scatter at near infrared wavelengthsthan optical wavelengths. So, the NIR may be use-ful as a diagnostic even in stars that have small spotsbut significant faculae and plage.

Interestingly, Reiners et al. (2013) found that theZeeman effect, which increases with wavelength, canspuriously increase the radial velocity signal at red-der wavelengths. The amplitude of the radial ve-locity signal caused by the Zeeman effect alone canbe comparable to that caused by temperature con-trast; a spot magnetic field of about 1000G can pro-duce a similar RV amplitude as a spot temperaturecontrast of about 1000K. For the active M dwarfAD Leo, Reiners et al. (2013) found that the radialvelocity signal increases at longer wavelengths, con-sistent with a strong influence of the Zeeman effect.Therefore, the RV signal depends on the combina-tion of spot temperature and magnetic field.

There are several instrumental challenges forEPRV with infrared spectrometers; these includedetector technology, thermal and environmentalcontrol, modal noise, wavelength calibration andsky background (Plavchan et al. 2013a,b; Anglada-Escude et al. 2012). For most of these issues,progress has lagged behind optical instruments.The use of adaptive optics may be the one areawhere NIR spectrographs have an advantage overoptical instruments and the use of single mode fiberfeeds to IR spectrographs (e.g., iLocator, Crepp2014) offers an interesting path forward.

4.3.1. Simulating Stellar Noise

The community has developed simulation toolsfor understanding and modeling stellar activity, in-cluding the SOAP Boisse et al. (2012), SOAP 2.0Dumusque et al. (2014) code for simulating realisticspectra that captures the effect of spots and faculae.A new code, StarSim (Herrero et al. 2015) producesrealistic synthetic time series spectra that accountsfor limb darkening, spots, faculae and convection us-ing a surface integration and includes photometricinformation88. The inputs to StarSim include stellarparameters (effective temperature, log g, metallic-ity, rotation, differential rotation, and inclination)information about the active regions (spot positionsand sizes, temperature contrast, faculae tempera-ture contrast, faculae to spot area factor, and evo-lution of the active region) and information aboutplanets (size, ephemeris, spin-orbit angle, impactparameter). The spectroscopic contribution fromthe photosphere, spots and faculae are synthesizedfrom the Phoenix BT-Settl models) and stored in aspherical grid representing the star. The synthetic

88 Presentation by Enrique Herrero

spectrum is calculated by integrating the surface el-ements that contain temperature, limb darkening,radial velocity and geometry (size and projection).Time series observations are produced as a functionof the rotational phase angle. By using the HARPSmask template, the CCF models can be producedand analyzed to try to recover the underlying sim-ulated noise.

4.3.2. RV Fitting Challenge

In advance of the workshop, Xavier Dumusque or-ganized a challenge89 for fitting Keplerian signals inradial velocity data 90. He provided simulated RVdata sets, using the time stamps of HARPS obser-vations for some well-sampled stars. The data con-tained stellar signals from from oscillations, granu-lation, spots and plages, magnetic cycles and Keple-rian signals. Eight teams participated in this simu-lation and used different techniques to recover plan-etary signals, as detailed in Table 2. The results ofthe RV fitting challenge are fully described in Du-musque (2016). Here, we summarize the take awaymessages of this exercise.

For the RV fitting challenge, 14 data sets wereprovided, including 4 data sets from real HARPSobservations and 10 simulated data sets. A total of48 planetary signals were present in the data, withsemi-amplitudes ranging from 0.16 to 5.85 m s−1.In Fig. 20, we summarize the results of the dif-ferent teams. For each signal detected, we assigna different color flag depending on the true signalspresent in the data. The different possibilities are:

• dark green: the group recovered a plane-tary signal that existed in the simulated data,and the group was confident in the detection,meaning that they would have published thisresult.

• light green: the group recovered a planetarysignal that existed in the data, however thegroup assigned a low confidence to the detec-tion.

• yellow: the group recovered a planetary sig-nal that existed in the data and was confidentenough for publication; however, the ampli-tude or period is slightly wrong compared tothe true signal, or an alias of the true signalwas detected.

• grey: the group recovered a planetary signalthat existed in the data, but was not confidentin the detection. The amplitude or period wasslightly wrong compared to the truth, or analias of the true signal was detected.

• orange: the group recovered a prospectiveplanetary signal that did not exist in the data,but assigned a low confidence level to the de-tection

89 https://rv-challenge.wikispaces.com90 Presentation by Xavier Dumusque


• red: false positive or false negative, i.e., thegroup recovered a planetary signal that doesnot exist in the data, but they were confidentenough in the detection for publication (falsepositive), or the group rejected the detectionof a true signal (false negative).

• white: a simulated planetary signal waspresent in the data that has an amplitudelarger than 1 m s−1, but this signal was notdetected.

