On High-Contrast Characterization of Nearby, Short-Period Exoplanets with Giant Segmented-Mirror Telescopes

0.7 MB·English

by  Ian J. M. Crossfield

Astronomy&Astrophysicsmanuscriptno.aa (cid:13)c ESO2013
January25,2013
On High-Contrast Characterization of Nearby, Short-Period
Exoplanets with Giant Segmented-Mirror Telescopes
IanJ.M.Crossfield
Max-PlanckInstitu¨tfu¨rAstronomie,Ko¨nigstuhl17,69117,Heidelberg,Germany
e-mail:[email protected]
A&AAccepted,24.Jan2013.
ABSTRACT
Measurementsofthefrequencywithwhichshort-periodplanetsoccuraroundmainsequencestarsallowsadirectpredictionofthe
3
numberandtypesofsuchplanetsthatwillbeamenabletocharacterizationbyhigh-contrastinstrumentsonfuturegiantsegmented-
1
mirrortelescopes(GSMTs).Adoptingconservativeassumptions,Ipredictoforder10planetswithradiiR “1´8R andequilibrium
0 P C
temperatures(cid:46) 400Kshouldbeaccessiblearoundstarswithin8pcoftheSun.Thesenumbersareroughlythesameforbothnear-
2
infraredobservationsofscatteredstarlightandmid-infraredobservationsofplanetarythermalemission,withthelatterobservations

n demonstratinggreaterrelativesensitivitytosmallerandcoolerplanets.AdoptingtheconservativeassumptionthatplanetswithR “
P
a 1´2R and2´4R occurwithequalfrequency,Ipredicta40%chancethataplanetwithR “1´2R andequilibriumtemperature
C C P C
J 200–250Kwillaccessibletohigh-contrastthermalinfraredcharacterization;thiswouldbeacompellingobjectforfurtherstudy.To

4 validatethesepredictions,moredetailedanalysesareneededoftheoccurrencefrequenciesoflow-massplanetsaroundMdwarfs,both
2 intheKeplerfieldandinthesolarneighborhood.Severalplanetsalreadydiscoveredbyradialvelocitysurveyswillbeaccessibleto
near-infraredhigh-contrastGSMTobservations,includingthelow-massplanetsαCenBband(dependingontheiralbedos)GJ139c
] andd,GJ876bandc,andτCetb,c,andd;τCetfwouldbeamenabletothermalinfraredcharacterization.Furthereffortstomodel
P thenear-infraredreflectanceandmid-infraredemissionoftheseandothershort-periodplanetsareclearlywarranted,andwillpave
E thewayfortheinterpretationoffuturehigh-contrastcharacterizationofavarietyofplanetsaroundtheneareststars.
.
h Key words. Planets and satellites: general — Planets andsatellites: detection — Instrumentation: adaptive optics — Techniques:
p highangularresolution—Methods:numerical
-
o
r
t 1. Introduction fluxesmaketheseplanetsthemostamenabletoremotecharac-
s
a terizationoftheiratmosphericand/orsurfacecompositions.
[ In recent years much effort has been devoted to preparing
A 1.1 Earth-mass (M ) planet candidate has been announced
C for observations of potential Earth analogues transiting cool M
1 around α Centauri B (Dumusque et al., 2012), and a family
v of five candidates with minimum masses 2–10M has been dwarf using, e.g., JWST (Deming et al., 2009; Kaltenegger &
C
4 announced around τ Ceti (Tuomi et al., 2012). If confirmed, Traub, 2009). However, because even short period planets are
8 unlikely to transit, the nearest accessible transiting planets will
the discovery of so many low-mass planets around stars very
8 be around rather fainter, more distant stars. The durations of
neartheSunwouldbeastrongsignthatsuchplanetsarecom-
5 these transits will be short and their signal to noise low, so
mon. Such a conclusion would be consistent with early results
1. from the Kepler mission, which indicate that the frequency of tens or hundreds of observations will be necessary for signifi-
0 planet candidates increases sharply toward smaller planetary cant atmospheric measurements. Phase curve observations pro-
3 radii(R (cid:46) 4R )fororbitalperiods P ă 250d(Howardetal., vide higher duty cycles and may be able to characterize small,
P C
1 non-transitingplanetsaroundstarsclosertotheSun(Selsisetal.,
2012;Dong&Zhu,2012;Fressinetal.,2013).TheseKeplerre-
: 2011; Maurin et al., 2012). Spacecraft capable of making such
v sultsalsosuggestadramaticincreaseinthefrequencyofsmall
measurements have been proposed (e.g., Vasisht et al., 2008;
i planets(radiiR “2´4R )orbitingcoolerstars(Howardetal.,
X P C Swain, 2010; Tinetti et al., 2012), but these observations will
2012).Becausesuchstarsaremorenumerousthansun-likestars,
r there should be many such planets in the Solar neighborhood. require extremely stringent spectrophotometric stability (better
a than10´4overperiodsofdays).Consideringthesevariouslimi-
BecausemostoftheseplanetsorbitMdwarfs,theirequilibrium
tations,itisreasonabletoexplorealternativemodesofexoplan-
temperaturesT arequitecool:typically200–400K.
eq
etarycharacterization.
Theprospectofnumeroustemperate,small,low-massplan- In this paper I present the first quantitative estimates of
ets orbiting nearby stars is an exciting one. Such planets may thelocalexoplanetpopulationaccessibletoground-basedhigh-
lieintheirhoststars’“habitablezones”andbecapableofsup- contrastobservations,andadiscussionofhowsuchobservations
portingliquidwateronanysolidsurface(Huang,1959;Kasting candirectlyconstrainthedemographicsofthelocalplanetpop-
et al., 1993; Pierrehumbert & Gaidos, 2011). These planets ulation. Though it has been appreciated for at least a decade
around nearby stars are also the only ones for which in situ that the next generation of ground-based giant segmented-
exploration could be even remotely feasible in the foreseeable mirror telescopes (GSMTs) can characterize small, cool plan-
future (e.g., Crawford, 2011, and references therein). For now, etsviasuchobservations(Angel,2003;Hawardenetal.,2003),
theproximityofnearbysystemsandtheirattendanthighphoton Kepler’sabilitytomeasureplanetfrequencyasafunctionof P,
1
Crossfield:GSMTHigh-ContrastCharacterizationofShort-PeriodExoplanets
RP,andstellareffectivetemperatureTeffwithunprecedentedpre- sion. Such a homogeneous stellar characterization effort would
cisionpermitsthefirstinformedestimateofthenumberofshort- behighlydesirable,andwouldreducetheneedfortheassump-
periodplanetsthatwillbeaccessibletofuturelarge-aperturefa- tionsaboutstellarparametersdescribedabove.
cilities.
