Table Of ContentAstronomy&Astrophysicsmanuscriptno.12378˙proofs˙corrected c ESO2010
(cid:13)
January19,2010
Transit detections of extrasolar planets around main-sequence
stars
∗
I. Sky maps for Hot Jupiters
R.Heller1,D.Mislis2,andJ.Antoniadis3
1 HamburgerSternwarte(Universita¨tHamburg),Gojenbergsweg112,21029Hamburg,Germany
e-mail:[email protected]
0 2 HamburgerSternwarte(Universita¨tHamburg),Gojenbergsweg112,21029Hamburg,Germany
1 e-mail:[email protected]
0 3 Aristotle University of Thessaloniki, Dept. of Physics, Section of Astrophysics, Astronomy and Mechanics, GR-54124
2 Thessaloniki,Greece
e-mail:[email protected]
n
a Received24April2009/Accepted03October2009
J
9 ABSTRACT
1
Context.Thefindingsofmorethan350extrasolarplanets,mostofthemnontransitingHotJupiters,haverevealedcorrelationsbetween
] themetallicityof the main-sequence (MS) host starsand planetary incidence. Thisconnection can be used tocalculatethe planet
P formationprobabilityaroundotherstars,notyetknowntohaveplanetarycompanions. Numerouswide-fieldsurveyshaverecently
E beeninitiated,aimingatthetransitdetectionofextrasolarplanetsinfrontoftheirhoststars.Dependingoninstrumentalproperties
. andtheplanetarydistributionprobability,thepromisingtransitlocationsonthecelestialplanewilldifferamongthesesurveys.
h
Aims.Wewanttolocatethepromisingspotsfortransitsurveysonthecelestialplaneandstriveforabsolutevaluesoftheexpected
p
numberoftransitsingeneral.Ourstudywillalsoclarifytheimpactofinstrumentalpropertiessuchaspixelsize,fieldofview(FOV),
-
andmagnituderangeonthedetectionprobability.
o
Methods.We used data of the Tycho catalog for 1 million objects to locate all the stars with 0m . m . 11.5m on the
r ≈ V
t celestial plane. Wetook several empirical relations between the parameters listed inthe Tycho catalog, such as distance to Earth,
s
m , and (B V),and those parameters needed to account for the probability of astar tohost anobservable, transitingexoplanet.
a V −
[ The empirical relations between stellar metallicityand planet occurrence combined withgeometrical considerations were used to
yieldtransitprobabilitiesfortheMSstarsintheTychocatalog.MagnitudevariationsintheFOVweresimulatedtotestwhetherthis
2 fluctuationswouldbedetectedbyBEST,XO,SuperWASPandHATNet.
v Results.WepresentaskymapoftheexpectednumberofHotJupitertransiteventsonthebasisoftheTychocatalog.Conditionedby
7 theaccumulationofstarstowardsthegalacticplane,thezoneofthehighestnumberoftransitsfollowsthesametrace,interruptedby
8 spotsofverylowandhighexpectationvalues.Thecomparisonbetweentheconsideredtransitsurveysyieldssignificantlydiffering
8 mapsoftheexpectedtransitdetections.WhileBESTprovidesanunpromisingmap,thoseforXO,SuperWASP,andHATNetshow
2 FsOVwithupto10andmoreexpecteddetections. Thesky-integratedmagnitudedistributionpredicts20HotJupiter transitswith
. orbitalperiodsbetween1.5dand50dandm < 8m,ofwhichtwoarecurrentlyknown.Intotal,weexpect3412HotJupitertransits
0 V
tooccurinfrontofMSstarswithinthegivenmagnituderange.ThemostpromisingobservingsiteonEarthisatlatitude = 1.
1 −
9 Keywords.Stars:planetarysystems–Occultations–Galaxy:solarneighborhood–Galaxy:abundances–Instrumentation:miscel-
0 laneous–Methods:observational
:
v
i
X
1. Introduction prototype,was unknownand previousconsiderationshad been
r basedonsystemssimilartothesolarsystem.Usinggeometrical
a A short essay by Otto Struve (Struve 1952) provided the first considerations, Rosenblatt (1971)1 found that the main contri-
published proposal of transit events as a means of exoplane- bution to the transit probabilityof a solar system planet would
tary detection and exploration. Calculations for transit detec- comefromtheinnerrockyplanets.However,thetransitsofthese
tion probabilities(Rosenblatt1971; Borucki&Summers1984; relativelytinyobjectsremainundetectablearoundotherstarsas
Pepper&Gaudi2006)andfortheexpectedpropertiesofthedis- yet.
covered planets have been done subsequently by many others
The first transit of an exoplanet was finally detected
(Gillonetal. 2005; Fressinetal. 2007; Beatty&Gaudi 2008).
around the sun-like star HD209458 (Charbonneauetal. 2000;
Untiltheendofthe1990s,whenthesampleofknownexoplan-
Quelozetal. 2000). Thanks to the increasing number of ex-
etshadgrowntomorethantwo dozen(Castellanoetal. 2000),
oplanet search programs, such as the ground-based Optical
the family of so-called ‘Hot Jupiters’, with 51 Pegasi as their
Gravitational Lensing Experiment (OGLE) (Udalskietal.