To study the statistics of exoplanetary popula-tions, it is most important that published planetswith correct parameters (dark green) are found. Itis also important to understand when false positiveor false negative signals (red) are reported and whenrelatively large signals with amplitudes that exceederror bars are missed (white). Signals that are pub-lished with modest errors in their parameters (yel-low) will not strongly corrupt the planet popula-tion statistics. The RV challenge also helped toillucidate trends regarding the signals (light green,grey, orange) that were either true or false, but thatwould not be published.

In Figure 20, the most successful groups shouldhave a larger dark green region, and smaller redand white regions. Given this metric for success, weseparate the teams in two different groups: teams1 to 5 (groups that used a Bayesian framework tocompare between models) and teams 6 to 8 (groupsthat did not use Bayesian models). Groups 1 to 4also used red noise models in addition to Kepleri-ans to account for stellar signals, and group 5 useda white noise model that was free to vary depend-ing on the activity level of the star in addition toKeplerian models. The other groups compared RVsignals with signals present in the activity observ-ables (log R′HK, FWHM, BIS SPAN) and rejectedsignificant signals it they were also in the RVs or inany of the stellar activity diagnostics.

According to Dumusque (2016), among the teamsthat used a Bayesian framework to compare be-tween models and red noise models to account forstellar signals, team 3 was the best at finding trueplanetary signals; they were confident in the ma-jority of their detections and they made a smallnumber of mistakes. This team detected 85% (17out of 20) of the true planetary signal present inthe data that had a semi-amplitude larger than 1m s−1. The remaining 3 signals that were not de-tected all have periods longer than 500 days andtheir non-detection could be explained either bymagnetic cycle RV effects, or simply by the fact thatteam 3 only fitted up to a second order polonomialto remove any RV trends in the data. This teamwould have only published 60% of these large am-plitude signals, leaving the remaining signals as ten-tative. When analyzing planetary signals with semi-amplitudes smaller than 1 m s−1, team 3 did alsothe best job at recovering those signals, with 14%detected (4 out of 20). However the team wouldhave only published 2 of those planets, with ampli-tudes of 0.48 and 0.69 m s−1. Finally team 3 re-

frained from announcing non-existing planets withsemi-amplitudes larger than 1 m s−1, and wouldhave only announced 2 non-existing systems withsmaller semi-amplitudes.

The next two best performing teams were Team1 and Team 4. While Team 4 ranked third, theyactually did a better job than Team 1 on the fittingfirst five systems. However it was difficult to makea fair comparison because they did not analyze theother systems.

In conclusion, the RV fitting challenge (Dumusque2016) showed that teams using a Bayesian frame-work that allows for model comparison, and thatincludes a red noise model to account for stellar sig-nals were more efficient at finding true planetarysignals, while limiting the number of false claims.Among the different red noise models, it the movingaverage model used by M. Tuomi and G. Anglada-Escude (Team 3) was the most efficient. The use ofGaussian Processes was also an efficient approach,however this technique seems to be sensitive to thea priori determination of the rotation period; itseems likely that some improvement can be madehere (Dumusque 2016). The apodized Kepleriantechnique (Team 4 Gregory 2016) also yields goodresults. Gregory (2016) find that it is possible toachieve a factor of about six reduction in the stellaractivity noise in the simulated radial velocity setswith the apodized Keplerian technique. Unfortu-nately, Team 4 only analyzed only the first 5 systemsas they were developing their technique, and thisultimately penalized their ranking. Finally, plan-etary signals with amplitudes above 1 m s−1weredetected almost all of the time, while only 14% (4out of 28) of true smaller signals were discovered.Out of these 4 true small signals, 2 would have beenpublished; however, 2 false planetary signals wouldhave been published as well. Therefore, even withthe best models of stellar signals, planetary signalswith amplitudes less than 1 m s−1 are rarely ex-tracted correctly with current precision and currenttechniques.

4.4. Aliasing

Radial velocity data sets will generally includealiased signals, which are interactions between gapsin data sampling and signals91. A sinusoidal signalin time series data is a delta function in the fre-quency domain. Because observations are taken atspecific times, a window function is applied to thedata; in the time domain this results in samplinggaps. The convolution of the sinusoidal frequencyand the window function produces multiple peaksin the frequency domain.

How do we know what the time sampling is forcomplex sampling patterns? Solar and sidereal dayand annual sampling gaps naturally appear in mostradial velocity data sets and these aliases and theirharmonics produce peaks at positions that can becalculated:

falias = |ftrue ± fsample| (7)

91 Presentation by Rebekah Dawson

34 Fischer et al.

Table 2Fitting Teams

Teams People Techniques

1 Torino M. Damasso, A. Sozzetti, R. Haywood Bayesian framework withA.S. Bonomo, M. Pinamonti, and P. Giacobbe Gaussian Process to account for red noise

2 Oxford V. Rajpaul and S. Aigrain Bayesian framework withGaussian Process to account for red noise

3 M. Tuomi M. Tuomi and G. Anglada-Escude Bayesian framework withMoving Average to account for red noise

4 P. Gregory P. Gregory Bayesian framework withApodised Keplerian to account for red noise

5 Geneva R. Diaz, D. Segransan and S. Udry Bayesian framework with white noise6 H. Hatzes H. Hatzes Pre-whitening7 Brera F. Borsa, G. Frustagli, E. Poretti and M. Rainer Filtering in frequency space8 IMCCE N. Hara, F. Dauvergne and G. Boue Filtering in frequency space