Sec. 2 discusses simulations of statistically representative
2.2. ModelingtheLocalExoplanetPopulation
planetary systems around nearby stars and an assessment of
high-contrast GSMT instruments’ ability to characterize these I estimate the distribution of the local exoplanet population us-
planets.Sec.3thenpresentsthenumberofplanetsaccessibleto ingananalysisofplanetfrequencyasafunctionofTeff, P,and
suchcharacterizationundervariousassumptionsofplanetaryoc- R from the Kepler planet candidate sample derived from the
P
currencefrequencyandinstrumentalcapabilities,anddiscusses firstthreequartersofKeplerobservations(Boruckietal.,2011;
the consequences of these assumptions. The main results are Howardetal.,2012).Althoughthesefrequenciesarecomputed
summarizedinTable1.Inbrief,oforder10planetsarepredicted forplanetcandidatesandnotfullyvalidatedplanets,theoccur-
to be amenable to such characterization at either near-infrared rence of false positives in the sample is below 15% (Morton &
(NIR,ă 2.5µm)ormid-infrared(MIR,„ 10µm)wavelengths, Johnson,2011;Fressinetal.,2013).Furthermore,planetcandi-
andthisnumbervariesbynomorethanafactorof2underrather dates with radii R “ 2´4R (the targets most accessible to
P C
moreoptimisticorpessimisticassumptions.Inaddition,thereis high-contrastcharacterization)haveacontaminationfractionof
significant likelihood (at least 40%, and probably „4ˆ higher) ă 7%(Fressinetal.,2013).ThustheKeplerfalsepositiverate
that such observations will be able to characterize an Earth or hasatmostaminoreffectontheresultspresentedhere.
Venusanalogue(RP “ 1´2RC,Teq “ 200´250K).Finally, Hot Jupiters are only half as frequent in the Kepler sample
I summarize the results of this work and suggest useful future as observed by radial velocity surveys (Howard et al., 2012).
workinSec.4. Theauthorsattributethisdiscrepancytothelowermetallicityof
theKeplersample,underwhichconditionsfewermassiveplan-
ets should be expected (Santos et al., 2004; Fischer & Valenti,
2. Methods
2005).Ifthisdiscrepancyisconfirmed,thenthesimulationspre-
sented here underestimate the frequency of large planets by as
2.1. DefiningtheLocal,ObservableStellarPopulation
muchasafactorof2;theseplanetsareintrinsicallyrare,sothis
To construct an observable sample of nearby stars, I take the is a small effect. The frequency of Neptune-mass and smaller
8pc sample of Kirkpatrick et al. (2012) and remove all white planetsdependslessstronglyonstellarmetallicitythandoesthe
dwarfsandspectraltypeslaterthanM7(toavoidbrowndwarfs). frequencyofJupiter-massobjects(Sousaetal.,2008;Buchhave
Whiteandbrowndwarfsmayhavelowmassplanets,andthese et al., 2012); since I show below that smaller planets comprise
planetscouldevenbetemperate(Andreeshchev&Scalo,2004; the bulk of the planet population accessible to high-contrast
Monteiro,2010),butatpresentthefrequencyofplanetsinsuch characterization,differencesbetweentheKeplerandlocalstellar
systemsremainsverypoorlyconstrained.Becausehigh-contrast populationsshouldnotstronglyaffecttheseresults(thisassump-
observations have difficulty attaining the contrast necessary for tionwillbetestedinthefuturebyhigh-precisionradialvelocity
planet characterization in the presence of nearby bright point surveys).
sources (mitigation strategies exist but require customized in- IbeginbydeterminingthefrequencyofplanetsofgivenR
P
struments;seee.g., Creppetal.,2010;Cadyetal.,2011),Ire- for each star, based on its Teff. I assume that binary stars have
move all known binaries with apparent separations (cid:46) 5”. Stars planetfrequenciesconsistentwiththoseofsinglestars,andthat
with fainter companions (e.g., Procyon A and Sirius A) are re- 4´8R and8´32R planetsoccurwithfrequenciesof1.7%
C C
tained.ForobjectslistedbyKirkpatricketal.(2012)witharange and 0.79%, respectively (see Figure 8 of Howard et al., 2012).
ofspectraltypes,Itakethemeanofthespecifiedrange.SomeM For 2 ´ 4R planets, I compute a frequency using Eq. 9 of
C
dwarfsarelistedwithoutanyspectraltype,andfortheseItake Howardetal.(2012),whichwasdefinedusingTeff intherange
thespectraltypesspecifiedbyRojas-Ayalaetal.(2012).Thefi- 3600–7100K.IextendthisrelationtolowerandhigherTeff by
nallistcontains92,20,6,2,and4starsoftypesM,K,G,F,and assumingthatbeyondthespecifiedrangethefrequencydistribu-
A,respectively. tionofplanetsisuniformandeverywherecontinuous.InSec.3.2
Accurate stellar parameters are not known for all these ob- I quantify the effect of this assumption. Howard et al. (2012)’s
jects, so I adopt a homogeneous approach and assign Teff and planet statistics are incomplete for RP ă 2RC, but their results
stellarradiiusingempirical,interferometrically-determinedval- suggest 1´2R planets are at least as common as 2´4R
C C
ues (Boyajian et al., 2012a,b) for each spectral type. Apparent planets. I conservatively assume that planets in these two size
V-band magnitudes are taken from the UCAC4 Catalogue rangesoccurwithequalfrequency,consistentwithmorerecent
(Zachariasetal.,2012),convertedtoabsoluteVmagnitudesus- analyses(Dong&Zhu,2012;Fressinetal.,2013).Throughout
ing the parallax values in Kirkpatrick et al. (2012), and con- thiswork,Iassumeauniformdistributionofplanetsizeswithin
verted to stellar masses using the mass-luminosity relationship eachoftheR rangesnotedabove.