1992),theHungarianAutomatedTelescope(HAT)(Bakosetal.
Skymaps(Figures1and3)canbedownloadedinelectronicform 2002, 2004), the Super Wide Angle Search for Planets
∗
attheCDSviaanonymousftptocdsarc.u-strasbg.fr(130.79.128.5)or
viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/. 1AcorrectiontohisEq.(2)isgiveninBorucki&Summers(1984).
2 R.Helleretal.:Transitdetectionsofextrasolarplanets–I.
(SuperWASP) (Streetetal. 2003), the Berlin ExoplanetSearch 1993(ESA 1997; Hoeg 1997). During the survey,roughly100
Telescope (BEST) (Raueretal. 2004), XO (McCulloughetal. observationsweretakenperobject.Fromthederivedastromet-
2005),theTransatlanticExoplanetSurvey(TrES)(Alonsoetal. ricandphotometricparameters,weusetherightascension(α),
2007), and the Tautenburg Exoplanet Search Telescope declination(δ),thecolorindex(B V),theapparentvisiblemag-
−
(TEST) (Eigmu¨ller&Eislo¨ffel 2009) and the space-based mis- nitude m , and the stellar distance d that have been calculated
V
sions ‘Convection, Rotation & Planetary Transits’ (CoRoT) fromthemeasuredparallax.Thecatalogisalmostcompletefor
(Baglinetal. 2002) and Kepler (Christensen-Dalsgaardetal. themagnitudelimitm . 11.5m,butwealsofindsomefainter
V
2007), the number of exoplanet transits has grown to 62 until starsinthelist.
September 1st 20092 and will grow drastically within the next
years.Thesetransitingplanetshaveveryshortperiods,typically
< 10d, and very small semimajor axes of usually < 0.1AU, 2. Dataanalysis
whichisaselectioneffectbasedongeometryandKepler’sthird
Thebasisofouranalysisisasegmentationofthecelestialplane
law (Kepleretal. 1619). Transitingplanetswith longerperiods
intoamosaicmadeupofmultiplevirtualfieldsofview(FsOV).
present more of a challenge, since their occultations are less
Inafirstapproach,wesubdividethecelestialplaneintoasetof
likelyintermsofgeometricalconsiderationsandtheyoccurless
181 361 = 65341 fields. Most of the current surveys do
frequently.
×
notusetelescopes,whichtypicallyhavesmallFsOV,butlenses
Usually, authors of studies on the expected yield of tran-
withFsOVoftypically8 8 .Thus,weapplythisextensionof
sit surveys generate a fictive stellar distribution based on stel- ◦ × ◦
8 8 andastepsizeof∆δ = 1 = ∆α,withanoverlapof7
lar population models. Fressinetal. (2007) use a Monte-Carlo ◦ × ◦ ◦ ◦
between adjacentfields, for our automatic scanningin orderto
procedure to synthesize a fictive stellar field for OGLE based
coverthecompletesky.Wechosethesmallestpossiblestepsize
onstarcountsfromGouldetal.(2006),astellarmetallicitydis-
in order to yield the highest possible resolution and the finest
tribution from Nordstro¨metal. (2004), and a synthetic struc-
screening,despitethehighredundancyduetothelargeoverlap.
tureandevolutionmodelofRobinetal.(2003).Themetallicity
Asmallerstepsizethan1 wasnotconvenientduetolimitations
correlation, however, turned out to underestimate the true stel- ◦
larmetallicitybyabout0.1d˙ex,asfoundbySantosetal.(2004) of computationaltime. An Aitoff projection is used to fold the
celestialsphereontoa2Dsheet.
andFischer&Valenti(2005).Intheirlateststudy,Fressinetal.
(2009)firstgenerateastellarpopulationbasedontheBesanc¸on
catalogfromRobinetal. (2003) andstatistics formultiple sys- 2.1.Derivationofthestellarparameters
temsfromDuquennoy&Mayor(1991)toapplythenthemetal-
licity distribution from Santosetal. (2004) and issues of de- One key parameter for all of the further steps is the effective
tectability (Pontetal. 2006). Beatty&Gaudi (2008) rely on a temperatureTeff ofthestarsinoursample.Thisparameterisnot
Galactic structure model by Bahcall&Soneira (1980), a mass givenintheTychocatalogbutwemayusethestellarcolorindex
functionassuggestedbyReidetal.(2002)basedonHipparcos (B V)todeduceTeff by
−
data,andamodelforinterstellarextinctiontoestimatetheover-
all outputof the currenttransit surveysTrES, XO, and Kepler. T =10[14.551 (B V)]/3.684K , (1)
eff − −
Intheirpaperonthenumberofexpectedplanetarytransitstobe
whichisvalidformain-sequence(MS)starswithT . 9100K
detected by the upcoming Pan-STARRS survey (Kaiser 2004), eff
as late as type M8 (Reed 1998). Althoughwe apply this equa-
Koppenhoeferetal.(2009)alsousedaBesanc¸onmodelaspre-
sentedinRobinetal.(2003)toderiveabrightnessdistributionof tion to each object in the catalog, of which a significant frac-
tionmightexceedT = 9100K,thiswillnotyieldaserious
starsinthetargetfieldandperformedMonte-Carlosimulations eff
challengesincewewilldismissthesespuriouscandidatesbelow.
tosimulatetheoccurrenceanddetectionsoftransits.Thesestud-
iesincludedetailedobservationalconstraintssuchasobserving Fromtheobject’sdistancetoEarthd andthevisiblemagnitude
m ,wederivetheabsolutevisiblemagnitudeM via
schedule, weather conditions, and exposure time and issues of V V
datareduction,e.g.rednoiseandtheimpactoftheinstrument’s
pointspreadfunction. M =m 5mlog d , (2)
V V
In our study, we rely on the extensive data reservoir of the − 10pc!