6

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Claimed planet with wrong K or P

Probable planet but wrong K or P

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Figure 20. Summary of the result of the RV fitting challenge for teams 1 to 8. The size of the circles represents the numberof systems analyzed: 14 systems for the large size circle, 5 for the medium size and 2 for the smallest size. The meaning of thecolors are defined in the legend and in the text (Courtesy of Xavier Dumusque)

Dawson & Fabrycky (2010) show that aliases im-print a set of predictable peaks; by modeling a noisefree data set, it can be possible to confirm Keple-rian signals in the presence of aliases. However, lowSNR data is more ambiguous when trying to iden-tify aliasing, and chromospheric activity can pro-duce a forest of peaks with associated aliasing sig-nals. Stellar activity does not produce an exactsinusoidal signal; instead, the imprinted perturba-tions are stochastic and quasi-periodic. The potentcombination of variable intensity in the stellar noisesignal and poor sampling leads to ambiguity in iden-tifying aliases that can sabotage the identification ofweak Keplerian signals.

4.5. Barycentric corrections

Corrections for the velocity of the Earth mustbe applied in order to recover precise radial ve-locity measurements of stars for exoplanet detec-tion.92 Wright & Eastman (2014) outline the mag-nitude of error contributions to the barycentric ve-locity correction, including rotational and orbitalmotion of the Earth, second order corrections to thenon-relativistic Doppler formula, secular accelera-tion, precession, nutation, gravitational redshifts,blueshifts, and the Shapiro delay (for light bendingaround the Sun). In their publicly available code

92 A breakout session on barycentric corrections was ledby Jason Eastman and Lars Buchhave.


for barycentric correction,93 the authors show thattheir calculations match those from the TEMPO2(Hobbs et al. 2006; Edwards et al. 2006) code at arms level of 0.3 mm s−1. The accuracy of TEMPO2is a gold standard with a precision better than 1cm s−1 that was demonstrated when measuring theDoppler effect of pulse arrival times for the detec-tion of Earth-mass exoplanets orbiting a neutronstar (Wolszczan & Frail 1992).

The barycentric correction for radial velocitymeasurements at the 10 cm s−1 level requires aprecision of about one second in the flux-weightedexposure time. This is generally accomplishedby monitoring the flux of starlight into the spec-trograph at regular intervals over the exposures.The barycentric velocity correction should be de-termined for the time the signals arrive at the solarsystem barycenter — i.e., at the Barycentric Juliandate in Barycentric Dynamical Time (BJDTDB).An error of 1 second in time introduces a semi-amplitude error of about 3 cm s−1, so to reach anerror of less than 1 cm s−1 the midpoint time mustbe accurate to about 250 milli-seconds (Eastmanet al. 2010; Wright & Eastman 2014).

An effect that was not addressed by (Wright &Eastman 2014) is the need to integrate the barycen-tric correction over the exposure time (Figure 21 isprovided from an article in prep, Buchhave, East-man & Wright 2016). A barycentric correctionshould be calculated for each sampled flux measure-ment and then weighted by the photon counts. Thisupdates the older procedure of calculating a singlebarycentric correction to the photon-weighted mid-point time. The older procedure was deemed as ac-ceptable for most state of the art Doppler surveysbecause the relatively short exposures incurred anerror from the acceleration term in the barycentricvelocity that was far below other terms in the er-ror budget. However, this is an error source thatmust be handled more carefully for higher precisionsurveys. Even assuming uniform flux during an ex-posure, the older procedure can introduce a velocityerror of ±25 cm s−1 for a 30 minute exposure; thisscales as the square of the exposure time.

The optimal flux sampling rate depends, unfor-tunately, on the apriori unknown rate of variabilityin the atmosphere. If the atmospheric opacity isconstant, then the midpoint time precision is inde-pendent of sampling and lower sampling rate is bal-anced by the benefit of extra photons. Even in anextreme scenario with a 6 second ”blackout” at theend of an otherwise uniform 5-minute exposure, in-tegrating flux in 1 minute bins would produce an er-ror in the flux-weighted midpoint time of only 0.6s.Although more detailed analysis is warranted on thesubject, binning flux every ∼10 seconds is reason-able for almost every imaginable weather conditionand still provides good sampling for short exposuretimes of about one minute. For extreme RV preci-sion, it is recommended that the exposure times arelimited to about 20 minutes to minimize the error inthe barycentric velocity calculation from nonlinear

