WASP-54b, WASP-56b and WASP-57b: Three new sub-Jupiter mass planets from SuperWASP

1.5 MB·English

by  F. Faedi

Astronomy&Astrophysicsmanuscriptno.w54w56w57 c ESO2012
(cid:13)
October9,2012
WASP-54b, WASP-56b and WASP-57b:
Three new sub-Jupiter mass planets from SuperWASP
F.Faedi 1,2,D.Pollacco 1,2,S.C.C.Barros3,D.Brown4,A.CollierCameron4,A.P.Doyle5,M.Gillon6,Y.Go´mez
∗ ∗
MaqueoChew 1,2,7,G.He´brard8,9,M.Lendl10,C.Liebig4,B.Smalley5,A.H.M.J.Triaud10,R.G.West11,P.J.
∗
Wheatley1,K.A.Alsubai12,D.R.Anderson5,D.Armstrong 1,2,J.Bento1,J.Bochinski13,F.Bouchy8,9,R.Busuttil13,
∗
L.Fossati14,A.Fumel6,C.A.Haswell13,C.Hellier5,S.Holmes13,E.Jehin6,U.Kolb13,J.McCormac 15,2,1,G.R.M.
∗
Miller4,C.Moutou3,A.J.Norton13,N.Parley4,D.Queloz10,I.Skillen15,A.M.S.Smith5,S.Udry10,andC.Watson2
2 1 DepartmentofPhysics,UniversityofWarwick,CoventryCV47AL,UK
1 e-mail:[email protected]
0 ∗ part of the work was carried out while at Queen’s University Belfast
2 2 Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, University Road, Belfast BT7
1NN.
t
c
O 3 AixMarseilleUniversit,CNRS,LAM(Laboratoired’AstrophysiquedeMarseille)UMR7326,13388,Marseille,France

8 4 SchoolofPhysicsandAstronomy,UniversityofSt.Andrews,St.Andrews,FifeKY169SS,UK

] 5 AstrophysicsGroup,KeeleUniversity,Staffordshire,ST55BG,UK
P
E 6 Universite´deLie`ge,Alle´edu6aouˆt17,SartTilman,Lie`ge1,Belgium
.
h
7 PhysicsandAstronomyDepartment,VanderbiltUniversity,Nashville,Tennessee,USA
p
-
o 8 Institutd’AstrophysiquedeParis,UMR7095CNRS,Universite´Pierre&MarieCurie,France
r
t 9 ObservatoiredeHaute-Provence,CNRS/OAMP,04870StMichell’Observatoire,France
s
a
[ 10 Observatoireastronomiquedel’Universite´deGene`ve,51ch.desMaillettes,1290Sauverny,Switzerland

1 11 DepartmentofPhysicsandAstronomy,UniversityofLeicester,Leicester,LE17RH
v
9 12 QatarFoundation,P.O.BOX5825,Doha,Qatar
2
3 13 DepartmentofPhysicalSciences,TheOpenUniversity,MiltonKeynes,MK76AA,UK
2
. 14 Argelander-Institutfu¨rAstronomiederUniversita¨tBonn,AufdemHgel71,53121,Bonn,Germany
0
1
15 IsaacNewtonGroupofTelescopes,ApartadodeCorreos321,E-38700SantaCruzdePalma,Spain
2
1
:
v Received;accepted
i
X
ABSTRACT
r
a Wepresentthreenewlydiscoveredsub-JupitermassplanetsfromtheSuperWASPsurvey:WASP-54bisaheavilybloatedplanetof
mass0.636+0.025 M andradius1.653+0.090 R.ItorbitsaF9star,evolvingoffthemainsequence,every3.69days.OurMCMCfitof
0.024 J 0.083 J
thesystemy−ieldsaslightlyeccentrico−rbit(e=0.067+0.033)forWASP-54b.Weinvestigatedfurthertheveracityofourdetectionofthe
0.025
eccentricorbitforWASP-54b,andwefindthatitcou−ldbereal.However,giventhebrightnessofWASP-54V=10.42magnitudes,we
encourageobservationsofasecondaryeclipsetodrawrobustconclusionsonboththeorbitaleccentricityandthethermalstructure
of theplanet. WASP-56band WASP-57bhave masses of 0.571+0.034 M and 0.672+0.049 M , respectively; and radii of 1.092+0.035
0.035 J 0.046 J 0.033
R forWASP-56band0.916+0.017 R forWASP-57b.Theyorbit−mainsequencestars−ofspectraltypeG6every4.67and2.84d−ays,
J 0.014 J
respectively.WASP-56band−WASP-57bshownoradiusanomalyandahighdensitypossiblyimplyingalargecoreofheavyelements;
possibly as high as 50 M in the case of WASP-57b. However, the composition of the deep interior of exoplanets remain still
undetermined.Thus,∼moreex⊕oplanetdiscoveriessuchastheonespresentedinthispaper,areneededtounderstandandconstraingiant
planets’physicalproperties.