Tycho catalog instead of assuming a stellar distribution or a
whereweneglectedeffectsofstellarextinction.Inthenextstep,
Galactic model. We first estimate the number of expected ex-
wecomputethestellarradiusR insolarunitsvia
oplanet transit events as a projection on the complete celestial ⋆
plane. We refer to recent results of transit surveys such as sta-
tistical, empirical relationships between stellar properties and R 5770K 4 1/2
pcXulOarnr,eeSntuatrplyoerwfWo-rbAmuSdaPgti,eoatnnbdruaHttehAsiT.ghNW-eeetffi)t,hcreieengnacurydselterbsasansosiifctopcbrhsoaegrrarvacamtteiosrin(saBtilcEcsSoonTf-, andthestellarRm⋆⊙as=sM bTyeff ! 10(4.83−MV)/2.5 (3)
⋆
straints mentioned above, and a simple model to test putative
transitswiththegiveninstruments.Withthisprocedure,weyield M =(4πR2σ T4 )1/β , (4)
⋆ ⋆ SB eff
skymaps,whichdisplaythenumberofexpectedexoplanettran-
sit detections for the given surveys, i.e. the transit sky as it is where σ is the Stefan-Boltzmannconstant. The coefficientβ
SB
seenthroughtheeyeglassesofthesurveys. in the relation L Mβ depends on the stellar mass. We use
∝
TheTychocatalogcomprisesobservationsofroughly1mil- the values and mass regimes that were empirically found by
lion stars taken with the Hipparcos satellite between 1989 and Cesteretal.(1983),whicharelisted inTable1 (seealso Smith
1983).
2Extrasolar Planets Encyclopedia (EPE): www.exoplanet.eu. Four Wededucethestellarmetallicity[Fe/H]⋆fromthestar’sef-
ofthese62announcedtransitingplanetshavenopublishedposition. fectivetemperatureTeff anditscolorindex(B V)by
−
R.Helleretal.:Transitdetectionsofextrasolarplanets–I. 3
Table 1.Empiricalvaluesforβinthemass-luminosityrelation In the next step, we analyze the probability of the putative
Eq.(4)asgiveninCesteretal.(1983). exoplanettoactuallyshowatransit.Consideringarbitraryincli-
nations of the orbital plane with respect to the observer’s line
β StellarMassRegime ofsightandincludingKepler’sthirdlaw,Gillilandetal.(2000)
foundthegeometrictransitprobabilitytobe
3.05 0.14 M .0.5M
± ⋆ ⊙
34..6786±±00..0051 0.6M1⊙.5.MM⊙⋆..M1⋆.5M⊙ ℘geo,i =23.8 MMi!−1/3 RRi!(cid:18)Pd(cid:19)−2/3 , (7)
⊙ ⊙
where P is the orbital period. A more elaborate expression –
includingeccentricity,planetaryradius,theargumentofperias-
tron and the semi-major axis instead of the orbital period – is
1 T
[Fe/H]⋆ = 411(cid:18) Keff −8423+4736(B−V)−1106(B−V)2(cid:19) , ngoivteenxbpylicSitelaygbrouvteimseptliacli.tl(y20d0e3p)e.nNdootnetthheats℘emgeio-,iminajEorqa.x(7is)adoveias
(5)
P = P(a)!Theprobabilityforanexoplanetarytransittooccur
as given in Santosetal. (2004). This relation, however, is
aroundtheith staristhengivenby
only valid for stars with 0.51 < (B V) < 1.33,
−
4495K < T < 6339K, 0.7 < [Fe/H] < 0.43, and
eff − ⋆ ℘ =℘ ℘ , (8)
log(g) > 4. We rejectthose stars fromthe sample thatdo not occ,i planet,i geo,i
∃ ·
complywithalltheseboundaryconditions.Ontheonehandwe
wherePistheremainingfreeparameter,alltheotherparameters
cleanseoursampleofnon-MSstars,ontheotherhandthesam-
are inferredfrom the Tychodata. Since we are headingfor the
pleisreducedseriously.Whileouroriginalreservoir,our‘master
expectationvalue,i.e. the numberof expectedtransits in a cer-
sample’,consistsof1031992starsfromtheTychocatalog,all
tain field of view (FOV), we need a probabilitydensity for the
therestrictionsmentionedabovediminishoursampleto392000
distribution of the orbital periods of extrasolar planets. On the
objects,correspondingtoroughly38%. basis of the 233exoplanetslisted in the EPE on July 6th 2007,
Jiangetal.(2007)usedapower-lawfitδ(P) = C(k) (P/d) k,
−
·
withC(k)asthenormalizationfunction,andtheboundarycon-
3. Transitoccurrenceandtransitdetection
ditionfortheprobabilitydensity ∞ dPδ(P) = 1toget
0
3.1.Transitoccurrence R
1 k P k
Nowthatwederivedthefundamentalstellarparameters,wemay δ(P)= − − (9)