P
ofHenry&McCarthy(1993);usingtheKbandrelationshipof Theprecedingstepsdeterminethenumberofplanetsofvary-
Delfosseetal.(2000)affectsthemassesthusderivedbyroughly ing R expected around a given star for P ă 50 d. In each of
P
15%,butthisdoesnotsignificantlyaffectmyresults.Finally,a 104 trials I assign to each star either no planet or a planet in
BT-Settlstellarmodel(Allardetal.,2011)isgeneratedbyinter- one of the four R bins listed above, with the appropriate fre-
P
polatinginloggandTeff tothestellarparameters,andaccount- quencies.IthenassumethatPineachradiusrangefollowsthat
ingforthestar’ssizeanddistancefromtheSun. givenbyEq.8andTable5ofHowardetal.(2012).Thoughtheir
Note that this 8 pc sample is sufficiently small that high- planet population statistics are limited to P ă 50 d, even over
qualityspectracouldbeobtainedforallthesetargetswithrela- thissmallrangethefrequencyofplanetsincreasesinlnPspace
tiveease.Spectraatlowresolutionwouldprovideausefulabso- for P ą 10 d. I conservatively assume that planet frequency is
lutefluxcalibration,andspectraathighresolutionwouldpermit flat for P ą 50d (see also Dong & Zhu, 2012). Letting planet
stellar parameters and abundances to be derived at high preci- frequencyincreasetowardlongerperiodsonlyslightlyincreases
2
Crossfield:GSMTHigh-ContrastCharacterizationofShort-PeriodExoplanets
the number of accessible planets, because the planets most ac- rors, sensed via a Mach-Zehnder pupil plane wavefront sensor.
cessibletohigh-contrastcharacterizationlieonshort-periodor- The wavefront sensing and science wavelengths are assumed
bits(seeSec.3.2).Futurestudiesshouldcharacterizeplanetfre- to be identical to minimize chromatic contrast errors (Guyon,
quency at longer orbital periods (this is a primary goal of the 2005).The relationsusedcompute rawcontrast andnotthe ef-
Kepler mission) and should explore the dependence of planet fectivecontrastlimitsfordetection;Ithereforeassumethatob-
frequencyonTeff ingreaterdetail. servationalandpost-processingtechniquescansuppressthein-
The result of this process is a planet population that pro- stantaneous PSF contrast by a factor of 30 at all angular sepa-
vides a direct estimate of the frequency of planets with R and rations;currenttechniques achievesuppressionfactorsof20 to
P
P around each star in the 8 pc sample. Planetary systems may severalhundredatseparationsassmallas4.5λ{D(Maroisetal.,
be more diverse than predicted by this simple model: for ex- 2008;Creppetal.,2011;Vogtetal.,2011),sothevalueassumed
ample, the M dwarf GJ 876 has multiple massive planets (e.g., here may be somewhat conservative. Finally, following Lunine
Baluev,2011)whileshort-periodplanetsofevenverylowmass et al. (2008) I impose an absolute contrast floor of 5 ˆ 10´9
have been excluded around the low-mass Barnard’s Star and in all cases. The result is a simulation of high-contrast perfor-
Proxima Centauri (Endl & Ku¨rster, 2008; Zechmeister et al., mance with the phenomenologically correct dependencies on
2009; Choi et al., 2012). Nonetheless the modeling approach wavelength,telescopesize,stellarflux,andotherparameters2.
described above has the advantages of being relatively simple In these performance estimates I also crudely account for
andofprovidingestimatesacrossabroadrangeofplanetaryand the effect of finite stellar sizes, which are significant for sev-
stellarparameterspacethatdecentlyapproximatetheplanetde- eralofthenearestandlargeststars.Forexample,bothαCenA
mographics presented by Howard et al. (2012). Future efforts andSiriusAhaveangulardiametersθ “ 8mas,comparableto
shouldstrivetoquantifyplanetfrequencyoverasbroadarange the diffraction-limited angular resolution (λ{D) of a 30m tele-
aspossibleofTeff,P,andRPtoobviatetheneedforsomeofthe scopeobservingat1.2µm.Resolvedsourcescausetheeffective
assumptionsmadeabove. throughput of high-contrast observations to decrease markedly
at the smallest separations (Guyon et al., 2006), though the
attainable contrast is not adversely affected for proper choice
2.3. EstimatingHigh-ContrastInstrumentPerformance
of coronagraph or other starlight suppression system (Crepp
Adaptiveoptics(AO)systemsdesignedtoprovideveryhighim- etal.,2009).Iapproximatethedeleteriouseffectsoffinitestel-
age quality are often termed “high contrast” systems, a name larsizebyimposingaminimuminnerworkingangle(IWA)of
which emphasizes their sensitivity to faint objects located near p2.2`0.4log10rθpλ{Dq´1sqλ{D,arelationwhichapproximates
much brighter ones; see Oppenheimer & Hinkley (2009) and the 50% throughput limit of an ideal coronagraph operating at
Mawetetal.(2012)forrecentreviewsonthistopic.Atleastone 10´10 contrast (Guyon et al., 2006). This minimum separation
high-contrastsystemisalreadyoperatingon-skyatthe5mHale increasesforlargerθ,moreextremecontrastlevels,andlessop-
telescopeandreachingcontrastlevelsof„10´7 (Oppenheimer timal coronagraph designs. In this work finite stellar size only
etal.,2012),andevenmorecapableinstrumentsareundercon- affectsafewstarsystems(thosewiththelargestθ),andonlyin
struction for existing 8m telescopes (Macintosh et al., 2006a; the2λ{DIWAcasedescribedinSec.3.3.1.Futurehigh-contrast
Beuzitetal.,2006).End-to-endsimulationsandtestingofthese observationsprobingnearorwithin1λ{D(Serabynetal.,2010)
latter instruments suggest they may reach final contrasts of shouldconsidertheseeffectsingreaterdetail.
roughly 10´8 (Mesa et al., 2011; Thomas et al., 2011; Wildi
etal.,2011).Atthislevelofperformance,short-periodexoplan-
2.4. EstimatingtheObservabilityofShort-PeriodPlanets
etswilllikelyremainbeyondthereachofsuchinstruments(see
Sec.3.3.1). I assess the accessibility of each simulated planet to high-
The next generation of GSMTs will have diameters rang- contrastobservationsbyconsideringbothscatteredstarlightand
ing from 25m (GMT; Johns, 2008) to 30m (TMT; Nelson & thermalemissionfromtheplanet.Iassumethatallplanetswill
Sanders,2008)to39m(E-ELT;Gilmozzi&Spyromilio,2007), be observed at quadrature, since radial velocity measurements
andallareprojectedtorelyheavilyonAO-assisted,diffraction- will allow optimal phasing of most interesting targets. I fur-
limitedobservationstomaximizethesciencegainsofthesenew ther assume that all planets are on circular orbits and exhibit
facilities. High-contrast NIR instruments have been proposed Lambertianscatteringprofiles,andthattheobservatorycanob-
and studied for all these telescopes (Macintosh et al., 2006b; serve all stars in the target sample (under currently published
Matsuo & Tamura, 2010; Brandl et al., 2010; Kasper et al., plansGSMTswillbelocatedinbothhemispheres).