Keywords.planetarysystems–stars:individual:(WASP-54,WASP-56,WASP-57,GSC04980-00761)–techniques:radialvelocity,
photometry
1
1. Introduction thoseobservedfromground-basedtransitsurveys,makingexo-
planetconfirmationand characterisationextremelychallenging
Todatethenumberofextrasolarplanetsforwhichprecisemea- ifnotimpossible.Thus,morebrightexamplesoftransitingplan-
surements of masses and radii are available amounts to more etsareneededtoextendthecurrentlyknownparameterspacein
than a hundred. Although these systems are mostly Jupiter– ordertoprovideobservationconstraintstotesttheoreticalmod-
like gas giants they have revealed an extraordinary variety of elsofexoplanetstructure,formationandevolution.Additionally,
physicalanddynamicalpropertiesthathavehadaprofoundim- bright gas giant planets also allow study of their atmospheres
pact on our knowledge of planetary structure, formation and via transmission and emission spectroscopy, and thus provide
evolution and unveiled the complexity of these processes (see interesting candidates for future characterisation studies from
Baraffeetal.2010,andreferencestherein).Transitsurveyssuch theground(e.g.VLTande-ELT)andfromspace(e.g.PLATO,
asSuperWASP(Pollaccoetal.2006)havebeenextremelysuc- JWST,EChO,andFINESSE).
cessful in providing great insight into the properties of extra- Here we describe the properties of three newly discov-
solar planets and their host stars (see e.g., Baraffeetal. 2010). ered transiting exoplanetsfrom the WASP survey: WASP-54b,
Ground-based surveys excel in discovering systems with pe- WASP-56b,andWASP-57b.Thepaperisstructuredasfollows:
culiar/exotic characteristics. Subtle differences in their observ- in 2 we describe the observations, including the WASP dis-
ing strategies can yield unexpected selection effects impacting cov§ery data and follow up photometric and spectroscopic ob-
the emerging distributions of planetary and stellar properties servationswhichestablishtheplanetarynatureofthetransiting
such as orbital periods, planetary radii and stellar metallicity objects.In 3wepresentourresultsforthederivedsystempa-
(seee.g.,Cameron2011foradiscussion).ForexampleWASP- rameters fo§r the three planets, as well as the individual stellar
17b(Andersonetal.2010b)isahighlyinflated(Rpl = 1.99RJ), andplanetaryproperties.Finally,in 4wediscusstheimplica-
very low density planet in a tilted/retrogradeorbit, HAT-P-32b tionofthesediscoveries,theirphysic§alpropertiesandhowthey
(Hartmanetal. 2011) has a radius equating that of its Roche addinformationtothecurrentlyexploredmass-radiusparameter
Lobethus possibly losingits gaseousenvelope(Rpl = 2.05RJ), space.
and the heavily irradiated and bloated WASP-12b (Hebbetal.
2009), has a Carbon rich atmosphere (Kopparapuetal. 2012;
Fossatietal. 2010),andisundergoingatmosphericevaporation 2. Observations
(Llamaetal.2011;LecavelierDesEtangs2010)losingmassto
itshoststaratarate 10 7 M yr 1 (Lietal.2010).Ontheop- Thestars1SWASPJ134149.02-000741.0(2MASSJ13414903-
− J −
posite side of the spe∼ctrum of planetaryparameters, the highly 0007410)hereafterWASP-54;1SWASPJ121327.90+230320.2
denseSaturn-massplanetHD149026bisthoughttohaveacore (2MASS J12132790+2303205) hereafter WASP-56; and
ofheavyelementswith 70M , neededto explainitssmallra- 1SWASP J145516.84-020327.5(2MASS J14551682-0203275)
dius(e.g.,Satoetal.200∼5,and⊕Carteretal.2009),andthemas- hereafterWASP-57;havebeenidentifiedinseveralnorthernsky
sive WASP-18b (M = 10M , Hellieretal. 2009), is in an or- catalogues which provide broad-band optical (Zachariasetal.
pl J
bit so close to its host star with period of 0.94 d and ec- 2005) andinfra-red2MASSmagnitudes(Skrutskieetal. 2006)
centricity e = 0.02, that it might induce sig∼nificant tidal ef- as well as proper motion information. Coordinates, broad-
fects probably spinning up its host star (Brownetal. 2011). band magnitudes and proper motion of the stars are from the
Observations revealed that some planets are larger than ex- NOMAD1.0catalogueandaregiveninTable1.
pectedfromstandardcorelessmodels(e.g.,Fortneyetal.2007,
Baraffeetal. 2008) and that the planetary radius is correlated
2.1.SuperWASPobservations
withtheplanetequilibriumtemperatureandanti-correlatedwith
stellar metallicity(see Guillotetal. 2006; Laughlinetal. 2011; TheWASPNorthandSouthtelescopesarelocatedinLaPalma
Enochetal. 2011; Faedietal. 2011). For these systems dif- (ORM-CanaryIslands)andSutherland(SAAO-SouthAfrica),
ferent theoretical explanations have been proposed for exam- respectively. Each telescope consists of 8 Canon 200mm f/1.8
ple, tidal heating due to unseen companions pumping up the focal lenses coupled to e2v 2048 2048 pixel CCDs, which
eccentricity (Bodenheimeretal. 2001; and Bodenheimeretal. yield a field of view of 7.8 7.8 ×square degrees, and a pixel
2003), kinetic heating due to the breaking of atmospheric scaleof13.7 (Pollaccoetal×.2006).