turntowardsthe statistical aspectsof planetaryoccurrence,ge- B1−k−A1−k (cid:18)d(cid:19)
ometric transit probability and transit detection. We start with withA = 1.211909dandB = 4517.4dasthelowerandupper
the probability for a certain star of the Tycho catalog, say the limitsfortheperioddistributionandk = 0.9277.Thisfunction
ith star, to host an exoplanet. For F, G, and K dwarfs with issubjecttosevereselectioneffectsandbasesondataobtained
−0.5 < [Fe/H]i < 0.5, Fischer&Valenti (2005) found the fromavarietyofsurveysandinstruments.Itoverestimatesshort-
empiricalrelationship periodplanetssinceJiangetal.(2007)includedtransitingplan-
etsandthe associatedselectioneffects. Whilethefunctionpre-
℘ planet,i =0.03 102·[Fe/H]i (6) sumablydoesnotmirrorthe truedistributionof orbitalperiods
∃ · ofexoplanets,itiscorrelatedtotheperioddistributiontowhich
forasetof850starswithananalysisofDopplermeasurements
currentinstrumentsaresensitive,inadditiontogeometricselec-
sufficient to detect exoplanets with radial velocity (RV) semi-
tioneffectsasgivenbyEq.(7).
amplitudes K > 30ms 1 and orbitalperiodsshorter than 4yr
− We nowsegmentthe celestialplane into a mosaic madeup
(seeMarcyetal.(2005)andWyattetal.(2007)foradiscussion
ofmultiplevirtualFsOV, asdescribedatthebeginningofSect.
oftheoriginofthisformulaanditsimplicationsforplanetfor-
2, to calculate the number of expected transits in that field. In
mation).Theseperiodsarenoboundaryconditionsforoursim-
Sect.3.2wewillattributetheFOVoftherespectiveinstrument
ulationssince we are onlyinterested in surveyswith observing
tothatmosaicandwewillalsoconsidertheCCDresolution.The
periodsof 50d. The additionalconstrainton the metallicity
≤ numberofstarscomprisedbyacertainFOVisn.Thenumberof
does not reduce our diminished sample of 392000 stars since
expectedtransitsaroundtheithstarinthatfield,N,withperiods
thereisnostarwith 0.7 < [Fe/H] < 0.5intheTychocat- i
alog. Similar to the−correlation weiuse, U−dry&Santos (2007) betweenP1andP2isthengivenby
found a metallicity distribution of exoplanet host stars equiv-
walaesntretostr℘ic∃tpeldanetto,i st=ars w0.i0th44[F·e/H10]⋆2.04·>[Fe/H0]i.siHncoewtehveeyr,stuhsipsefictt Ni =Z P2dPδ(P)℘occ,i (10)
tworegimesofplanetformation.Sozzettietal.(2009)extended P1
ttphhoeewbueenrs-iltfaodwramt℘as∃fiaptml.anTpetlh,eie=soef1rF.e3icse·cn1ht0esr2t·[&uFde/ViHea]silea+nlsCtoi,(sC2u0g0∈g5e{)s0ta,tn0hd.a5t}f,othtuoenrdyeietehxlde- =℘∃planet,i·23.8 MM⊙i!−1/3 RR⊙i! B1−1k−−kA1−k
1
itsritbsuatipornevfoioru[Fsley/Hun]rec<og0n.izTeadktianiglEinqt.h(e6)pwlaenetht-umsertaatlhleicriutynddeisr-- × 1/3 k P12/3−k−P11/3−k d2/3 |A<P1<P2<B ,
⋆ − (cid:16) (cid:17)
estimatethetrueoccurrenceofexoplanetsaroundthestarsfrom
andthenumberofexpectedtransitsinthewholeFOVis
theTychocatalog.ThemetallicitybiasofsurveysusingtheRV
methodforthedetectionofexoplanetsissupposedtocancelout
n
the bias of transit surveys (Gouldetal. 2006; Beatty&Gaudi N = N . (11)
i
2008).
Xi=1
4 R.Helleretal.:Transitdetectionsofextrasolarplanets–I.
Ourtransitmapallowsusto constrainconvenientlocations
for future ground-based surveys. A criterion for such a loca-
tion is the number of transit events that can be observed from
a givenspot atlatitude l on Earth.To yield an estimate, we in-
tegrate N overthatpartof the celestial planethat is accessable
fromatelescopesituatedatl.We restrictthisobservablefanto
l 60 < δ < l + 60 , implying that stars with eleva-
◦ ◦
−
tions > 30 above the horizon are observable.The number of
◦
thetransiteventswithm . 11.5m thatisobservableatacer-
V
tainlatitudeonEarthisshownintherightpanelofFig.2.This
distribution resembles a triangle with its maximum almost ex-
actlyattheequator.Itssmoothnessiscausedbythewideangle
of120 thatflattensallthefinestructuresthatcanbeseeninFig.