2010).Theseinitialstudiessuggestthatwithmoderateandrea- I assign a Bond and wavelength-independent geometric
sonabletechnologicaladvances,suchinstrumentswillbesensi- albedo (A and A , respectively) to each planet by drawing a
B g
tive to objects at separations and contrast levels unprecedented value from a uniform random distribution spanning 0.0–0.4, a
foroptical/infraredtelescopes. rangewhichisaroughlyrepresentativeforsolarsystemplanets
High contrast instruments generally require highly special- (seealsoHuetal.,2012).AlthoughA andA describedifferent
B g
izeddesignstoachievetheirgoals,andtheirperformancevaries physical quantities (A determines the strength of scattering at
g
across different targets, telescopes, and wavelengths. I estimate agivenwavelength,whileA determinesaplanet’sequilibrium
B
the performance of a generic GSMT high-contrast instrument temperature T , and thus its thermal blackbody emission; see
eq
using the analytic relations of Guyon (2005) and adopting the e.g.,Seager,2010),forsimplicityIusethesamevalueforeach
parametersinTable4ofthatworkunlessnotedotherwise(vari- planet’sA andA .Thisequalityholdstowithinafactoroftwo
B g
ationsofinstrumentparametersarediscussedinSec.3.3)1.The for planets in the Solar System. At NIR wavelengths most ob-
instrument is assumed to correct both phase and amplitude er- servableplanetsinthesimulationsbelowareonlyaccessiblein
1 Note that Eqs. 16 and 17 of Guyon (2005) contain an error: the 2 A Python software module used to calculate these quantities is
coefficient0.484shouldbe0.0484(O.Guyon,privatecommunication, availablefromtheauthor’swebsite,located(asofpublication)athttp:
Jan2013). //www.mpia.de/homes/ianc/
3
Crossfield:GSMTHigh-ContrastCharacterizationofShort-PeriodExoplanets
reflected light, so higher or lower albedos will respectively in-
10-3
ctlherneeagestffheseo.crTtodiseecraercevhaesrpeselatdhneefotsrIizoaeblssooefravtshasetiigoanncscaeahstsetiahbtelerrempdaliaslntirenitbfrupatorieopdnulwfaataicovtone-r; 10-4 8421−−−−38422RRRREEEE 2><032000−0030KK0K
(f; Seager, 2010) drawn from a uniform random distribution st 10-5
spanningtherange(0.25,0.66),wheretheextremaofthisrange ntra
respectively indicate zero and full redistribution of the incident o 10-6
C
stellarflux.Theredistributionfactordoesnotsignificantlyaffect ar
thedetectabilityofplanetsinreflectedlight,butwouldaffectthe et/st 10-7
thermalinfraredobservationsdescribedinSec.3.3.2. n
a
UsingA , f,andthephysicalsystemparametersIthencom- Pl 10-8
B
puteT foreachplanet,andIassumethattheplanetradiatesas
eq
ablackbodywiththistemperature.Finally,theplanettostarflux 10-9
contrastinagivenbandpassistheratioofthesumoftheplanet’s
reflected and thermal photon flux to the photon flux from the 10-1100-2 10-1 100
host star. The planet is assumed to be observable if its contrast Separation [arcsec]
liesabovethesensitivitylimitscomputedinSec.2.3.
Fig.1 SimulatedplanetpopulationsforαCenBinthebaseline
3. SimulationResults
scenario outlined in Sec. 3.1, observing at 1.2µm with an in-
strument similar to TMT/PFI or TMT/SEIT. Planets above and
InthissectionIdiscussthelocalpopulationofplanetsaccessible
to the right of the dashed line would be accessible to high-
to characterization by high-contrast observations under a num-
berofdifferentassumptionsaboutplanetpopulationparameters contrast spectroscopic characterization. The star symbol indi-
catesαCenBb(assumingaradiusof1.1R ).Eachcircle’ssize
and instrumental configurations. I begin by presenting a set of C
andcolorreferstoasimulatedplanet’sR andT ,asindicated
baselineastrophysicalandobservationalparametersinSec.3.1. P eq
Sec. 3.2 discusses the effects of varying the parameters of the inthelegend.Mostofthesimulatedplanetsshownaredetected
inscatteredstarlight,thoughthermalemissioncontributestothe
localplanetarypopulation,andSec.3.3discussestheimpactof
shortest-periodplanets(includingαCenBb).
various telescope and instrument design choices. For all cases
discussed,thenumberofplanetsofvariousR andT accessi-
P eq
bletohigh-contrastcharacterizationislistedinTable1.
10-3
8 32R
3T.h1e.bBaasseelilnineeoSbsceernvaartiioonal parameters are a 30m telescope ca- 10-4 421−−−−842RRREEEE 2><032000−0030KK0K
pableofobservingdowntoanIWAof3λ{D:thisinstrumentis ast 10-5
analogoustoTMT’sPFIorSEITinstruments(Macintoshetal., ntr
2006b;Matsuo&Tamura,2010),butwithbetterwavefrontsen- ar Co 10-6
stioornpmerifdowrmayanbceetw.Tehenistbhaes2e5linmeGcaMseTparonvdid3e9smanEa-EngLuTl.aIrardesoopltua- et/st 10-7
n
baselineobservingwavelengthof1.2µm(Jband),wherefuture Pla 10-8
AOsystemsshouldachievegoodcorrectionandwhichprovides
good angular resolution. Observations at J band are also inter- 10-9
estingbecauseoftheirpotentialtodescrythe1.27µmO band
2 10-10
expected in oxygen-rich planetary atmospheres (e.g., Turnbull 10-2 10-1 100
et al., 2006; Kawahara et al., 2012). In terms of astrophysical Separation [arcsec]
parameters, the baseline scenario assumes that 1 ´ 2R and
C
2 ´ 4R planets occur with equal frequencies (as described
C Fig.2 SameasFig.1,butfortheMdwarfGJ876.Fromleftto
inSec.2.2,thismaybeaconservativeunderestimate),andthat
right,thestarsymbolsanderrorbarsshowthecontrastexpected
planet frequency is flat in lnP space for P ą 50 d (the longest
forplanetsc,b,andeovertherangeofalbedosandrecirculation
periodsconsideredbyHowardetal.,2012).