′′
waves(Guillot&Showman2002),enhancedatmosphericopac-
ity (Burrowsetal. 2007), semi convection (Chabrier&Baraffe WASP-56 (V = 11.5) is located in the northern hemi-
2007),andfinallyohmicheating(Batyginetal.2011,2010;and spherewith Declinationδ +23hand thusit is onlyobserved
Pernaetal.2012).Whileeachindividualmechanismwouldpre- by the SuperWASP-North∼telescope; WASP-54 and WASP-57
sumablyaffectallhotJupitersto some extent,theycan notex- (V = 10.42 and V = 13.04, respectively) are located in an
plain the entirety of the observed radii (Fortney&Nettelmann equatorialregionofskymonitoredbybothWASPinstruments,
2010; Leconteetal. 2010; Pernaetal. 2012). More complex however only WASP-54 has been observed simultaneously by
thermalevolutionmodelsarenecessarytofullyunderstandtheir bothtelescopes,withasignificantlyincreasedobservingcover-
coolinghistory. ageonthetarget.InJanuary2009theSuperWASP-Ntelescope
Recently,theKeplersatellite mission releaseda largenum- underwentasystemupgradethatimprovedourcontroloverthe
berofplanetcandidates(>2000)andshowedthatNeptune-size mainsourcesofrednoise,suchastemperature-dependentfocus
candidates and Super-Earths (> 76% of Kepler planet candi- changes(Barrosetal.2011;Faedietal.2011).Thisupgradere-
dates) are common around solar-type stars (e.g., Boruckietal. sultedinbetterqualitydataandincreasedthenumberofplanet
2011, and Batalhaetal. 2012). Although these discoveries are detections.
fundamentalforastatisticallysignificantstudyofplanetarypop- All WASP data for the three new planet-hosting stars were
ulations and structure in the low–mass regime, the majority of processedwiththecustom-builtreductionpipelinedescribedin
thesecandidatesorbitstarsthatareintrinsicallyfaint(V>13.5 Pollaccoetal. (2006).Theresultinglightcurveswereanalysed
for 78% of the sample of Boruckietal. 2011) compared to using our implementationof the Box Least-Squaresfitting and
∼
FaediF.:ThreenewexoplanetsfromWASP
SysRem de-trending algorithms (see CollierCameronetal. Table 1. Photometricpropertiesof the starsWASP-54, WASP-
2006; Kova´csetal. 2002; Tamuzetal. 2005), to search for 56 and WASP-57. The broad-bandmagnitudesand propermo-
signaturesofplanetarytransits.Oncethecandidateplanetswere tionareobtainedfromtheNOMAD1.0catalogue.
flagged, a series of multi-season, multi-camera analyses were
performed to strengthen the candidate detection. In addition Parameter WASP-54 WASP-56 WASP-57
differentde-trendingalgorithms(e.g.,TFA,Kova´csetal.2005) RA(J2000) 13:41:49.02 12:13:27.90 14:55:16.84
were used on one season and multi-season light curves to Dec(J2000) 00:07:41.0 +23:03:20.2 02:03:27.5
− −
confirm the transit signal and the physical parameters of the B 10.98 0.07 12.74 0.28 13.6 0.5
± ± ±
planet candidate.These additionaltests allow a more thorough V 10.42 0.06 11.484 0.115 13.04 0.25
± ± ±
R 10.0 0.3 10.7 0.3 12.7 0.3
analysis of the stellar and planetary parameters derived solely
± ± ±
I 9.773 0.053 11.388 0.087 12.243 0.107
from the WASP data thus helping in the identification of the ± ± ±
J 9.365 0.022 10.874 0.021 11.625 0.024
bestcandidates,aswellastorejectpossiblespuriousdetections. ± ± ±
H 9.135 0.027 10.603 0.022 11.292 0.024
± ± ±
K 9.035 0.023 10.532 0.019 11.244 0.026
- WASP-54 was first observed in 2008, February 19. The µ (mas/yr) 9.8± 1.3 34.9± 0.8 22.0± 5.4
samefieldwasobservedagainin2009,2010and2011byboth µα(mas/yr) −23.5± 1.2 −2.9 ±0.7 −0.6 ±5.4
WASPtelescopes.Thisresultedinatotalof29938photometric δ − ± ± − ±
datapoints,ofwhich1661areduringtransit.Atotalof58par-
tialorfulltransitswereobservedwithanimprovementinχ2 of
the box-shapedmodeloverthe flatlightcurveof ∆χ2 = 701,
−
and signal-to-red noise value (CollierCameronetal. 2006) of
SN = 13.02. When combined, the WASP data of WASP-
red
−
54, showed a characteristic periodic dip with a period of P =
3.69days,durationT 270mins,andadepth 11.5mmag.
14
∼ ∼
igure 1 shows the discovery photometry of WASP-54b phase
foldedontheperiodabove,andthebinnedphasedlightcurve.
-WASP-56wasfirstobservedduringourpilotsurveyinMay
2004bySuperWASP-North.Thesamefieldwasalsoobservedin
2006and2007yieldingatotalof16441individualphotometric
observations.SuperWASPfirst beganoperatingin the northern
hemisphere in 2004, observing in white light with the spectral
transmission defined by the optics, detectors, and atmosphere.
Duringthe2004seasonthephasecoverageforWASP-56bwas
too sparse to yield a robust detection with only 10 points
∼
fallingduringthe transitphase. Laterin 2006a broad-bandfil-
ter(400–700nm)wasintroducedandwithmoredataavailable
multi-seasonrunsconfirmedthetransitdetection.Overthethree Fig.1. Upperpanel:DiscoverylightcurveofWASP-54bphase
seasonsatotalof14partialorfulltransitswereobserved,yield- foldedontheephemerisgiveninTable 4. Lowerpanel:binned
ing 300 observations in transit, with a ∆χ2 = 213 improve- WASP-54b light curve. Black-solid line, is the best-fit tran-
−
mentovertheflatlightcurve,andSNred = 7.02.Thecombined sit model estimated using the formalism from Mandel&Agol
−
WASPlightcurves,plottedinFigure2,showthedetectedtransit (2002).
signalofperiod=4.61days,depth= 13mmag,andduration
∼
T 214mins.