◦
1.
3.2.Transitdetection
So far, we have computed the sky and magnitude distributions
Fig.1. Sky map of the expected number of exoplanet tran-
ofexpectedexoplanettransitswithorbitalperiodsbetween1.5d
sit events, N, with orbital periods between P = 1.5d and
1 and 50d, based on the stellar parameters from the Tycho data
P = 50donthebasisof392000objectsfromtheTychocat-
2 and empirical relations. In order to estimate if a possible tran-
alog. The published positions of 58 transiting planets from the
sit can actuallybe observed,one also has to consider technical
EPEasofSeptember1st2009areindicatedwithsymbols:6de-
issuesofacertaintelescopeaswellastheefficiencyandthese-
tectionsfrom the space-basedCoRoT mission are labeled with
lectioneffectsofthe data reductionpipelines.Thetreatmentof
triangles,52ground-baseddetectionsmarkedwithsquares.The
thepipelinewillnotbesubjectofourfurtheranalysis.Therel-
axesonlyrefertothecelestialequatorandmeridian.
evantaspectsforourconcernarethe pixelsize oftheCCD, its
FOV, them rangeoftheCCD-telescopecombination,andthe
V
declinationfanthatiscoveredbythetelescope.
Weemphasizethatthisisnotyetthenumberofexpectedtransit To detect a transit, one must be able to distinguish the pe-
detectionswithinacertainFOV(seeSect.4)butthenumberof riodic transit pattern within a light curve from the noise in the
expectedtransitstooccurwithinit. data. Since the depth of the transit curve is proportionalto the
AgraphicalinterpretationofthisanalysisispresentedinFig. ratioA /A ,whereA andA arethesky-projectedareasofthe
P ⋆ P ⋆
1, where we show a sky map of the expected number of exo- planetandthestar,respectively,andR /R = √A /A ,withR
P ⋆ P ⋆ P
planet transits around MS stars with m . 11.5m for orbital astheplanetaryradius,thedetectionprobabilityforacertainin-
V
periodsbetweenP = 1.5dandP = 50d.Thismapbaseson strumentisalsorestrictedtoacertainregimeofplanetaryradii.
1 2
severalempiricalrelationshipsandonsubstantialobservational Assuming that the transit depth is about 1%, the planetary ra-
biastowardsclose-inJupiter-likeplanets,butneverthelessitrep- diuswould have to be largerthan R /10. We do notinclude
⋆
≈
resentsthe transitdistributionto whichcurrentinstrumentation an elaborate treatment of signal-to-noise in our considerations
has access to. The pronounced bright regions at the upper left (see Aigrain&Pont2007). Since ourfocusis on MS stars and
andthelowerrightaretheanti-centerandthecenteroftheMilky ourassumptionsforplanetaryoccurrencearebasedonthoseof
Way,respectively.Theabsolutevaluesof0.5 . N . 5forthe HotJupiters,ourargumentationautomaticallyleadstoplanetary
mostoftheskyareverywellinlinewiththe experiencesfrom transitsofexoplanetscloseto R /10.
⋆
≈
wide-fieldsurveysusinga6 6 field.Mandushevetal.(2005) We also do not consider observational aspects, such as in-
◦ ◦
×
stated5to20ormoreexoplanettransitcandidates,dependingon tegration time and an observer on a rotating Earth with ob-
Galactic latitude,anda ratioof 25 : 1 betweencandidates servation windows and a finite amount of observing time (see
and confirmedplanets, whichis≈equivalentto 0.2 . N . 1. Flemingetal. 2008, for a review of these and other observa-
Ourvaluesarealittlehigher,probablyduetotheslightlylarger tionalaspects).Instead,wefocusonthetechnicalcharacteristics
FOV of 8 8 used in Fig. 1and dueto the effectof blends offourwell-establishedtransitsurveysandcalculatethecelestial
◦ ◦
×
andunresolvedbinaries(seediscussioninSect.5). distributionofexpectedexoplanettransitdetectionsinprinciple
In the left panel of Fig. 2, we show the distribution of ex- byusingoneoftheseinstruments.Theimpactoflimitedobserv-
pected transits from our simulation as a function of the host ingtimeisdegradedtoinsignificancebecausethespanoforbital
stars’ magnitudescomparedto the distribution of the observed periods we consider in Eq. (10) reaches only up to P = 50d.
2
transiting exoplanets. The scales for both distributions differ After repeatedobservationsof the same field, such a transiting
about an order of magnitude, which is reasonable since only a companionwouldbedetectedafter. 3yr,whichisthetypical
fractionofactualtransitsisobservedasyet.Form <8m,only dutycycleofcurrentsurveys.