93 http://astroutils.astronomy.ohio-state.edu/exofast/

terms discussed above.For an accuracy in the barycentric velocity of ∼ 1

cm s−1 it is also important to sample photon countsas a function of wavelength. For example, if ob-servations are taken at large zenith angle withoutan atmospheric dispersion compensator (ADC) theimage of the star will be chromatically dispersed;if guiding favors collection of the red light for thefirst half of the exposure and then collection of bluelight for the second half of the exposure, the flux-weighted midpoint would be different for the redand blue photons. However, even with a good ADC,variable wavelength-dependent extinction can occuras the telescope tracks the star through a rangeof hour angle, even for short exposures. A basicexposure meter design might use a dichroic to di-vide the light between two channels; however, alow resolution spectrometer with 8 - 10 channelsis probably preferable for providing a better correc-tion as long as a fast readout can maintain ∼10 sec-ond sampling with high SNR. Once the wavelength-dependent barycentric correction has been derived,it should be interpolated (linearly or weighted withan extinction curve) for each wavelength chunk ororder and applied when weighting and combiningthe velocities from different parts of the spectrum.For example, if each order is cross-correlated, then abarycentric correction can be calculated for the cen-tral wavelength and applied on an order-by-orderbasis before calculating the average velocity.

Recommendations for good practices in derivingprecise barycentric corrections include sampling theflux during the exposure (at least every minute, butideally every few seconds), recording all times ex-plicitly as a function of wavelength, ensuring theaccuracy of the time stamp in the file headers, andincluding the time standard (usually GMT or UT).

4.6. Telluric contamination

Telluric absorption lines from many species (e.g.,H2O,O2,CH4,CO2) are imprinted in a stellar spec-trum when starlight passes through the Earth’s at-mosphere. Some molecular species are well-behavedwith only small seasonal variations in column den-sity, while the lines associated with water can varyin depth with changing humidity throughout thenight (temporally) or with different positions onthe sky (spatially). There is some variability in thewavelengths and line profiles of telluric lines becauseof atmospheric winds, generally limited to Dopplershifts of about 10 m s−1 (Figueira et al. 2010a), cor-responding to a fraction of a pixel. More important,the telluric lines raster across the stellar spectrumwith time because of the barycentric velocity of theEarth.

Like any attribute that perturbs the shape ofthe SLSF, telluric contamination must be properlytreated for high precision radial velocity measure-ments.94 Left untreated, telluric contamination is

94 The telluric contamination breakout session was orga-nized by Sharon Wang with panel members Jason Wright,Cullen Blake, Pedro Figueira, Nuno Santos, Peter Plavchan,Andreas Seifahrt, Claire Moutou, Francois Bouchy.

36 Fischer et al.

0.0 0.5 1.0 1.5 2.0JD - 2456707

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Figure 21. Radial velocity error when acceleration of the barycentric velocity is not properly handled (i.e., when a singlebarycentric correction is derived for the flux-weighted midpoint time, which is current standard practice in the community). Thissimulation assumes 30-minute observations of Tau Ceti taken from CTIO with uniform flux during the observation. Velocityerrors are only calculated for times when the star would be observable (i.e., airmass less than 2 and the Sun below −18 degreetwilight). (left) RV errors that could be incurred over a 2-day diurnal cycle. (right) RV errors over a full year when the sameobserving constraints are applied. (Figure courtesy of Lars Buchhave, Jason Eastman, Jason Wright)

most important in the near infra-red (NIR) whereit has an impact of at least a few meters per second(Bean et al. 2010) and where telluric lines can bequite opaque (with τ > 0.2). The impact at opti-cal wavelengths is of order ∼ 0.2−−1 m s−1 where(Figure 22) micro-telluric lines have depths of 0.2 –2% (Cunha et al. 2014; Artigau et al. 2014b).

Most groups correct or model telluric lines withphysically motivated synthetic models that havea comprehensive line list and use radiative trans-fer with accurate atmospheric profiles, which isdemonstrated to be more accurate than empiricalcorrection using telluric calibration frames (Gul-likson et al. 2014; Smette et al. 2015). Mostcodes are base on the line-by-line radiative transfermodel (LBLRTM; Clough et al. 2005) and the HighResolution Transmission (HITRAN) line database(Rothman et al. 2013). Examples of published codesare: TAPAS (Bertaux et al. 2014), TelFit (Gullik-son et al. 2014), Molecfit (Smette et al. 2015), andTERRASPEC (Bender et al. 2012). A model of thetelluric spectrum from 0.3 to 30 microns is shownin Figure 23. These codes model telluric lines to aprecision of 2 – 5%; however, for deep lines or lineswith large uncertainties in the HITRAN database,the precision is not as good. Poorly fitted lines aremasked out or rejected (Bean et al. 2010; Seifahrtet al. 2010; Blake et al. 2010).