parametersdescribedinSec.2.4.Planetsbandcwillbeaccessi-
Fig. 1 shows a representative planet sample and the com-
bletocharacterizationinscatteredlightifA pR {R q2 (cid:38)19and
putedsensitivitylimitsasappliedtoαCenB.Itisnotablethat g P C
6,respectively.
the recently discovered low-mass planet candidate α Cen Bb
(Dumusqueetal.,2012)presentsacontrastof10´7 andisemi-
nentlyobservableinthisbaselinescenario(assumingaradiusof
1.1RC,obtainedbyconvertingmsinitoRPviaEq.1of Lissauer Ag (cid:38) 0.4),andtheplanetcandidatesτCetb,c,anddcouldbe
et al., 2011). A simulation of the GJ 876 system is shown in characterizedforA pR {R q2 (cid:38)0.08,0.4,and1.2,respectively
g P C
Fig. 2; despite the worse contrast achieved on this fainter star, (A ą0.04,0.14,and0.35).Theoreticaleffortstomodelallthese
g
themassiveplanetsGJ876bandc(Delfosseetal.,1998;Marcy planets’NIRreflectanceareclearlywarranted.
et al., 1998, 2001; Baluev, 2011) can be directly characterized The number of accessible planets in this baseline scenario
if A pR {R q2 (cid:38) 19 and 6, respectively (A (cid:38) 0.02, with radii are shown in Fig. 3 as a function of T and R , and these re-
g P C g eq P
estimatedasdescribedpreviously).Thoughnotshown,thecur- sults are summarized in the first row of Table 1. In all results I
rentlyknownplanetsGJ139candd(Pepeetal.,2011)canalso sorttheplanetsbysize(intherangesdescribedpreviously)and
becharacterizedifA pR {R q2 (cid:38)0.9and1.8,respectively(i.e. according to whether T is below, within, or above the range
g P C eq
4
Crossfield:GSMTHigh-ContrastCharacterizationofShort-PeriodExoplanets
appearsthatthisrelationdoesnotapplytoR ă2R ;nonethe-
P C
less, Table 1 shows that approximately equal numbers of plan-
etsinthetwosmallestsizerangeswouldbeaccessibletochar-
acterization if the trend held to smaller radii (i.e., if Kepler’s
completeness is significantly overestimated for R ă 2R ;
P C
Howard et al., 2012; Dong & Zhu, 2012; Fressin et al., 2013).
However, because the smaller planets must be closer to their
hoststarstopresentthesamecontrastratioasthelargerplanets,
theadditional1´2R planetshaveratherwarmertemperatures
C
(T „400K)thanthebaselinepopulation.
eq
Mybaselinescenarioconservativelyassumesthatplanetfre-
quencyflattensoutfor P ą 50d,consistentwithrecentresults
usingadditionalKeplerdata(Dong&Zhu,2012).Arecentanal-
ysis of the first six quarters of Kepler data extends planet fre-
quencyestimates(Dong&Zhu,2012).Thatworkindicatesthat
the frequency of planets in lnP space for P ă 250 d appears
flat for R ă 4R , but continues to increase for larger plan-
P C
ets; this is consistent with radial velocity surveys, which show
that the frequency of massive planets continues to increase out
to2000d(Cummingetal.,2008).Iinvestigatetheimpactmore
Fig.3 Predictednumberofplanets(asafunctionofR andT ) frequentplanetoccurrenceonlongerperiodsbylettingHoward
P eq
expectedtobecharacterizedinthebaselinehigh-contrastGSMT etal.(2012)’splanetfrequencyrelationsincreaseatlongerperi-
observingscenariooutlinedinSec.3.1.Thecolorsandthesmall ods (instead of arbitrarily flattening the distributions). Table 1
numbers in each cell both indicate the expectation value for shows that compared to the baseline scenario, two additional
that combination of R and T , and the histograms show the planets (one each with sizes 4 ´ 8R and 8 ´ 32R ) would
P eq C C
marginalizeddistributions.Notethatthebaselinescenariosimu- be accessible to high-contrast characterization in this scenario.
latedhereconservativelyassumesthatplanetsinthetwosmallest Because these additional planets occur on longer periods, they
R rangesoccurwithequalfrequency(seeSecs.2.2and3.2). arerathercooler(T ă200K)thanthebaselinepopulation.
P eq
Perhaps the least conservative assumption in my baseline
200–300 K (a range which corresponds crudely to the Teq of scenario is the decision to assign planets to stars with Teff ă
Mars and a low-albedo Venus). Fig. 3 shows that the planets 3600 K, below the range explored by Howard et al. (2012).
detected in the baseline scenario typically have T ă 400 K Large-scale radial velocity campaigns have been conducted for
eq
and RP ă 4RC: these planets are visible mainly via scattered afewsuchstarsandhavefoundnoplanetsdownto„10MC in
starlight and not intrinsic thermal emission. Although Howard short periods (e.g. Proxima Centauri and Barnard’s Star; Endl
et al. (2012) show that planets with R ă 4R are most fre- & Ku¨rster, 2008; Zechmeister et al., 2009; Choi et al., 2012).