V
HD209458bandHD189733bare currentlyknowto show tran- Our computations are compared for four surveys: BEST,
sitswhereaswepredict20ofsuchtransitswithperiodsbetween XO,SuperWASP,andHATNet.Thissamplecomprisesthethree
1.5dand50dtooccurintotal.Wealsofindthatthenumberof mostfruitfulsurveysintermsoffirstplanetdetectionsandBEST
detectedtransitingplanetsdoesnotfollowtheshapeofthesim- – a search program that used a telescope instead of lenses.
ulated distribution for m > 9m. This is certainly inducedby While observations with BEST have been ceased without any
V
a lack of instruments with sufficient sensitivity towards higher confirmed transit detection, XO has announced detections and
apparent magnitudes, the much larger reservoir of fainter stars SuperWASP and HATNet belong the most fruitful surveys to
thathasnotyetbeensubjecttocontinuousmonitoring,andthe date. An overview of the relevant observational and technical
higherdemandsontransitdetectionpipelines. propertiesofthesesurveysisgiveninTable2.Foreachsurvey,
R.Helleretal.:Transitdetectionsofextrasolarplanets–I. 5
Fig.2.Sky-integratednumberoftransitspermagnitude(leftpanel)andasafunctionoflatitude(rightpanel).Left:Whilethegreen
linerepresentsoursimulations,therosybarsshowthenumberoftransitingplanetspermagnitudebindiscoveredsofar.Notethe
different scales at the left and right ordinates! Right: The triangle represents the expected number of transits that can be seen at
elevationshigherthan30 overthehorizonatagivenlatitudeonEarth.
◦
wefirstrestricttheTychomastersampletotherespectivemag- 4. Results
nituderange,yieldinganm -restrictedsample.Inthenextstep,
V We develop a procedure for the calculation of the number of
we virtually observe the subsample with the fixed FOV of the
expectedtransiteventsto occur aroundMSstarsbased onem-
surveytelescope,successivelygrazingthewholeskywithsteps
piricalrelationsbetweenthestarsandplanets.Thisprocedureis
of1 betweenadjacentfields.TheFOViscomposedofanum-
◦ thenappliedtomorethan1millionstarsfromtheTychocatalog
ber of CCD pixels and each of these pixels contains a certain
tovisualizethetransitprobabilityforallstarswithm . 11.5m
number of stars, whose combined photon fluxes merge into a V
as a sky map. We also computethe celestial distributionof the
count rate. Efficient transit finding has been proven to be pos-
number of expected transit detections for four different, well-
sible from the ground in crowded fields, where target objects
establishedwide-fieldsurveys.
are not resolved from neighbor stars. To decide whether a hy-
pothetical transit around the ith star in the pixel would be de- In Fig. 3 we present the number of expected transit detec-
tions for the technical properties of BEST, XO, SuperWASP,
tected,wesimulatetheeffectofatransitingobjectthatreduces
thelightfluxcontributionl oftheiht staronthecombinedflux andHATNet.Asageneralresultfromthesemaps,wefindthat
nl ofthestarswithinapiixel.Iftheithmagnitudevariationon the size of the FOV governsthe detection efficiency of a cam-
thek pkixel-combinedlightis ∆m 0.01m, whichisa typical era. For the method applied here, the CCD resolution, i.e. the
P V,i ≥ pixelsize,hasalmostnoimpactsinceweneglecteffectsofnoise,
accuracy limit of current ground-based surveys, then we keep
whereasingeneralthedetectionlimitsfortransitingplanetsde-
thisstarforfurtheranalysisofthetransitdetectionasdescribed
pend on the CCD resolution in terms of noise (Kova´csetal.
inSects.2and3.1,otherwiseitisrejected.Thefluxes,however,
2005; Tamuzetal. 2005; Pontetal. 2006). In Table 2 you see
arenotlisted intheTychocatalog;instead,wecanuse thevis-
that the restriction of ∆m > 0.01m almost doesn’t reduce
iblemagnitudem ofastarandcalculateitsrelativeflux f/f V
V,i i 0
thesample.AlargeFOV,collectingthelightofrelativelymany
withrespecttoareferenceobjectwithflux f atmagnitudem :
0 V,0
stars,outweighsalowerCCDresolution–atleastfortherange
of pixel sizes considered here. Even for the zones around and
fi =10(mV,0−mV,i)/2.5 . (12) in the galactic center and anti-center where the stellar density
f increases drastically, the number of detectable transit events
0
reachesitsmaximum.Thiswasnotforeseeablesinceblending,
Themagnitudevariationcanthenbecomputedvia simulatedbyEq.(13),couldhavereducedtheefficiencyoftran-
sitdetectionwithinthecrowdedzones.
