Astrometry and Exoplanet Characterization: Gaia and Its Pandora's Box

0.71 MB·English

by  A. Sozzetti

Astrometry and ExoplanetCharacterization: Gaiaand ItsPandora’s Box
Sozzetti, A.1
1. INAF-OsservatorioAstronomicodiTorino
ViaOsservatorio20,I-10025PinoTorinese,Italy
[email protected]
Introduction
In its all-skysurvey, Gaia will monitorastrometricallyhundredsof thousandsof main-sequencestars within
≈200 pc, looking for the presence of giant planetary companions within a few AUs from their host stars. In-
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deed, Gaia observations will have great impact is the astrophysics of planetary systems (e.g., Casertano et al.
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2008),inparticularwhenseenasacomplementtoothertechniquesforplanetdetectionandcharacterization(e.g.,
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2 Sozzetti 2011). In this paper, I briefly address some of the relevanttechnical issues associated with the precise
and accurate determinationof astrometric orbitsof planetarysystems using Gaia data. I then highlightsome of
n
theimportantsynergiesbetweenGaia high-precisionastrometryandotherongoingandplanned,indirectanddi-
a
J rectplanet-findingandcharacterizationprograms,bothfromthe groundandinspace, andovera broadrangeof

7 wavelengths,providingpreliminaryresultsrelatedtoonespecificexampleofsuchsynergies.
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]
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1. ExoplanetOrbitswithGaiaAstrometry:TheChallenge
E
h. We are about to enter the age of micro-arcsecond(m as) astrometry with Gaia. In the matter of astrometric
p detectionofplanetary-masscompanionsaroundnearbystars,theimprovementofovertwoordersofmagnitudein
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single-measurementprecisionwithrespecttopresent-dayHipparcosastrometryisabsolutelymandatorytofinally
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r putanendtothelonglistof‘blunders’thatthistechniquehasdelivered(forareview,seeSozzetti2010).However,
t
s theimprovedaccuracyoftheGaiameasurementswillnotresolvebyitselfthetechnicalproblemsassociatedwith
a themodelingoftheastrometricsignaturesofplanetarysystems,whichwillhavetobecarefullydealtwith.
[

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1.1 OrbitalFitsofPlanetarySystems
v
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8 TheproblemofthecorrectdeterminationoftheastrometricorbitsofplanetarysystemsusingGaiadata(highly
4 non-linear orbital fitting procedures, with a large number of model parameters) will present many difficulties.
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For example, it will be necessary to assess the relative robustness and reliability of differentproceduresfor or-
.
1 bital fits. Consistency checks between differentsolution algorithmswill be mandatoryas a way of learning the
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lessons of radial-velocity surveys, that are showing us, particularly in the case of multiple-planetsystems, how
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disagreementonorbitalsolutiondetails,andsometimenumberofplanets!,basedonthesamedatasetsisnotthat
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: uncommon (e.g., Forveille et al. 2011, and references therein; Hatzes et al. 2011, and references therein). A
v
detailedunderstandingofthestatisticalpropertiesoftheuncertaintiesassociatedwiththemodelparameterswill
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X havetobedeveloped,basedontherelativemeritofdifferentmetricstailoredtothistask,suchascovariancema-
r trices,c 2 surfacemapping,andbootstrappingprocedures. Formultiplesystems,atrade-offwillhavetobefound
a
betweenaccuracyinthedeterminationofthemutualinclinationanglesbetweenpairsofplanetaryorbits,single-
measurement precision and redundancyin the number of observations with respect to the number of estimated
modelparameters. Itwillconstitutea challengeto correctlyidentifysignals(andtheassociated)withamplitude
closetothemeasurementuncertainties,particularlyinthepresenceoflargersignalsinducedbyothercompanions
and/orsourcesofastrophysicalnoiseofcomparablemagnitude. Finally,incasesofmultiple-componentsystems
wheredynamicalinteractionsareimportant(asituationex-periencedalreadybyradial-velocitysurveys),fullydy-
namical(Newtonian)fitsinvolvingann-bodycodemighthavetobeusedtoproperlymodeltheGaiaastrometric
dataandtoensuretheshort-andlong-termstabilityofthesolution(seeSozzetti2005).