14
∼
- WASP-57b was first observed in March 2008 and sub-
sequently in Spring 2010. A total of 30172 points were taken PIRATE telescope in the Observatori Astronomic de Mallorca
of which about 855 were during transit. About 65 full or par- (Holmesetal. 2011), together with the James Gregory 0.94 m
tial transits were observed overall with a ∆χ2 = 151, and telescope(JGT)attheUniversityofSt.Andrews,providehigher
−
SN = 6.20. Figure 3-upper panel shows the combined precision, higher spatial resolution photometryas compared to
red
−
WASP light curves folded on the detected orbital period of WASP, and thus have an importantrole as a link in the planet-
2.84days.Additionally,forWASP-57bthereisphotometriccov- findingchain,reducingtheamountoflargetelescopetimespent
eragefromtheQatarExoplanetSurvey(QES,Alsubai2011)and onfalse-positives.ObservationsofWASP-56wereobtainedwith
the phase folded QES light curve is shown in Figure 3-middle both PIRATE and JGT, while observations of WASP-54 were
panel.InbothWASPandQESlightcurvesthetransitsignalwas obtainedonlywithPIRATE.
identified with a period 2.84 days, duration T14 138 mins, MultipleMarkov-ChainMonteCarlo(MCMC)chainshave
∼ ∼
andtransitdepthof 17mmag. been obtained for both systems to assess the significance of
∼
adding the PIRATE and JGT light curvesto the corresponding
datasetindeterminingthetransitmodel,inparticulartheimpact
2.2.LowS/Nphotometry
parameter,the transitduration,anda/R . We concludethatfor
⋆
Several observing facilities are available to the WASP consor- WASP-54theeffectisnotsignificant,nevertheless,thePIRATE
tiumandaregenerallyusedtoobtainmulti-bandlow-resolution lightcurveswereincludedinourfinalanalysispresentedinsec-
photometrytoconfirmthepresenceofthetransitsignaldetected tion 3.2.InthecaseofWASP-56instead,becauseweonlyhave
§
in the WASP lightcurves.Thisis particularlyusefulin case of apartialTRAPPISTlightcurve(seesection 2.4),thefullJGT
§
unreliableephemerides,andincasethetransitperiodissuchthat light curve, although of lower quality, is crucial to better con-
follow up from a particular site is more challenging. Small-to- strainthetransitingress/egresstime,impactparameteranda/R ,
⋆
mediumsizedtelescopessuchastheremote-controlled17-inch allowingustorelaxthemainsequencemass-radiusconstraint.
3
FaediF.:ThreenewexoplanetsfromWASP
Fig.2. Upperpanel:DiscoverylightcurveofWASP-56bphase Fig.3. Upperpanel:DiscoveryWASPlightcurveofWASP-57b
foldedontheephemerisgiveninTable 5. Lowerpanel:binned phase folded on the ephemerisgivenin Table 5. Middle panel:
WASP-56b light curve. Black-solid line, is the best-fit tran- QESlightcurveofWASP-57b.Lowerpanel:binnedWASPlight
sit model estimated using the formalism from Mandel&Agol curveofWASP-57b.Black-solidline,isthebest-fittransitmodel
(2002). estimatedusingtheformalismfromMandel&Agol(2002).
ofdifferentstellarspectraltypes(e.g.F0,K5andM5).Foreach
2.3.Spectroscopicfollowup
maskweobtainedsimilarradialvelocityvariations,thusreject-
WASP-54,56and57wereobservedduringourfollowupcam- ingablendedeclipsingsystemofstarswithunequalmassesasa
paigninSpring2011withtheSOPHIEspectrographmountedat possiblecauseofthevariation.
the1.93mtelescope(Perruchotetal.2008;Bouchyetal.2009) WepresentinTables6,7,and8thespectroscopicmeasure-
at Observatoire de Haute-Provence (OHP), and the CORALIE ments of WASP-54, 56 and 57 together with their line bisec-
spectrographmountedatthe1.2mEuler-SwisstelescopeatLa tors (V ). In each Table we list the Barycentric Julian date
span
Silla,Chile(Baranneetal.1996;Quelozetal.2000;Pepeetal. (BJD),thestellarradialvelocities(RVs),theiruncertainties,the
2002). We used SOPHIE in highefficiencymode(R = 40000) bisector span measurements, and the instrument used. In col-
andobtainedobservationswithverysimilarsignal-to-noiseratio umn 6, we list the radial velocity measurementsafter subtract-
( 30), in order to minimise systematic errors (e.g., the Charge ingthezeropointoffsettoCORALIEandSOPHIEdatarespec-
∼
Transfer Inefficiency effect of the CCD, Bouchyetal. 2009). tively (the zero-point offsets are listed in Table 4, and Table 5
Wavelength calibration with a Thorium-Argon lamp was per- respectively). In column 7 we also give the line bisectors af-
formedevery 2hours,allowingtheinterpolationofthespectral ter subtracting the mean value for SOPHIE and CORALIE re-
drift of SOPH∼IE (< 3 ms 1 per hour; see Boisseetal. 2010). spectively,andfinally,incolumn8,theradialvelocityresiduals
−
Two 3 diameteropticalfibers were used;the first centeredon tothebest-fitKeplerianmodel.TheRoot-Mean-Square(RMS)
′′
thetargetandthesecondontheskytosimultaneouslymeasure of the residuals to the best-fit Keplerian models are as follow:
thebackgroundtoremovecontaminationfromscatteredmoon- RMS =18.9ms 1forWASP-54,RMS =19.5ms 1forWASP-
− −
light.DuringSOPHIEobservationsofWASP-54,56and57the 56,andRMS =24.4ms 1forWASP-57.