Thefoursurveyskymapsportraytheverydistinctefficien-
ciesofthetelescopes.ThemapofBESTreflectsthestellardis-
n
tributionof the Tychodata bestdueto the relativelyhighreso-
0.99 f + f
· i k lution of the CCD. However, the small FOV leads to very few
0.01≤! ∆mV,i =−2.5·log0.99 Xnkfi +fkXk,ni fk (13) eut1ihsxp1eepp.5xeesmcckrlt.yeue,Tnddcdhetoudriamssin,n1psa4aiFtmsrieidggdwe.nt3hteiofiaiclc.tetiahBotnehnEtesoSc.TtToBhyneEactrlrhSsisobTouu’crcstvaoiotvevaynielssorio.bsgfTltieshshtemaecrsoasXmmgiOnanpilsltlpieuedrtsdeeotejoptechnocuiltrsyttyiraouaitenpntlhgdotoeesf
=−2.5·log ·Xfnk0 ff0kXk,i f0 . tfvatihoeeemrrssSlueoeucfnmhpseeeaxmrsgWp.noeBAircteutuSetdpPdedroduacmneeutditetsociHonttfiAgho9enTssNkreyte<hlatam,tnitvamhepSeVl,uy,dpoilXewffarrOeeWgdreeAantpcSochiPexiteehiavlennesdlstiahzrHleeogAwaemnrTeadrFNgOandentieV.tnuaAsddoies-f-
cuts with respectto the Tychocatalog is negligiblefor XO but
Without loss of generality we chose m = 30m as reference tendstoresultinanunderestimationoftheexpecteddetections.
V,0
magnitude. ThatpartoftheSuperWASPmapthatisalsomaskedbyHATNet
6 R.Helleretal.:Transitdetectionsofextrasolarplanets–I.
looksvery similar to the map of the latter one. While HATNet camerasandthediverseobservingstrategiesamongthesurveys
reachesslightlyhighervaluesfortheexpectednumberofdetec- (McCulloughetal. 2005; Cameronetal. 2009) bias the speed
tionsat mostlocations,the coveredarea of SuperWASPis sig- andefficiencyofthemappingprocedure.Thiscontributestothe
nificantly larger, which enhances its efficiency on the southern dominanceofSuperWASP(18detections,14ofwhichhavepub-
hemisphere. lishedpositions)3overHATNet(13detections,allofwhichhave
The total of expected transiting planets in the whole sky is publishedpositions)3,XO(5detections,allofwhichhavepub-
3412 (see Fig. 1). By summing up all these candidates within lishedpositions)3,andBEST(nodetection)3.
anobservationalfanof30◦ elevationabovethehorizon,we lo- It is inevitable that a significant fraction of unresolved bi-
calize the most convenient site on Earth to mount a telescope narystarswithintheTychodatablursourresults.Theimpactof
fortransit observations(see rightpanelin Fig. 2):it is situated unresolvedbinaries withoutphysicalinteraction, which merely
at geographicallatitude l = 1◦. Given that the rotation of the happento be alignedalongthe line of sight, is significantonly
−
Earthallowsaground-basedobserverattheequator,whereboth inthecaseofextremecrowding.AsshownbyGillon&Magain
hemispheres can be seen, to cover a larger celestial area than (2007),thefractionofplanetsnotdetectedbecauseofblendsis
at the poles, where only one hemisphere is visible, this result typically lower than 10%. The influence of unresolved physi-
couldhavebeenanticipated.Duetothenon-symmetricdistribu- cal binaries will be higher. Based on the empirical period dis-
tionofstars,however,theshapeofthesky-integratednumberof tribution for binary stars from Duquennoy&Mayor (1991),
expectedtransitsasafunctionoflatitudeisnotobvious.Figure Beatty&Gaudi(2008) estimate the fraction of transiting plan-
2 shows that the function is almost symmetric with respect to etsthatwouldbedetecteddespitethepresenceofbinarysystems
theequator,withslightlymoreexpectedtransitsatthenorthern to be 70%. Both the contributionof binarystarsalignedby
hemisphere.Furthermore,thenumberofexpectedtransitstobe chanc≈eandphysicallyinteractingbinariesresultinanoveresti-
observableattheequatorisnottwiceitsvalueatthepoles,which mation of our computations of 40%, which is of the same
isduetothe inhomogeneousstellar distribution.Infact,an ob- order as uncertainties arising fr≈om the empirical relationships
serverattheequatortriplesitsnumberofexpectedtransitswith weuse.Moreover,asWillemsetal.(2006)haveshown,theden-
respect to a spot at the poles and can survey almost all of the sityofeclipsingstellarbinarysystemsincreasesdramaticallyto-
3412transitingobjects. wardstheGalacticcenter.Tocontrolthefractionoffalsealarms,
Based on the analysis of the magnitude distribution (left efficientdatareductionpipelines,andinparticulardataanalysis
panel in Fig. 2), we predict 20 planets with mV < 8 to algorithms, are necessary (Schwarzenberg-Czerny&Beaulieu
show transits with orbital periods between 1.5d and 50d, 2006).
whiletwo arecurrentlyknown(HD209458bandHD189733b). Recentevidencefortheexistenceofultra-shortperiodplan-
These objects have proven to be very fruitful for follow-up ets around low-mass stars (Sahuetal. 2009), with orbital peri-
studies such as transmission spectroscopy (Charbonneauetal. ods < 1d, suggests that we underestimated the number of
2002; Vidal-Madjaretal. 2004; Knutsonetal. 2007; Singetal. expectedtransits to occur,as presentedin Sect. 3.1. The possi-
2008;Grillmairetal.2008;Pontetal.2008)andmeasurements ble underestimation of exoplanets occurring at [Fe/H] < 0
⋆
of the Rossiter-McLaughlin effect (Holt 1893; Rossiter 1924; also contributes to a higher number of transits and detections
McLaughlin 1924; Winnetal. 2006, 2007; Wolfetal. 2007; than we computed here. Together with the fact that the Tycho
Naritaetal. 2007; Cochranetal. 2008; Winnetal. 2009). Our catalog is only complete to m . 11.5m, whereas the surveys
V
analysis suggests that a significant number of bright transiting consideredhere are sensitive to slightly fainter stars (see Table
planetsiswaitingtobediscovered.Welocalizethemostpromis- 2), these trendstowardshighernumbersofexpectedtransitde-
ingspotsforsuchdetections. tectionsmightoutweightheoppositeeffectofunresolvedbinary
stars.