The current telluric modeling precision is lim-

ited by: missing lines in the HITRAN database,uncertainties or errors in attributes such as theline position, strength, or shape, limitations in cur-rent modeling codes for deriving correct line pro-files (i.e., velocity dependence, line mixing effects),insufficient knowledge of real time atmospheric con-ditions (e.g. water column density variations), andwind-induced line shifts. There are annual meet-ings on HITRAN where help could be requestedfor specific lines or species under a range of physi-cal conditions (excitation levels, temperatures). Itis also possible that telluric modeling can be im-proved with empirical corrections using on-sky dataor a Fourier Transform Spectrograph (FTS) obser-vation although micro-tellurics will be difficult toobserve with high SNR. Perhaps a version of HI-TRAN can be designed for astronomy applicationsthrough compilation and modeling of a large volumeof telluric calibration data. This “Astro-HITRAN”would be simpler but more robust for astronomicaluses for certain molecular species, and it would al-low for scaling of line strengths, for example, for dif-ferent amount of water vapor content. The variablewater species still present a modeling challenge, andBlake & Shaw (2011) have suggested a clever useof global positioning satellite measurements of pre-cipitable water vapor as a prior when scaling thesefeatures.


Figure 22. Reproduced Fig 1 from Cunha et al. (2014). Spectrum of micro-telluric lines in the optical spectrum between 442and 570 nm. (Figure courtesy of Diana Cunha and Nuno Santos).

5. SYNERGY WITH OTHER FIELDS

Precision radial velocities are critical to the suc-cess, efficiency and scientific yield of future spacemissions95. There is obvious synergy with tran-sit missions (TESS, CHEOPS, PLATO) in deriv-ing bulk densities for thousands of exoplanets. Newconnections will be made with Gaia, where of or-der 10,000 new gas giant planets are expected tobe detected. The combination of Gaia astrometryand radial velocities will illuminate several ques-tions about planet formation: the true mass dis-tribution of jovian planets beyond the ice line, thefrequency of solar system analogs, whether superEarths are regularly accompanied by giant planetsand how gas giant planets affect the presence of ter-restrial planets.

Radial velocity measurements can also enhance

95 Presentation by Alessandro Sozzetti

the productivity of direct imaging missions by pro-viding orbital phase information and informationabout inner companions. The ideal targets for di-rect imaging are young stars where the gas giantplanets will be brighter; these will be amenable toRV follow-up if successful techniques are developedfor mitigating photospheric noise in these activestars.

6. SUMMARY

A comparison of several ongoing Doppler sur-veys shows that most teams have reached about 1m s−1 in single measurement radial velocity pre-cision. The best performing spectrometer is thepurpose-built vacuum-enclosed HARPS instrument,with R=115,000, a broad wavelength range from400-700 nm, and a fiber feed system that utlizesoctagonal fibers and an optical double scrambler.HARPS reaches a precision of about 0.8 m s−1 forobservations with SNR of 200 in 3 km s−1 bins

38 Fischer et al.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

00.20.40.60.8

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wavelength [µm]

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sion

O3 (Huggins bands)

Chappuis ozone absorption bands

O2(γ band) O2 (B band)

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1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

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sion

H2O

O2

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CO2

CH4

CH4

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CO2 CO2

Figure 23. Reproduced Fig 1 from Smette et al. (2015). Spectrum of telluric lines synthesized with a line-by-line radiativetransfer code using the annual mean profile for Cerro Paranal at a resolution of about 10,000. (Figure courtesy of WolfgangKausch, Alain Smette, Stefan Kimeswenger, Stefan Noll).


at 500 nm. The next generation instruments willneed to improve upon HARPS with better illumi-nation stability, higher fidelity spectra (more sta-ble spectral line spread function, higher resolutionand higher SNR), broader wavelength bandpassesand more stable and precise wavelength calibration,and improved detector performance and character-ization efforts.

Tremendous progress has been made over thepast five years on technology development for high-resolution optical spectrometers. In particular, thedevelopment of frequency combs for the wavelengthcalibration of spectrometers for Doppler planetsearches is now mature technology. Laboratoryexperiments and initial tests on HARPS indicatethat wavelength calibration is likely not the primarylimitation in achieving 10 cm s−1 Doppler preci-sion. Frequency combs have become powerful toolsfor characterizing spectrometer drift, estimating thespectral line spread function across the instrumentbandpass, and characterizing and calibrating detec-tor imperfections. The remaining work to be donewith frequency comb technology is primarily tech-nical implementation, including making systems ro-bust and reliable, and mitigating modal noise whencoupling comb light into the spectrograph. A turn-key laser frequency comb is now available fromMenlo Systems that shows great promise as a long-term calibration device. The Menlo combs havebeen in operation at the VTT solar telescope inTenerife (since 2012), at HARPS in La Silla (per-manent since 2015), at FOCES in Munich at USM(since 2015) and at Xinglong China (since February2016). At USM the LFC has been running continu-ously for several months. Beyond the more clas-sical astro-comb calibration technologies, there issignificant innovation in the fields of microcombs,electro-optical modulation combs, tunable Fabry-Perots, and stabilized etalons as well.