P C
quently found around cooler stars, I find that few planets or- Table 1 shows that even if all cool stars have zero planets,
biting M dwarfs are accessible at distances (cid:38)3.5 pc as a result roughlyfiveplanetswouldstillremainforfuturestudies.
of these stars’ intrinsic faintness, and the consequent degrada-
tionofachievablecontrast.Finally,Iestimatea6%chancethat
The immediately preceding assumption is of course overly
in this baseline scenario an Earth/Venus analogue (1 ´ 2R ,
C pessimistic, since planets with msini ą 10M have been dis-
T “ 200´250K)canbeobserved.Thisprobabilityislikely C
eq coveredaroundanumberofMdwarfs(e.g.,Butleretal.,2004;
an underestimate for the reasons described in Sec. 2.2; such a
Bonfilsetal.,2005,2007,2012).Furthermore,asystematicra-
planetwouldmostlikelybefoundaroundProxima Centaurior
Barnard’s Star. The probability increases to ą 50% when con- dial velocity survey of a large number of cool (Teff ă 3600 K)
hasrecentlyindicatedaplanetoccurrencefrequencyofroughly
sidering planets with R “ 1´4R ; these temperate planets
P C 90%formsini“1´100M ,Pă100d(Bonfilsetal.,2013).
alsomostlikelytobefoundaroundnearbyMdwarfs. C
UsingtheplanetpopulationstatisticsreportedinTable11ofthat
survey(insteadofextendingtheHowardetal.,2012frequencies)
3.2. AbilitytoQuantifytheLocalExoplanetaryDemographics for stars with Teff ă 3600 K, I predict numbers and types of
planetsamenabletohigh-contrastcharacterizationnearlyidenti-
Several assumptions were made in Sec. 2.2 to extrapolate the caltothatpredictedbythebaselinescenario(seeTable1).Inthis
KeplerpopulationstatisticsofHowardetal.(2012)tolongeror- simulationIassumelog-uniformfrequenciesof2.7%and3%for
bitalperiodsandcoolerstars,andinthissectionItesttheeffects planetswith102´103and10´102M ,respectively,whilethe
C
of these assumptions. The results of these tests are all listed in leastmassiveplanets(1´10M )havefrequenciesof36%for
C
thesecondsectionofTable1. P“1´10dand52%forlongerperiods.IconvertmsinitoR
P
Howardetal.(2012)findroughlyequaloccurrencefrequen- asinSec.3.1(Lissaueretal.,2011),andimposeamaximumra-
cies for 1´2RC and 2´4RC planets. The baseline scenario diusof1.3RJ.Thecloseagreementbetweenthissimulationand
describedinSec.3.1conservativelyassumesthat2´4RCplan- thebaselinescenarioofSec.3.1hintsthattheresultsofHoward
ets and 1 ´ 2RC planets occur with equal frequency, an as- et al. (2012) and Bonfils et al. (2013) are consistent for small
sumptionalsoconsistentwithmorerecentresults(Dong&Zhu, planetsorbitinglow-massstarsunderfairlysimpleassumptions.
2012;Fressinetal.,2013).Forlargerradii,Howardetal.(2012) Aconclusivetestofsuchaclaimis,however,beyondthescope
find a planet frequency 9R´2 (around sun-like stars). It now ofthiswork.
P
5
Crossfield:GSMTHigh-ContrastCharacterizationofShort-PeriodExoplanets
3.3. EffectsofInstrumentalCapabilities bothdecrease.Nonetheless,Table1suggeststhatseveralplanets
shouldexistwhichareaccessibletocharacterizationacrossfrom
In this section I examine how the accessible exoplanet popula- at least 1´2.2µm. The number of Earth/Venus analogues ex-
tiondependsonvariousobservationalparameters:telescopedi-
pectedtoaccessibletocharacterizationisamaximumat1.6µm,
ameterD,innerworkingangle(IWA),andobservingwavelength a value which presumably represents a tradeoff between angu-
λ.Theresultsofallthesetestsarelistedinthebottomsectionof
larresolutionandthestellarfluxavailableforwavefrontsensing
Table1.
andcorrection.
Intriguingly, thermal-infrared observations appear to be
3.3.1. AngularResolution:DiameterandInnerWorking more attractive than observations at intermediate wavelengths
Angle such as 3.5µm. All three GSMT projects have proposed AO-
assisted MIR instruments (Brandl et al., 2010; Tokunaga et al.,
AsdiscussedinSec.2.3,severalGSMTdesignshavebeenpro- 2010; Okamoto et al., 2010; Hinz et al., 2012). The longer
posed,eachwithdifferentdiametersD.Thebaselineinstrument wavelengths at which these instruments would operate roughly
used in this work has an IWA defined as 3λ{D, so the angu- correspond to the Wien peak of cool planets’ blackbody emis-
lar magnitude of this IWA decreases as D increases. Planets at sion, thereby providing a method to measure radiometric radii
thesmallestseparationshavethehighestobservablecontrast(in (Morrison, 1973), the surface compositions of airless planets
bothscatteredlightandthermalemission),sonaturallyTable1 (Huetal.,2012),andthepotentialtodetectexoplanetaryozone
showsthatthenumberofaccessibleplanetsincreases(bynearly (e.g.,Rugheimeretal.,2012, andreferencestherein).
a factor of two) when D increases from 30m (TMT) to 39m The MIR instrument simulated here is not conservative in
(E-ELT). The number decreases by a similar factor when D is onerespect:asinthiswork’sothersimulations,Iassumethatthe
reducedto25m(GSMT). instrument’swavefrontsensorandscienceinstrumentoperateat
Table1alsoshowsthatatmostasingleshort-periodplanet thesamewavelength.Currentdesignsforsuchinstrumentstypi-
ispredictedtobeaccessibletohigh-contrastinstrumentsoncur- callyrelyonfacilityAOsystems,whosewavefrontsensorsoper-
rent8mtelescopes,ifinstrumentsonthesetelescopescanreach ateatshorterwavelengths.Undersuchastrategy,chromaticef-
contrastlevelsof5ˆ10´9.Inthiscase,theworkpresentedhere fectsmaydegradetheachievablecontrasttothepointthatshort-
predictsaą1%chanceofaccessibleplanetsforonlyfourstars: period planets become inaccessible (Guyon, 2005). Instrument
αCenAB(15–20%each),ProcyonA(5%),andSiriusA(3%). designersshouldthereforeconsiderthefeasibilityofMIRwave-
These expectation values drop by only a factor of 2 if such fa- front sensing for these instruments, either with a separate MIR
cilities can only achieve contrasts of 10´8. These star systems wavefront sensor or (to minimize non-common wavefront er-
should therefore be high-priority targets for deep observations rors) via phase retrieval and correction using the main science
inimminent8mhigh-contrastsurveys. camera(e.g.,Malbetetal.,1994;Borde´ &Traub,2006).