−
contributionfrom scattered moonlightwas negligible as it was For all Figures presented in the paper we adopted the con-
well shifted from the targets’ radial velocities. The CORALIE ventionforwhichSOPHIEdataarealwaysrepresentedasfilled
observationsof WASP-54 and WASP-57 were obtained during circles and CORALIE data are represented as open squares.
dark/greytime to minimise moonlightcontamination.The data In Figures 4 to 9 we present the RVs, V , and the residuals
span
wereprocessedwiththeSOPHIEandCORALIEstandarddata O–C diagrams for the three systems. Both CORALIE and
reductionpipelines, respectively.The radialvelocityuncertain- SOPHIE data sets are offset with respect to the radial velocity
tieswereevaluatedincludingknownsystematicssuchasguiding zeropoint,γ andγ ,respectively(seeTables4and
SOPHIE CORALIE
and centering errors (Boisseetal. 2010), and wavelength cali- 5). We examined V to search for asymmetries in spectral
span
brationuncertainties.Allspectraweresingle-lined. lineprofilesthatcouldresultfromunresolvedbinarityorindeed
For each planetary system the radial velocities were com- stellar activity. Such effects would cause the bisector spans to
puted from a weighted cross-correlation of each spectrum vary in phase with radial velocity. For the three systems no
with a numerical mask of spectral type G2, as described in significant correlation is observed between the radial velocity
Baranneetal.(1996)andPepeetal.(2002).Totestforpossible and the line bisector, or the bisector and the time at which
stellarimpostorsweperformedthecross-correlationwithmasks observation were taken. This supports each signal’s origin as
4
FaediF.:ThreenewexoplanetsfromWASP
Fig.4. Upper panel: Phase folded radial velocity measure- Fig.5.Upperpanel:ThebisectorspanmeasurementsofWASP-
ments of WASP-54 obtained combining data from SOPHIE 54 as a functionofradialvelocity,valuesare shifted to a zero-
(filled-circles) and CORALIE (open-squares) spectrographs. mean(<V > = 29ms 1,<V > =48ms 1).
span SOPHIE − span CORALIE −
−
Superimposed is the best-fit model RV curve with parameters Lower panel:The bisector span measurementsas a functionof
from Table 4. The centre-of-mass velocity for each data set time(BJD–2450000.0).Thebisectorspanshowsnosignificant
was subtracted from the RVs (γ = -3.1109 kms 1 and variationnorcorrelationwiththeRVs,suggestingthatthesignal
SOPHIE −
γ =-3.1335kms 1).Lowerpanel:ResidualsfromtheRV ismainlyduetoDopplershiftsofthestellarlinesratherthanstel-
CORALIE −
orbitalfitplottedagainsttime. larprofilevariationsduetostellaractivityorablendedeclipsing
binary.
being planetary, rather than due to a blended eclipsing binary
system,ortostellaractivity(seeQuelozetal.2001).
- WASP-54’s follow up spectroscopy was obtained from both
the SOPHIE and CORALIE spectrographs (see Figures 4 and
5).TheRMS forSOPHIEandCORALIEradialvelocityresid-
uals to the best-fit model are RMS = 33.6 ms 1 and
SOPHIE −
RMS =8.2ms 1.TypicalinternalerrorsforCORALIE
CORALIE −
andSOPHIEareof10–15ms 1.ThesignificantlyhigherRMS
−
of the SOPHIE residuals is mostly due to one outlier (RV =
134ms 1).RemovingthismeasurementresultsinaRMS
− SOPHIE
= 18 ms 1, which is comparable to the quoted internal error.
−
Thisdiscrepantvaluecouldhaveresultedfromobservationsob-
tainedinpoorweatherconditions.
- WASP-56 has radial velocity data only from SOPHIE (see
Figures 6 and 7). The RMS of the RV residuals to the best-fit
model is 19.4 ms 1. When removing the only discrepant RV
−
value at phase 0.5 (RV = 61 ms 1) the overallRMS reduces
−
to12ms 1,comparableto−SOPHIEinternalerror.-Finally,for
−
WASP-57theRMS oftheSOPHIEandCORALIEradialveloc-
ity residualsto the best-fitmodelare RMS = 22.3ms 1 Fig.6. Upper panel: Similar to Figure 4, the phase folded ra-
SOPHIE −
and RMS = 26.5 ms 1, respectively (see Figures 8 dial velocity measurements of WASP-56. The centre-of-mass
CORALIE −
and9).These become14ms 1 and17.4ms 1 respectivelyfor velocity for the SOPHIE data was subtracted from the RVs
− − (γ = 4.6816 kms 1). Lower panel: Residuals from the
SOPHIE and CORALIE data sets when ignoringthe two mea- SOPHIE −
−
RVorbitalfitplottedagainsttime.
surementswiththelargesterrors.
5
FaediF.:ThreenewexoplanetsfromWASP
Fig.7. Upper panel: The bisector span measurements for Fig.9. Upper panel:Same as Figures 5 and 7 we show the bi-
WASP-56 as a function of radial velocity, values are shifted sector span measurements for WASP-57 as a function of ra-
to a zero-mean (<V > = 40 ms 1). Lower panel: dialvelocity,valuesareshiftedtoazero-mean(<V > =
span SOPHIE − span SOPHIE
−
The bisector span measurements as a function of time (BJD– 2ms 1,<V > = 22ms 1).Lowerpanel:Thebisec-
− span CORALIE −
2450000.0).Nocorrelationwithradialvelocityandtimeisob- −torspanmeasurementsasafunctionoftime(BJD– 2450000.0).
served suggesting that the Doppler signal is induced by the Nocorrelationwithradialvelocityandtimeisobservedsuggest-
planet. ingthattheDopplersignalisinducedbytheplanet.