1.2 ExoplanetsTreatmentintheGaiaDataProcessingPipeline
AlltheaboveissuescouldhaveasignificantimpactonGaia’scapabilitytodetectandcharacterizeplanetary
systems. Forthesereasons,withinthepipelineofCoordinationUnit4(objectprocessing)oftheGaiaDataPro-
Figure1: DU437ActivityDiagram.
cessingandAnalysisConsortium(DPAC),inchargeofthescientificprocessingoftheGaiadataandproduction
ofthefinalGaia cataloguetobe releasedsometimein 2021,a DevelopmentUnit(DU437)hasbeenspecifically
devotedtothemodellingoftheastrometricsignalsproducedbyplanetarysystems. TheDUiscomposedofsev-
eraltasks,whichimplementmultiplerobustproceduresfor(singleandmultiple)astrometricorbitfitting(suchas
MarkovChainMonteCarloandgeneticalgorithms)andthedeterminationofthedegreeofdynamicalstabilityof
multiple-componentsystems. Iprovidehereaquick-lookviewofthesoftwareanditsstatus.
1.3 FittingAlgorithms: Highlights
Figure1showstheactivitydiagramofDU437.Themainfeatureofthissoftwaremoduleconsistsoftheuseof
twodifferentsolutionalgorithmsforfittingastrometricorbitsofplanetarysystemstoGaiadata.
The first algorithm is based on a hybrid Markov Chain Monte Carlo (MCMC) approach. The global non-
linear least-square problem is partially linearized in then paramters a , w , W , and i (for j =1,...,n, where
j j j j
n is the number of planets) using the Thiele-Innes elements representation (Green 1985). An iterative period
search provides seeds for initializing the MCMC procedure (a parallel-tempering algorithm upgrade is in the
works).AnMCMCchainisthenrunonthenonlinearparameters(e ,P,t ),drawingfromGaussianindependent
j j j
distributions. Each step of the chain drivesa linear LSQ solver (SVD). Multiple MCMC chains are run (one is
usedforinference),andconvergenceischeckedviatheGelman-Rubintest. Finally,thesetofparameterswiththe
highestlikelihoodistheseedforalocalnon-linearminimizationintheleast-squaressenseusingtheLevemberg-
Marquardtalgorithm.
The second otbital solution module implements an approach based on a genetic algorithm (GA). The first
step consists of the generation of a population of 7∗n chromosomes. The fitness of each chromosome in the
populationisevaluated,andtheselectionof‘parent’chromosomepairsismadefromthepopulationaccordingto
theirfitness. Thenextstep includesthe iterativemodelingusinga set ofoperatorssuch asmutation,cross-over,
Levemberg-Marquardt,andperiodscan. Finally, acceptanceof newoffspringsin the populationis realized, and
furtheriterationsofthealgorithmusingthenewpopulationarecarriedout.
ThelastimportantelementoftheDU437softwaremoduleisconstitutedbyitsorbitalstabilityanalysiscompo-
nent.Atpresent,asimpleHillstabilitycriterionisapplied(Marchal&Bozis1982).Foratwo-planetconfiguration,
thesystemwillbeconsideredHill-stableifthefollowinginequalityissatisfied:
2M m m
− c2h>1+34/3 1 2 , (1)
G2M⋆3 m23/3(m1+m2)4/3
whereM isthetotalmassofthesystem, m andm aretheplanetmasses(thesubscript1referstotheinner
1 2
Figure2: Left:First-passperiodogramforastarwithalong-periodplanet.Right: Theperiodogramafterthe
removalofthesignatureoftheouterplanet.
planet), m is the mass of the star, G is the gravitational constant, M =(m m +m m +m m ), c is the total
3 ⋆ 1 2 1 3 2 3
angularmomentumof thesystem, andh is theenergyThisissufficienttodouble-checkdynamicallypathologic
(whilepotentiallycorrectinac 2sense!)solutionsets(e.g.,orbit-crossingduetoe∼1.0)obtainedbytheMCMC
andGAalgorithms.LimiteduseofanN-bodyintegrator(e.g.,Burlisch-Stöer)isbeingtestedatthetimeofwriting.