Fiber optic cables are also a well-understood tech-nology. Not only does optical fiber technology allowfor spectrometers to be placed in convenient loca-tions relative to telescope focus, but modern fiberscan also improve instrument illumination stabilitysignificantly while maintaining high efficiency. Caremust be taken when connectorizing instrument fibercables to ensure stress-free mounting (thereby min-imizing FRD.) Standard fibers used in astronomicalinstruments do incur modal noise penalties, as onlya finite number of modes can be populated withinthe fiber, but much of this can be mitigated throughmechanical agitation. However, modal noise is asignificant issue for coherent sources, such as laserfrequency combs, and our community must developnew mitigation techniques if the exquisite precisionof next generation wavelength calibration sources isto be fully realized by future spectrometers

Telluric contamination is another area that thecommunity will need to address for high precisionDoppler measurements. The problem is most chal-lenging for infrared observations, but micro-telluricsat optical wavelengths are also a concern at submeter per second precision. Current approaches in-volve forward modeling to fit for tellurics or masking

out contaminated pixels in the spectrum. Routinemonitoring of atmospheric conditions (water vapordistribution and column density, wind etc) is rec-ommended and this information should be storedas meta-data with the spectra.

Barycentric corrections have been demonstratedto be accurate to about 2 cm s−1 (Wright & East-man 2014). The flux-weighted exposure midpointtime should not be used for the correction; instead,barycentric velocity corrections should be calculatedthroughout an exposure and combined by weight-ing each point by the exposure meter data. Color-dependent barycentric corrections should also becalculated by collecting the chromatic flux time se-ries as a function of wavelength (in a few or severalwavelength bins). Any stellar exposure with suffi-cient SNR to achieve < 1 m s−1 precision shouldprovide enough photons for time series at severalwavelength bins. The final Doppler velocity is thecombination of measured velocities from a set oflines or wavelength bins; each bin or line would thenbe corrected according to the BC from the appropri-ate wavelength region. A high performance atmo-spheric dispersion corrector (ADC) will reduce thesensitivity to flux-weighted barycentric corrections.

The community is now exploring correct statis-tical techniques with the goal of improving repro-ducibility and extracting weaker signals in the pres-ence of time-correlated noise. Frequentist tech-niques are faster, but Bayesian techniques are morereliable in estimating the true errors and uncover-ing underlying exoplanet populations from our data.There is common misuse of null hypothesis testslike the p-value or Kolmogorov-Smirnoff test. As-tronomers are encouraged to team up with statisti-cians to avoid the pitfalls of applying statistical testsas black boxes. Many of the techniques that seemnew to astronomers are well understood techniquesfor statisticians.

There was extensive discussion about how to han-dle stellar noise. In the past, it was adequate toidentify and decorrelate trends in radial velocitiesbased on calcium H & K emission, or the FWHMor line bisector of the cross correlation function.However, we now appreciate that photospheric ve-locities, or jitter, is fundamentally imprinted in thespectrum differently from a Keplerian Doppler shift.There are many techniques that show promise indistinguishing jitter from center of mass velocities,including principal component analysis of spectrallines or the cross correlation function. Stellar jitteris currently the main limitation in the detection ofsmall rocky planets and it merits significant effortby the community. It will not work to avoid starswith jitter (because stellar activity varies over time).We are advancing our understanding of the physicsof stellar noise with solar data and photometry fromKepler. Plage is a more important contributor (90%level) to stellar jitter than spots (a 10% problem)for slowly rotating stars.

It is not an adequate strategy to average downhundreds of observations; this wastes precious tele-scope time and systematic errors don’t necessarily

40 Fischer et al.

average down as the square root of the number ofobservations. The RV challenge led by Xavier Du-musque showed that the community has not beensuccessful in detecting velocity amplitudes that aresmaller than the single measurement precision, evenwhen hundreds of observations are obtained. Wemust improve single measurement precision as a firststep toward detecting low amplitude exoplanetarysystems. We must learn how to distinguish stellarnoise from Keplerian velocities.

There has been negative advocacy by some in theexoplanet field who claim that a fundamental floorof precision is imposed by photospheric velocities,or stellar jitter at the level of 1 m s−1. That state-ment may be true for many of the current spec-trometers and analysis techniques. At a resolu-tion of 50,000 on spectrometers that are not sta-bilized, stellar noise from chromospherically quietstars cannot be distinguished from Keplerian veloc-ities. Fortunately, the community at large has con-tinued to press forward on this issue and it seemslikely that an instrumental precision of 10 cm s−1

will be achieved with the next generation of highfidelity spectrometers. We do not yet know howthis will translate into detectability for low ampli-tude signals in the presences of unavoidable stellarnoise; however, it is premature to speculate thatwe cannot do better. This is an area of active re-search in the community and there has been promis-ing progress. Research to distinguish stellar activityfrom center of mass Doppler shifts must continueto be a high priority, simply because the exoplanetendeavor cannot expand96 if we do not solve thisproblem and extract weaker signals in the presenceof time-correlated noise.