Aradicalrefinementofbothourmapsfortransitsoccurrence
5. Discussion
anddetectionswillbeavailablewithinthenextfewyears,once
Our valuesfor the XO projectare muchhigherthanthose pro- the‘PanoramicSurveyTelescopeandRapidResponseSystem’
vided by Beatty&Gaudi (2008), who also simulated the ex- (Pan-STARRS) (Kaiseretal. 2002) will run to its full extent.
pected exoplanet transit detections of XO. This is due to their Imagingroughly6000squaredegreeseverynightwitha sensi-
muchmoreelaborateinclusionofobservationalconstraintssuch tivitydowntom 24,thissurveywillnotonlydrasticallyin-
V
asobservationalcadence,i.e.hoursofobservingpernight,me- creasethenumber≈ofcatalogedstars–thusenhanceourknowl-
teorologicconditions,exposuretime,andtheirapproachofmak- edge of the localization of putative exoplanetary transits – but
ingassumptionsaboutstellardensitiesandtheGalacticstructure couldpotentiallydetecttransitsitself(Dupuy&Liu2009).The
insteadofusingcatalog-baseddataaswedid.Giventhesediffer- Pan-STARRScatalogwillprovidetheidealskymap,ontopof
encesbetweentheirapproachandours,the resultsarenotone- which an analysis presented in this paper can be repeated for
to-one comparable. While the study of Beatty&Gaudi (2008) anyground-basedsurveywiththeaimoflocalizingthemostap-
definitely yields more realistic values for the expected number propriatetransitspotsonthecelestialplane.Thebottleneckfor
of transit detections considering all possible given conditions, the verification of transiting planets, however, is not the local-
weprovideestimatesforthecelestialdistributionofthesedetec- izationofthemostpromisingspotsbuttheselectionoffollow-
tions,neglectingobservationalaspects. up targets accessible with spectroscopic instruments. The ad-
In addition to the crucial respects that make up the effi- vance to fainter and fainter objects thus won’tnecessarily lead
ciencyoftheprojects,aspresentedinTable2,SuperWASPand tomoretransitconfirmations.Upcomingspectrographs,suchas
HATNet benefitfrom the combinationof two observationsites theESPRESSO@VLTandtheCODEX@E-ELT(Pepe&Lovis
and several cameras, while XO also takes advantage of twin 2008), can be used to confirm transits around fainter objects.
lenses but a single location. Each survey uses a single camera These next-generation spectrographs that will reveal Doppler
typeandbothtypeshavesimilarproperties,asfarasourstudyis fluctuationsontheorderofcms 1willalsoenhanceourknowl-
−
concerned. The transit detection maps in Fig. 3 refer to a sin- ·
gle camera of the respective survey. The alliance of multiple 3EPEasofSeptember1st2009
R.Helleretal.:Transitdetectionsofextrasolarplanets–I. 7
Fig.3. Sky maps with expected number of transit detections for BEST (a), XO (b), SuperWASP (c), and HATNet (d). Note the
different scales of the color code! The published detections of the surveys, taken from the EPE as of September 1st 2009, are
indicatedwithsymbols.
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Table2.Instrumentalpropertiesofthetreatedsurveys.
Survey δrange FOV CCDPixelSize m Range δ&m δ,m &∆m δ,m ,∆m &MS
V V V V V V
[Mag.] LimitedSample LimitedSample LimitedSample
BEST −16◦ <δ<90◦ 3.1◦ 5.5′′/mm 8<mV <14 546382 (52.94%) 516524 (50.05%) 222854 (21.59%)
XO −39◦ <δ<90◦ 7.2◦ 25.4′′/mm 9<mV <12 620477 (60.12%) 597842 (57.93%) 263213 (25.51%)
SuperWASP −44◦ <δ<90◦ 7.8◦ 13.8′′/mm 7<mV <12 745227 (72.21%) 703707 (68.19%) 311404 (30.18%)
HATNet −28◦ <δ<90◦ 8.3◦ 14.0′′/mm 7<mV <12 721473 (69.91%) 686927 (66.56%) 283350 (27.46%)
InthelastthreecolumnswelistthereducedTychomastersampleof1031992starsafterweappliedthesubsequentboundaryconditions:the
survey’ssky-coverage(δrange),itsm limitation,magnitudevariation∆m > 0.01mforthetransitofaJupiter-sizedobjectaroundtheithstarin
V V
apixel,andtheboundaryconditionsforMSstars,forwhichtheempiricalrelationshipshold(seeSect.2.1).Inbracesweindicatetheportionof
theTychomastersample.