Table2.PhotometryforWASP-54,WASP-56andWASP-57
Planet Date Instrument Filter Comment
06/04/2011 EulerCam Gunnr fulltransit
WASP-54b
27/02/2012 TRAPPIST I+z partialtransit
16/05/2011 TRAPPIST I+z partialtransit
WASP-56b
11/03/2012 JGT R fulltransit
05/05/2011 TRAPPIST I+z partialtransit
WASP-57b 10/06/2011 TRAPPIST I+z fulltransit
10/06/2011 EulerCam Gunnr fulltransit
2.4.followupMulti-bandPhotometry
In order to allow more accurate light curve modelling of the
three new WASP planets and tightly constrain their param-
eters, in-transit high-precision photometry was obtained with
the TRAPPIST and Euler telescopes located at ESO La Silla
Observatory in Chile. The TRAPPIST telescope and its char-
acteristics are described in Jehinetal. (2011) and Gillonetal.
(2011).Adetaileddescriptionofthephysicalcharacteristicsand
instrumental details of EulerCam can be found in Lendletal.
(2012).
All photometric data presented here are available from the
Fig.8. Upper panel: Similar to Figures 4 and 6 for WASP-
NStED database 1. One full and one partial transits of WASP-
57. The centre-of-mass velocity for each data set was sub-
54b have been observed by EulerCam in 2011 April 6 and
tractedfromtheRVs(γ = 23.214kms 1 andγ =
23.228kms 1).LowerSpOaPHnIeEl:R−esidualsfrom−theRVCoOrbRiAtaLIlEfit TRAPPIST in 2012 February 26, respectively. Only a partial
− − transitofWASP-56bwasobservedbyTRAPPISTin2011May
plottedagainsttime.
16, and a full transit was observed by JGT in 2012 March
1 http://nsted.ipac.caltech.edu
6
FaediF.:ThreenewexoplanetsfromWASP
Fig.10. Euler r band and TRAPPIST ‘I + z band follow up Fig.11.TRAPPIST‘I+z bandandJGTR-bandfollowuphigh
′ ′
− − −
highsignal-to-noisephotometryofWASP-54duringthetransit signal-to-noisephotometryof WASP-56 duringthe transit (see
(see Table 2). The TRAPPIST lightcurvehasbeen offsetfrom Table 2). The JGT light curve has been offset from zero by an
zerobyanarbitraryamountforclarity.Thedataarephase-folded arbitrary amount for clarity. The The data are phase-folded on
ontheephemerisfromTable4.Superimposed(black-solidline) theephemerisfromTable5.Superimposed(black-solidline)is
isourbest-fittransitmodelestimatedusingtheformalismfrom our best-fit transit model estimated using the formalism from
Mandel&Agol(2002).Residualsfromthefitaredisplayedun- Mandel&Agol(2002).Residualsfromthefitaredisplayedun-
derneath. derneath.
11. A partial and a full transit of WASP-57b were captured
by TRAPPIST on the nights of 2011 May 5 and June 10 re-
spectively,whileafulltransitofWASP-57bwasobservedwith
imagesusingtheIRAF/DAOPHOT2 aperturephotometrysoft-
EulerCamin2011June10.Asummaryoftheseobservationsis
wareStetson(1987).Afteracarefulselectionofreferencestars
giveninTable2.
differentialphotometrywasthenobtained.
We show in Figures 10, 11, and 12 the high S/N follow up
photometry(EulerCamandTRAPPIST)forWASP-54b,WASP-
56bandWASP-57brespectively.Ineachplotweshowthediffer-
2.6.Eulerr–bandphotometry
entialmagnitudeversusorbitalphase,alongwiththeresidualto
thebest-fitmodel.Thedataarephasefoldedontheephemerides Observations with the Euler-Swiss telescope were obtained in
derivedbyouranalysisofeachindividualobject(see 3.2).In theGunnrfilter.TheEulertelescopeemploysanabsolutetrack-
§
Figures10and12someofthelightcurvesareassignedanarbi- ing system which keeps the star on the same pixel during the
trarymagnitudeoffsetforclarity. observation,by matchingthe pointsourcesin each image with
acatalogue,andadjustingthetelescopepointingbetweenexpo-
suresto compensatefor drifts(Lendletal. 2012). WASP-54b’s
2.5.TRAPPIST‘I+z’–bandphotometry
observationswere carried outwith a 0.2 mm defocusand one-
TRAPPIST photometry was obtained using a readout mode of port readout with exposure time of 30 s. All images were cor-
2 2 MHz with 1 1 binning, resulting in a readout time of rectedforbiasandflatfield effectsandtransitlightcurvewere
6.1×sandreadoutno×ise13.5e pix 1,respectively.Aslightdefo- obtainedbyperformingrelativeaperturephotometryofthetar-
− −
cuswasappliedtothetelescopetooptimisetheobservationeffi- getandoptimalbrightreferencestars. ForWASP-57bnodefo-
ciencyandtominimisepixeltopixeleffects.TRAPPISTusesa cuswasapplied,andobservationswereperformedwithfour-port
special‘I+z’filterthathasatransmittance> 90%from750nm readout,and60sexposures.Sixreferencestarswereusedtoper-
tobeyond1100nm.Thepositionsofthestarsonthechipwere formrelativeaperturephotometrytoobtainthefinallightcurve.
maintainedto withina fewpixelsthanksto the‘softwareguid-
ing’systemthatregularlyderivesanastrometricsolutiontothe
mostrecentlyacquiredimageandsendspointingcorrectionsto 2 IRAF is distributed by the National Optical Astronomy
the mount, if needed (see e.g., Gillonetal. 2011 for more de- Observatory, which is operated by the Association of Universities
tails).Astandardpre-reduction(bias,dark,flatfieldcorrection), forResearchinAstronomy,Inc.,undercooperativeagreementwiththe
was carried out and the stellar fluxes were extracted from the NationalScienceFoundation.