1.4 AReadinessTest
I show in Figure 2 and Figure 3 some results from the application of the MCMC algorithm on a simulated
Gaiadataforastellarsampleof100nearby(d<100pc)solar-massstarswithGaiamagnitudeG<10magand
orbitedbytwo planetswithperiodsuptotwice thenominal5-yrmissioneduration. Giventhepresent-dayGaia
astrometric error model, inclusive of the effects of a gate scheme to avoid saturation at the bright end (G<13
mag), in this sample ≈1/3 of the systems were not detectable in Gaia astrometry, ≈1/3 had one detectable
planet,and≈1/3hadtwodetectablecompanions. Forexample,inatwo-planetsystemwithalong-periodplanet
identifiedin the initial periodogram(Figure2, left panel), the correctremovalof the outer planet’sorbitunveils
intheperiodogramtheclearsignalofthesecond,innerplanet(Figure2, rightpanel). Similarly,inthecaseofa
systemwithtwoplanetsinducinglow-S/Nsignaturesofcomparablemagnitude,theperiodicityanalysiscorrectly
identifiestheperiodsofbothcomponentsalreadyinthefirstpass(Figure3,leftpanel).Theresultingqualityofthe
fittedperiods(showninFigure3,rightpanel)indetectabletwo-planetsystemsisingoodagreementwithearlier
results(Casertanoetal. 2008).
2. TheGaia-ExoplanetsSynergyPotential
Gaia’s maincontributionto exoplanetscience will be its unbiasedcensusofplanetarysystemsorbitinghun-
dredsof thousandsnearby(d <200pc), relatively bright(G<13)stars across all spectraltypes, screenedwith
constantastrometricsensitivity.Asaresult,theactualimpactofGaiameasurementsinexoplanetsscienceisbroad,
andratherstructured.TheGaiadatahavethepotentialto:a)significantlyrefineourunderstandingofthestatistical
propertiesofextrasolarplanets;b)helpcruciallytesttheoreticalmodelsofgasgiantplanetformationandmigra-
tion; c) achieve key improvements in our comprehension of important aspects of the formation and dynamical
evolutionofmultiple-planetsystems;d)aidintheunderstandingofdirectdetectionsofgiantextrasolarplanets;e)
provideimportantsupplementarydatafortheoptimizationofthetargetselectionforfutureobservatoriesaimingat
thedirectdetectionandspectralcharacterizationofhabitableterrestrialplanets. Forareview,seeSozzetti(2010).
ThebroadrangeofapplicationstoexoplanetsscienceissuchthatGaiadata canbe seenasanidealcomple-
ment to (and in synergy with) many ongoing and future observing programs devoted to the indirect and direct
detectionandcharacterizationofplanetarysystems,bothfromthegroundandinspace,andacrossabroadrange
of wavelengths. Gaia will contribute critically, for example, to the definition of input catalogues for proposed
quasi-all-skyphotometrictransit surveys(PLATO,TESS); it will informground-baseddirectimaging programs
(e.g.,SPHERE/VLT,EPICS/E-ELT)andspectroscopiccharacterizationprojects(e.g.,EChO,FINESSE)aboutthe
epochandlocationofmaximumbrightnessof(primarilynontransiting)exoplanets,inordertoestimatetheirop-
Figure3: Left:First-passperiodogramforastarwithtwolow-S/Nplanets. Right:Fittedvs. truevaluesofthe
orbitalperiodfordetectabletwo-planetsystems.
timalvisibility,andwillhelpinthemodelingandinterpretationofgiantplanets’phasefunctionsandlightcurves.