Similarly, using a narrower or wider IWA than the baseline Fig.4showstheplanetpopulationexpectedaroundτCetand
scenarioofSec.3.1respectivelyincreasesordecreasesthenum- theexpectedsensitivitylimitsforanE-ELT/METIS-likeinstru-
ber of accessible planets, as expected (see Table 1). However, ment(λ “ 10µm,D “ 39m,andaconservativeminimumcon-
varying IWA has a weaker impact than varying D, even when trastof10´7;Brandletal.,2012).Notethattheplanetcandidate
theangularscaleoftheIWAisheldconstant.Thisresultmayat τCetf(Tuomietal.,2012)wouldbeamenabletohigh-contrast
firstseemsurprising:2λ{Dona30mtelescopegivesasmaller characterizationat10µm,assumingareasonablealbedo((cid:46)0.7).
angularseparationthandoes3λ{Dona39mtelescope,yetmore Ahigh-contrastMIRinstrumenthasamuch-reducedangular
planets are accessible for characterization under the latter con- resolutioncomparedtoNIRobservations,butplanetarythermal
ditionsthanundertheformer.Theincreasedsensitivityatlarger emissionbooststheplanet/starcontrastratiossignificantlyabove
DforconstantangularIWAresultsfromtheD´1dependenceof thevaluesseenatshorterwavelengths;consequently,compara-
PSF speckle amplitude on phase and amplitude errors (Guyon, blenumbersofplanetsareexpectedtobeaccessibletoNIRand
2005). Thus for two high-contrast instruments with equal IWA MIR characterization. Fig. 5 shows the accessible local planet
(inangularunits),theinstrumentwiththelargerprimarymirror populationasafunctionofR andT forthethermalimaging
P eq
canreachbettercontrastlevels. simulation,andthelastrowofTable1summarizestheseresults.
High-contrast thermal-IR instruments thus offer the poten-
tialtodirectlymeasurethermalemissionfromshort-periodplan-
3.3.2. ObservingWavelength:ScatteredStarlightand
ets down to very small planetary radii. Thermal imaging shifts
ThermalEmission
the distribution of sampled planets to substantially cooler T
eq
The choice of observing wavelength λ has a number of impor- (ă200K)ascomparedtotheNIRbaselinescenarioofSec.3.1
tant consequences: with D it sets the angular scale of the IWA (which is sensitive to rather hotter planets at smaller separa-
(typically specified in λ{D), it determines the stellar flux avail- tions). The number of 1 ´ 2R planets accessible to thermal
C
able for sensing and correction of phase and amplitude errors, infraredcharacterizationiscomparabletothenumberexpected
anditmodifiestheplanet/starfluxcontrast(inthiswork,byde- intheNIRbaselinescenario.However,eventheseconservative
termining the planet’s thermal blackbody emission). Naturally, planetarypopulationstatisticsimplya40%chanceoffindingan
observationsatmultipleinfraredwavelengthsarealsodesirable Earth/Venus analogue (R “ 1´2R , T “ 200´250 K);
P C eq
toobservespectralfeaturesofdifferentmolecularspeciesand/or thisprobabilityderivesmainlyfromK-typestarswithTeff inthe
surfacecompositions(e.g.,Kuiperetal.,1947;Huetal.,2012). range3900–5500K,andsomaybelesssensitivetotheassump-
Table1showsthatthenumberofplanetsaccessibletohigh- tionsmadeinSec.2.2forplanetfrequenciesaroundcoolerstars.
contrast characterization drops steadily as the observing wave- As discussed in Secs. 2.2 and 3.2, if 1´2R planets are 4ˆ
C
lengthincreasesfrom1.0µmto3.5µm.Thedetectedplanetsare morefrequentthan2´4R planetsthentheexpectationvalue
C
coolandseeninreflectivelight,sotheirplanet/starcontrastre- increases to 1.6. Thus it may be considered likely that such an
mainsapproximatelyconstantevenasangularresolutionandthe object will be found; such an event would excite considerable
photon flux available for AO wavefront sensing and correction interest.
6
Crossfield:GSMTHigh-ContrastCharacterizationofShort-PeriodExoplanets
4. ConclusionsandFutureWork
10-3
These simulation of a mostly generic high-contrast instrument
10-4 indicatethat,withreasonableextrapolationsofplanetfrequency
rates from the Kepler mission and/or radial velocity surveys
st 10-5 (Howard et al., 2012; Bonfils et al., 2013), of order 10 short-
a
ntr period planets will be accessible to characterization via high-
Co 10-6 contrast imaging and spectroscopy from the next generation of
ar ground-based giant segmented-mirror telescopes (GSMTs). In
et/st 10-7 Table 1, the accessible planet population is summarized and
n
Pla 10-8 showntobeinsensitivetomoderatechangesintheassumptions
8 32R made about planet frequencies (see Sec. 3.2) and future instru-
10-9 421−−−−842RRREEEE 2><032000−0030KK0K menTtaalrgceatpsafboirlitfiuetsur(eseheigShe-cc.o3n.3tr)a.stcharacterizationarealready
10-10 knowntoday.Atwavelengthsnear1.2µm,theplanetsGJ876b
10-2 10-1 100
andc(seeFig.2)andplanetcandidatesαCenBb(seeFig.1)and
Separation [arcsec]
τCetbshouldbedetectabletotheNIRbaselineinstrumentcon-
sideredinSec.3.1.GJ139canddandτCetcanddshouldalso
Fig.4 SameasFig.1butforτCetinthethermalimagingsce- bedetectableiftheirgeometricalbedosareą 0.15´0.4.Thus
nariodescribedinSec.3.3.2,observingat10µmwithaninstru- perhaps a half-dozen suitable planets with a range of masses
ment similar to E-ELT/METIS. The planets here are detected (andpresumablyradii)arealreadyknown;thisnumberislarge
mainly via their thermal emission. From left to right, the star enough that one suspects the modest predictions presented in
symbols and error bars show the contrast expected for planets thisworkmayunderestimatethetruesizeoftheaccessibleexo-
candidates b, c, d, e, and f (Tuomi et al., 2012) over the range planet population. This could be the case if the local exoplanet
ofalbedosandrecirculationparametersdescribedinSec.2.4.If population differs substantially from that observed by Kepler,
confirmed,planetfwouldbeamenabletodirectcharacterization oriftheassumptionsmadeinSec.2.2areshowntobeinvalid.
ofitsthermalemission. Futurehigh-precisionradialvelocityobservations,especiallyof
Mdwarfs,willenablefurthertestsofthesepredictions.