7
FaediF.:ThreenewexoplanetsfromWASP
WASP-54: Our spectral analysis yields the following
results: T = 6100 100 K, logg = 4.2 0.1 (cgs), and
eff
± ±
[Fe/H]= 0.27 0.08 dex, from which we estimate a spectral
− ±
type F9. WASP-54’s stellar mass and radius were estimated
using the calibration of Torresetal. (2010). We find no sig-
nificant detection of lithium in the spectrum of WASP-54,
with an equivalentwidth upperlimitof 0.4mÅ,corresponding
to an abundance upper limit of logA(Li) < 0.4 0.08. The
±
non-detection of lithium together with the low rotation rate
implied by the vsini⋆(P = 17.60 4.38 d), and the lack
rot
of stellar activity (shown by the abse±nce of Ca ii H and K
emission), all indicate that the star is relatively old. From the
estimated vsini⋆ we derived the stellar rotation rates, and
we used the expected spin-down timescale (Barnes 2007) to
obtain a value of the stellar age through gyrochronology. We
estimate an age of 4.4+7.4 Gyr. This value also suggest the
2.7
system is old. Althoug−h the age is not well constrained by
gyrochoronlogy, it is in agreement with the results obtained
from theoretical evolutionary models discussed below, which
implythatWASP-54hasevolvedoffthemainsequence.
WASP-56andWASP-57:Bothstellarhostsareofspectral
type G6V. From our spectral analysis we obtain the following
parameters:T = 5600 100K, andlogg = 4.45 0.1(cgs)
eff
± ±
Fhiiggh.1s2i.gnEaull-etor-rn−obisaendphaontdomTeRtrAyPoPfISWTA‘SIP+-5z7′−dbuarnindgfothlleowtraunp- ffoorrWWAASSPP--5567,.TAeffs b=ef5o6r0e0th±e1s0t0elKla,ramndaslsoegsgan=d4r.a2d±ii0a.r1e(ecsgtsi-)
sit (see Table 2). The TRAPPIST light curveshave been offset mated using the Torresetal. (2010) calibration. With a metal-
fromzerobyanarbitraryamountforclarity.Thedataarephase- licity of [Fe/H]= 0.12 dex WASP-56 is more metal rich than
folded on the ephemeris from Table 5. Superimposed (black- thesun,whileourspectralsynthesisresultsforWASP-57show
solidlines)arethebest-fittransitmodelsestimatedusingthefor- that it is a metal poor star ([Fe/H]= 0.25dex). For both stars
−
malismfromMandel&Agol(2002).Theresidualsfromeachfit thequotedlithiumabundancestakeaccountnon-localthermody-
aredisplayedunderneaththerelativelightcurves. namicequilibriumcorrections(Carlssonetal.1994).Thevalues
forthelithiumabundancesifthesecorrectionsareneglectedare
as follows: logA(Li) = 1.32 and logA(Li) = 1.82 for WASP-
56 and WASP-57, respectively. These values imply an age of
> 5 Gyr for the former and an age of > 2 Gyr for the latter
3. Results
(∼Sestito&Randich 2005). From vsini⋆∼we derived the stellar
3.1.Stellarparameters rotation period Prot = 32.58 18.51 d for WASP-56, imply-
±
ing a gyrochronological age (Barnes 2007) for the system of
For all the three systems the same stellar spectral analysis has 5.5+10.6 Gyr. Unfortunately, the gyrochronological age can
been performed,co-addingindividualCORALIE and SOPHIE o∼nly p−r4o.6vide a weak constraint on the age of WASP-56. For
spectrawithatypicalfinalS/Nof 80:1.Thestandardpipeline WASP-57 we obtaina rotationperiodof P = 18.20 6.40d
reduction products were used in th∼e analysis, and the analysis correspondingtoanageof 1.9+2.4Gyr.Borotththeabov±eresults
was performedusing the methodsgivenin Gillonetal. (2009). areinagreementwiththes∼tellar−a1g.2esobtainedfromtheoretical
The Hα line was used to determine the effective temperature evolutionmodels(seebelow)andsuggestthatWASP-56isquite
(Teff).Thesurfacegravity(logg)wasdeterminedfromtheCai old,whileWASP-57isarelativelyyoungsystem.