7. FINDINGS AND CONCLUSIONS

There have been several reports highlighting theimportance of precise radial velocities for support-ing NASA missions, including the 2006 ExoplanetTask Force (Lunine et al. 2008), the 2010 DecadalSurvey (Blanford 2010), and the 2012 NSF PortfolioReview report (Eisenstein 2012). The cancellationof the $2B Space Interferometry Mission was ac-companied by a statement that ground-based radialvelocity measurement precision could be pushed to10 cm s−1, enabling at least partial characterizationof the architectures of nearby planetary systems.The NASA ExoPAG commissioned a report ”RadialVelocity Prospects Current and Future” (Plavchanet al. 2015) with findings from the precision ra-dial velocity community97 that complements andforeshadows many of the findings from the EPRVworkshop. This report highlights a key challenge:EPRVs have transitioned from small PI-based pro-grams to “big” science that requires dedicated re-sources; however, the NASA and NSF budget mod-els have not kept up with this. While radial velocityprecision has been stuck at 1 m s−1 for the past sev-eral years, there has been progress in technology andanalysis techniques that offers promise for moving

96 Survey input from Rosemary Mardling97 Presentation by Scott Gaudi

toward 10 cm s−1 precision and this progress needsto be communicated to the astronomy communityat large and to the funding agencies.

The “Big Three” science goals for extreme preci-sion radial velocities are:

• Confirmation and characterization of themany transiting planets discovered by tran-sit surveys (ground-based, Kepler, K2, TESS,CHEOPS, PLATO). EPRV measurementswill uniquely provide mass measurementsneeded for bulk density measurements.

• Identification and orbital characterization ofplanets down to ice giant masses around FGKstars to be imaged by WFIRST-AFTA.

• The discovery of potentially habitable planetsaround the nearest and brightest stars.

Resources will be required to meet these ambi-tious goals. Habitable planets around FGK typestars have velocity semi-amplitudes of order 10cm s−1 and periods of about one year. The dis-covery of these planets requires high statistical pre-cision and high cadence. Additional work needs tofocus on reducing any systematic errors or astro-physical noise to considerably less than 10 cm s−1.In additional to controlling systemic errors resultingfrom instrumental and calibration effects, consider-able additional work needs to focus on the criticaland difficult task of removing, suppression, or sepa-ration of intrinsic stellar noise to considerably bet-ter than 10 cm s−1. This is in principle a tractableproblem because the Doppler variation due to or-biting bodies has a unique signature: all of thelines move by a known amount without changingtheir shape. Current instruments and detection al-gorithms are not going to solve this problem; theRV fitting challenge by Xavier Dumusque (Section4.3.2) showed that no one can reliably detect planetswith amplitudes below 1 m s−1 in current data sets.We need higher fidelity spectra to make progressand this is a problem that will require the next gen-eration instruments.

7.1. Recommendations

In support of the key role that precision spec-troscopy has for space missions, NASA has commis-sioned the Extreme Precision Doppler Spectrograph(EPDS) for the WIYN 3.5-m telescope98. This is astart, but one new instrument is not enough. Thereis a role for small telescopes with high cadence ob-servations and larger aperture telescope that obtainhigh resolution, high SNR observations. Partici-pants at this workshop discussed the big ideas thatcould catapult progress in the field and enable suc-cess for the highest priority science goals of precisionDoppler surveys.

1. Dedicated moderate to large aperturetelescopes. High SNR and very high cadencedata are required over long time baselines; this

98 Presentation by Mario Perez


could be achieved for hundreds of stars us-ing dedicated 4 to 10 meter class telescopes.Most of the struggles we have with aliasingand stellar activity is complicated by under-sampled data sets. In the same way that Ke-pler transit detections benefited from high ca-dence sampling, Doppler measurements wouldbenefit from a paradigm shift with many moreobservations, perhaps a world-wide effort withcoordinated observations at several longitudesfor a few stars.

2. Stable Spectrometers. Instruments withexquisite long-term stability are required:spectrometers that are fiber fed with high il-lumination stability, excellent wavelength cali-bration, and precise temperature and pressurecontrol represent the immediate future of pre-cision RV measurements. Optical spectrom-eters contain significant amounts of Dopplerinformation for solar-type stars, but radial ve-locities from NIR spectrometers have less con-tamination from stellar activity (spots as wellas plages). Based on current technology, solu-tions to the technical challenges presented atthe workshop seem within reach for the spec-trometers that are being built today.

3. Proper treatment of stellar noise. Itis likely that distinguishing between stellaractivity and Keplerian velocities will requirevery high resolution (perhaps ∼150,000), andexpanded wavelength coverage (optical plusnear infrared). The high resolution is notrequired for measuring line centroids; theline centroid information is resolved at R ∼60, 000. However, the need to measure higher-order line shape variations, which are a clearsignal of stellar activity or changes in the in-strumental line spread function rather thana true Doppler shift, likely require muchhigher resolution and sampling, as well ashigher SNR. Simultaneous high-resolution op-tical and infrared monitoring can mitigateany pathological cases where stellar activityor instrumental effects may cause line cen-troid shifts without strong line shape varia-tions, since these shifts are neverthless likelyto wavelength dependent. In particular, theionization and line formation depth in thephotosphere depends on the wavelength, andthus so do the absorption line shapes throughthe photospheric velocities.