Anothercriticalaspectwillconcernthelargeeffortintermsofground-basedfollow-upactivitiesto improvethe
characterizationofastrometricallydetectedsystems(andpossiblythosefoundtransitingbyGaiaphotometry).For
example,high-precisionradial-velocitycampaigns(bothatvisibleandinfraredwavelengths)willbeanecessary
complement,withthethree-foldedaimofimprovingthephasesamplingoftheastrometricorbitsfoundbyGaia,
extendingthetimebaselineoftheobservations(toputstringentconstraintsonoractuallycharacterizelong-period
companions),andsearchforadditional,low-massand/orshort-periodcomponentswhichmighthavebeenmissed
byGaiaduetolackofsensitivity.
2.1 ASynergeticExample:TheGaiasurveyofNearbyMDwarfs
Cool,nearbyMdwarfswithinafewtensofparsecsfromtheSunarebecomingthefocusofdedicatedexper-
iments in the realm of exoplanetsastrophysics. This is due to the shift in theoreticalparadigmsin light of new
observations,andtotheimprovedunderstandingoftheobservationalopportunitiesforplanetdetectionandchar-
acterizationprovidedbythissample. Gaia,initsall-skysurvey,willdeliverprecisionastrometryforamagnitude-
limited(G=20)sampleofMdwarfs, providinganinventoryofcoolnearbystarswitha muchhigherdegreeof
completeness(particularlyforlatesub-types)withrespecttocurrentlyavailablecatalogs.
IpresentherepreliminaryfindingsofasimulationexperimentaimedatgaugingtheGaiapotentialforprecision
astrometryofexoplanetsorbitingasampleofknown,nearbydMstars(Lépine2005). Gaiasensitivitythresholds
areexpressedasafunctionofsystemparametersandinviewofthelatestmissionprofile,includingthemostup-to-
dateastrometricerrormodel. Thesimulationsalsoprovideinsightonthecapabilityofhigh-precisionastrometry
toreconstructtheunderlyingorbitalelementsandmassdistributionsofthegeneratedcompanions. Theseresults
willhelpinevaluatingthecompleteexpectedGaiaplanetpopulationaroundlate-typestars.
The synergy between the Gaia data on nearby M dwarfs and other ground-basedand space-borne programs
forplanetdetectionandcharacterizationisalsoinvestigated,withaparticularfocuson: a)thepotentialforGaia
topreciselydeterminetheorbitalinclination,whichmightindicatetheexistenceoftransitinglong-periodplanets;
b) the ability of Gaia to carefully predict the ephemerides of (transiting and non-transiting) planets around M
stars; and c) its potentialto help in the precise determinationof the emergentflux, for systematic spectroscopic
characterizationoftheiratmosphereswithdedicatedobservatoriesinspace,suchasEChO.
Simulation Scheme The basis is constituted by the Casertano et al. (2008) simulation setup. This has been
updatedbyincludingthelatesGaiascanninglaw,foranominalT =5yrmissionduration. Themostup-to-date
errormodelas a functionof Gaia G-band mag has been utilized, with the exclusion of the presently envisioned
gate scheme (affecting only some 20% of bright (G<12) M dwarfs). Single-measurementerrors are typically
s m∼100m as. Theactuallistoftargetsencompasses3150Mdwarfs(0.09−0.6M⊙)within33pcfromtheSun
fromtheLSPM-NorthCatalog(Lp´ine2005),withaverageG∼14.0mag. Oneplanetwasgeneratedaroundeach
star,withmassM =1M ,orbitalperiodP<3T,andmoderateeccentricities(e<0.6).Allotherorbitalelements
p J
Figure4: Left:Fractionalerrorontheinclinationangleiasafunctionofiitself. Right: Degradationrateinthe
predictionforthevalueoforbitalseparationoftheplanetasafunctionofitsorbitalperiod.