Thermal infrared observations will be desirable, because
they offer the possibility to directly characterize the thermal
emissionspectraandenergybudgetsoftheseshort-periodplan-
ets,andthus(viaradiometricradii)breaktheradius-albedode-
generacy inherent in reflected light observations. In particular,
thermalinfraredobservationssignificantlyimprovethechances
offindingEarthorVenusanalogues(planetswithR “1´2R
P C
andT “200´250K;seeTable1,andcf.Figs.3and5).The
eq
planetcandidateτCetf(seeFig.4)istheonlycurrentlyknown
planetwhichcouldbecharacterizedbythesemid-infraredobser-
vations,andradialvelocitysurveysseemlikelytoprovideaddi-
tionaltargetsinthecomingdecade.
Theopportunitytoobserveandcharacterizetheatmospheres
of relatively small (R ă 4R ) and cool (T ă 300 K) plan-
P C eq
ets is an exciting one, not least because such planets could be
similar to Earth and are particularly compelling objects in the
study of exoplanetary habitability. A useful avenue for future
study will be to examine in more detail what discernible dif-
ferencesmightbeusedtodistinguishEarth-likeandVenus-like
planets(whichexhibitsimilarinfraredemissionspectra)onthe
basisofmid-infraredobservations.Oneinitialavenuemightbe
toextendplanetclassificationeffortsusingopticalcolors(Crow
Fig.5 Predictednumberofplanets(asafunctionofR andT )
P eq etal.,2011;Hegde&Kaltenegger,2012)tolongerwavelengths.
expectedtobecharacterizedforthe10µmimagingscenariode-
Future, more detailed simulations are required to estimate
scribedinSec.3.3.2.Thecolorsandthesmallnumbersineach
the signal to noise with which the accessible planets discussed
cell both indicate the expectation value for that combination of
herecanbecharacterized.Kawaharaetal.(2012)havepresented
R and T , and the histograms show the marginalized distri-
P eq an excellent first step toward this goal with their recent deter-
butions. Compared to the planet population accessible in the
minationthatGSMTswillallowlow-resolutionspectroscopyof
baseline NIR case shown in Fig. 3, thermal infrared observa-
smallplanetsat1.27µminjustafewhours.Furthersuchworkat
tionsmainlydetectthermalemissionfromcoolerplanetsaround
bothshorterandlongerwavelengthswillhelpdeterminewhether
warmer stars. Note that the scenario simulated here conserva-
spectroscopy will be possible, or whether characterization will
tivelyassumesthatplanetsinthetwosmallestR rangesoccur
P belimitedtobroadbandphotometry.Suchestimateswouldalso
withequalfrequency(seeSecs.2.2and3.2).
permitpredictionsoftheprecisionwithwhichhigh-contrastob-
servationscouldmeasureshort-periodplanets’orbitalproperties
(via astrometry), radiometric radii (via MIR observations), and
perhapseventuallymeasurerotationperiods(Fordetal.,2001),
7
Crossfield:GSMTHigh-ContrastCharacterizationofShort-PeriodExoplanets
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9
Crossfield:GSMTHigh-ContrastCharacterizationofShort-PeriodExoplanets
Table1. NumberofShort-PeriodPlanetsAccessibletoHigh-ContrastCharacterization
PlanetSize,R {R EquilibriumTemperature,T /K
P C eq
SimulationParameters 1´2 2´4 4´8 ă200 200´300 ą300 N a Totalb
EVA
BaselineScenario(seeSec.3.1): 1˘1 5`2 1`2 2`2 2`2 4˘2 0.06 8˘3
´3 ´1 ´1 ´1
EffectsofAstrophysicalParameters(seeSec.3.2):
ManySmallPlanets(f “4f ) 4˘2 5`2 1`2 3`1 3`1 6`2 0.24 11`4
1´2RC 2´4RC ´3 ´1 ´2 ´2 ´3 ´3
MoreLonger-PeriodPlanets(forPą50d) 1˘1 5˘2 2`2 4˘2 3`1 4˘2 0.06 10`4
´1 ´2 ´3
NoPlanetsAroundCoolStars(Teff ă3600K) 1˘1 3˘2 1˘1 0`´10 1˘1 4`´12 zero 5˘2
RVStatisticsforCoolStars(Teff ă3600K) 1`´11 4`´12 1˘1 2`´21 2˘1 4`´12 0.05 8˘3
EffectsofInstrumentalParameters(seeSec.3.3):
LargerDiameter(39m) 2`2 9˘3 2`2 4˘2 4˘2 7`2 0.14 15˘4
´1 ´1 ´3
SmallerDiameter(25m) 0`1 3`1 1˘1 1`2 1˘1 2`2 0.04 5˘2
´0 ´2 ´1 ´1
MuchSmallerDiameter(8m) 0 0`1 0 0 0 0`1 zero 0`1
´0 ´0 ´0
NarrowerIWA(2λ{D) 1`2 7`2 2`1 3`1 3`1 6`2 0.07 11`4
´1 ´3 ´2 ´2 ´2 ´3 ´3
WiderIWA(4λ{D) 1`0 3`2 1˘1 2`2 2`1 3`1 0.06 6`3
´1 ´1 ´1 ´2 ´2 ´2
ShorterWavelength(1.0µm) 1˘1 5˘2 1`2 2`1 2`2 4`3 0.05 9˘3
´1 ´1 ´1 ´2
LongerWavelength(1.6µm) 1˘1 4˘2 1˘1 2`2 2`1 3`1 0.08 7˘3
´1 ´2 ´2
LongerWavelength(2.2µm) 1`0 2`2 1˘1 2`1 1˘1 2`1 0.05 5˘2
´1 ´1 ´2 ´1
LongerWavelength(3.5µm) 1`0 1`2 1`0 1˘1 1`0 2`2 zero 3`2
´1 ´1 ´1 ´1 ´1 ´1
ThermalIR,LargerDiameter(10µm,39m,10´7) 1`2 3˘2 1˘1 3˘2 1˘1 1˘1 0.41 6`2
´1 ´3
aExpectednumberofaccessibleEarth/Venusanalogues(R “1´2R ,T “200´250K),assumingplanetswithR “1´2R
P C eq P C
and2´4R occurwiththesamefrequency(seeSecs.2.2and3.2).
C
bBecauseofrounding,thesumofeachrow’svaluesmaynotmatchtheTotalvaluelisted.
10