All of this leads to a vision for precision radialvelocity “dream machines” requiring large aper-ture telescopes with dual optical and infrared chan-nels (0.4 to 1.7 µm), very high optical resolution(R > 150, 000), high IR resolution (R > 50, 000),fiber-fed with a very high scrambling gain, environ-mentally stabilized, and with advanced wavelengthcalibration (e.g., laser frequency combs). The costwould be of order $20 M per instrument and ideallythere would be few of these at various longitudes.

In order to carry out the science, these machineswould require an assurance of a significant alloca-tion of observing time over several years.

This is a cost that at first glance seems out ofreach. However, if precisions approaching 10 cm s−1

can be achieved, Doppler surveys may be able to lo-cate the host stars of planets that would be observedby the next generation of flagship direct imagingmissions, such as the Habitable Exoplanet ImagingMission and the Large UV-Optical-IR (LUVOIR)mission, both of which will be studied by NASAover the next few years (see PAG Reports: Sembach2015; Boch 2012; Gaudi et al. 2016). The cost forsuch missions is to be determined, but is certainlygreater than one billion (by definition for a flagship),and may be up to ten(s) of billions of dollars for themore ambitious architectures that will be consid-ered. The choice of the flagship mission, the techni-cal specifications and the scientific productivity of aflagship mission may well be dependent on whetherexoplanets are already known or whether they needto be discovered and it still be helpful to measurethe mass of the planet after they are discovered bythese direct imaging missions. EPRV is likely to bethe only techniques that offers promise for detect-ing low mass planetary systems around nearby starsbefore the launch of the next flagship mission. Aninvestment at the $100M level would be a wise in-vestment that could ultimately save billions of dol-lars toward the goal of characterizing small rockyplanets.

We thank the anonymous referee for providingan exceptionally careful review of this paper andfor many suggested changes which improved thequality of the paper. We are grateful to YaleUniversity, to the National Science Foundationgrant AST-1458915 and to the NASA ExoplanetScience Institute (NExScI) for providing financialsupport that enabled this workshop and providedsupport for participants. D. A. Fischer thanksNASA NNX12ACG01C for inspiring the study ofextreme precision radial velocity measurements.R. I. Dawson acknowledges the Miller Institute atthe Univ of California, Berkeley for Basic Researchin Science. S. A. Diddams acknowledges supportfrom NIST and the NSF grant AST-1310875.X. Dumusque would like to thank the Societyin Science for its support through a BrancoWeiss Fellowship. E. B. Ford was supportedin part by NASA Exoplanet Research Programaward NNX15AE21G. Work by B. S. Gaudi waspartially supported by NSF CAREER GrantAST-1056524. G. Laughlin acknowledges supportfrom the NASA Astrobiology Institute througha cooperative agreement between NASA AmesResearch Center and the University of Californiaat Santa Cruz, and from the NASA TESS Missionthrough a cooperative agreement between M.I.T.and UCSC. A. Reiners acknowledges support fromthe European Research Council under the FP7Starting Grant agreement number 279347 and fromDFG grant RE 1664/9-1. N. C. Santos and P.

42 Fischer et al.

Figueira acknowledge support by Fundacao para aCiencia e a Tecnologia (FCT) through the researchgrants UID/FIS/04434/2013 and PTDC/FIS-AST/1526/2014 as well as through InvestigadorFCT contracts of reference IF/01037/2013 andIF/00169/2012, and POPH/FSE (EC) by FEDERfunding through the program “Programa Op-eracional de Factores de Competitividade —COMPETE.” P. Figueira further acknowledgessupport from FCT in the form of an exploratoryproject reference IF/01037/2013CP1191/CT0001.A. Szentgyorgyi thanks the Giant Magellan Tele-scope Organization for their support for much thework described in his contribution to this paperunder Contract No. GMT-INS-CON-00584. S.X. Wang is supported by a NASA Earth andSpace Science Fellowship (NNX14AN81H). S. X.Wang and J. T. Wright acknowledge support fromNSF grant AST-1211441 for the work on telluriccontamination. J.T. Wright acknowledges NSFgrant AST1109727 and NASA grant NNX12AC01Gfor work on barycentric corrections. The Centerfor Exoplanets and Habitable Worlds is supportedby the Pennsylvania State University, the EberlyCollege of Science, and the Pennsylvania SpaceGrant Consortium. The PARAS program is fullysupported and funded by the Department of Space,Govt. of India and Physical Research Laboratory(PRL), Ahmedabed, India. The PARAS teamwould like to acknowledge the support of theDirector, PRL, and the Mt. Abu Observatorystaff for running the program and Francesco Pepe(Geneva Observatory) and Larry Ramsey (PenState University) for many scientific and technicalinputs. Two of the PARAS team members, SuvrathMahadevan and Arpita Roy would like to thank theCentre of Exoplanets and Habitable Worlds at PennState University for their partial support. TheMcDonald Observatory planet search is currentlysupported by the National Science Foundationunder Astrophysics grant AST-1313075, and hasbeen supported in the past by various NASAgrants.

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