Figure5:Left: Errorontheplanetaryphasefunction(assumingaLambertsphere)asafunctionofuncertainty
onthereconstructedplanetaryphase. Right:Predictedplanetaryemergentflux(anduncertainty)asafunctionof
orbitalseparationfromtheMdwarfprimary.
wereuniformlydistributedwithintheirrespectiveranges.
PreliminaryResults Themainfindingsinthisexperimentcanbesummarizedasfollows: 1)Fordetectedgiant
planetswithperiodsintherange0.2−5yr(i.e.,withaccuratelydeterminedmassesandorbits),inclinationangles
will be determined with enough precision (<1%, see Figure 4, left panel) so that it will be possible to identify
long-periodplanetswhicharelikelytotransit;2)forwell-sampledorbits(P<T),theuncertaintiesonplanetary
ephemerides,separationr andpositionangleJ , willdegradeattypicalratesofD r <0.01AU/yr(seeFigure4,
right panel) and D J <1 deg/yr, respectively. These are over an order of magnitude smaller than the degrada-
tionlevelsattainedbypresent-dayephemeridespredictionsbasedonmilli-arcsecprecisionHST/FGSastrometry
(Benedictetal. 2006);3)Planetaryphaseswillbe measuredwith typicaluncertaintiesD a ofa few degrees,re-
sulting (assuming a simple purely scattering atmosphere) in average errors on the phase function DF (a )≈0.1
(Figure 5, left panel), and expected uncertainties in the determination of the emergent flux of wide-separation
(a>0.3AU)giantplanetsof∼15%(Figure5,rightpanel).
AlltheaboveconclusionshelptoquantifytheactualrelevanceoftheGaiaobservationsofthelargesampleof
nearbyMdwarfsforinasynergeticefforttooptimizetheplanningandinterpretationoffollow-up/characterization
measurementsofthediscoveredsystemsbymeansoftransitsurveyprograms,andupcomingandplannedground-
based as well as space-borne observatories for direct imaging (e.g., SPHERE, EPICS) and simultaneous multi-
wavelengthspectroscopy(e.g.,EChO).
Conclusion
Thelargestcompilationofhigh-accuracyastrometricorbitsofgiantplanets,unbiasedacrossallspectraltypes
up to d <200 pc, will allow Gaia to crucially contribute to several aspects of planetary systems astrophysics
(formation theories, dynamical evolution), in combination with present-day and future extrasolar planet search
programs.
Inthispaper,I havefirst discussedsomeofthe relevantissue relatedtothe robustassessmentof astrometric
orbits of planetary systems detected by Gaia, with a focus on readiness tests of the DU437 software module
in charge of providing(single and multiple) orbital solutions for exoplanetswithin the contextof the Gaia data
processingpipeline. Then,I havepresentedpreliminaryresultsonan investigationofthesynergybetweenGaia
astrometryonnearbyMdwarfsandotherground-basedandspace-borneprogramsforexoplanetcharacterization,
focusing on: a) the potential for Gaia to precisely determine the orbital inclination, which might indicate the
existenceoftransitinglong-periodplanets;b)theabilityofGaiatocarefullypredicttheephemeridesof(transiting
andnon-transiting)planetsaroundMstars;andc)itspotentialtohelpintheprecisedeterminationoftheemergent
flux,forsystematicspectroscopiccharacterizationoftheiratmosphereswithdedicatedobservatoriesinspace.
Acknowledgements
TheauthorwishestothankM.G.Lattanzi,R.Morbidelli,G.Micela,G.Tinetti,P.Giacobbeandthecolleagues
of(DPACCU4)DU437D.Ségransan,D.Sosnowska,andN.Rambauxfortheirhelp,discussions,andinputs.
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