lines at 6122Å, 6162Å and 6439Å along with the Na i D and For each system we used the stellar densitiesρ , measured
⋆
Mg i b lines. The elementalabundanceswere determinedfrom directly from our Markov-Chain Monte Carlo (MCMC) anal-
equivalentwidthmeasurementsofseveralcleanandunblended ysis (see 3.2, and also Seager&Malle´n-Ornelas 2003), to-
lines. A value for micro-turbulence (ξt) was determined from gether wit§h the stellar temperatures and metallicity values de-
Fe i using the method of Magain (1984). The quoted error rived from spectroscopy, in an interpolation of four different
estimates include that given by the uncertainties in Teff, logg stellar evolutionary models. The stellar density, ρ⋆, is directly
andξt,aswellasthescatterduetomeasurementandatomicdata determined from transit light curves and as such is indepen-
uncertainties. The projected stellar rotation velocity (vsini⋆) dentoftheeffectivetemperaturedeterminedfromthespectrum
wasdeterminedbyfittingtheprofilesofseveralunblendedFei (Hebbetal. 2009), as well as of theoretical stellar models (if
lines. For each system a value formacro-turbulence(vmac) was Mpl M⋆ is assumed).Four theoreticalmodelswere used:a)
assumedbasedonthetabulationbyBrunttetal.(2010),andwe theP≪adovastellarmodels(Marigoetal.2008,andGirardietal.
usedthetelluriclinesaround6300Åtodeterminetheinstrumen- 2010),b)theYonsei-Yale(YY)models(Demarqueetal.2004),
talFWHM.Thevaluesforthev andtheinstrumentalFWHM c) the Teramo models (Pietrinfernietal. 2004) and finally d)
mac
aregiveninTable3.Therearenoemissionpeaksevidentinthe the Victoria-Regina stellar models (VRSS) (VandenBergetal.
Ca H+K lines in the spectra of the three planet host stars. For 2006). In Figures13, 14, and15, we plotthe inversecube root
each stellar host the parameters obtained from the analysis are ofthestellardensityρ 1/3 =R /M 1/3 (solarunits)againstef-
⋆− ⋆ ⋆
listedinTable3anddiscussedbelow: fectivetemperature,T ,fortheselectedmodelmasstracksand
eff
isochrones, and for the three planet host stars respectively.For
8
FaediF.:ThreenewexoplanetsfromWASP
Table3.StellarparametersofWASP-54,WASP-56,andWASP-
57fromspectroscopicanalysis.
Parameter WASP-54 WASP-56 WASP-57
T (K) 6100 100 5600 100 5600 100
eff ± ± ±
logg 4.2 0.1 4.45 0.1 4.2 0.1
ξ (kms 1) 1.4±0.2 0.9 ±0.1 0.7±0.2
vtsini⋆(−kms 1) 4.0±0.8 1.5±0.9 3.7±1.3
−
[Fe/H] 0.27± 0.08 0.12±0.06 0.25± 0.10
[Na/H] −0.30±0.04 0.32±0.14 −0.20±0.07
[Mg/H] −0.21±0.05 0.24±0.06 −0.19±0.07
[Si/H] −0.16±0.05 0.31±0.07 −0.13±0.08
[Ca/H] −0.15±0.12 0.09±0.12 −0.21±0.11
[Sc/H] −0.06±0.05 0.35±0.13 −0.08±0.05
[Ti/H] −0.16±0.12 0.18±0.06 −0.18±0.07
[Cr/H] −0.21±0.12 0.20±0.11 − –±
[Co/H] − –± 0.35±0.10 –
[Ni/H] 0.29 0.08 0.21±0.07 0.25 0.10
− ± ± − ±
logA(Li) <0.4 0.08 1.37 0.10 1.87 0.10
± ± ±
Mass(M ) 1.15 0.09 1.03 0.07 1.01 0.08
Radius(R⊙ ) 1.40±0.19 0.99±0.13 1.32±0.18
Sp.Type ⊙ F±9 G±6 G±6
Distance(pc) 200 30 255 40 455 80
± ± ±
Note:Massand radiusestimateusingtheTorresetal.(2010)calibra-
tion.SpectraltypeestimatedfromT usingthetableinGray(2008).
Fig.13. Isochrone tracks from Marigoetal. (2008) and eff
Girardietal.(2010)forWASP-54usingthemetallicity[Fe/H]=
0.27dexfromourspectralanalysisandthebest-fitstellarden-
−
sity0.2ρ .Fromlefttorightthesolidlinesareforisochronesof:
1.0,1.3,⊙1.6,2.0,2.5,3.2,4.0,5.0,6.3,7.9,10.0and12.6Gyr.
Fromleftto right,dashedlinesareformasstracksof:1.4,1.3,
1.2,1.1and1.0M .
⊙
Fig.15. Isochrone tracks from Demarqueetal. (2004) for
WASP-57 using the metallicity [Fe/H]= 0.25 dex from our
−
spectralanalysisand the best-fit stellar density 1.638ρ . From
left to right the solid lines are for isochrones of: 0.1, 0⊙.6, 1.0,
1.6,2.0,2.5,3.0,4.0,5.0and6.0Gyr.Fromlefttoright,dashed
linesareformasstracksof:1.1,1.0,0.9and0.8M .
⊙
Fig.14. Isochrone tracks from Demarqueetal. (2004) for
WASP-56usingthemetallicity[Fe/H]=0.12dexfromourspec-
WASP-54andWASP-56thestellarpropertiesderivedfromthe
tralanalysisandthebest-fitstellardensity0.88ρ .Fromleftto
rightthesolidlinesareforisochronesof:1.8,2.0⊙,2.5,3.0,4.0, four sets of stellar evolution models (Table 9) agree with each
other and with those derived from the Torresetal. (2010) cali-
5.0,6.0,7.0,8.0,9.0,10.0,11.0,12.0,13.0and14.0Gyr.From
bration,within their 1–σ uncertainties.For WASP-57 the best-
lefttoright,dashedlinesareformasstracksof:1.2,1.1,1.0,0.9
fit M from our MCMC analysis agrees with the values de-
and0.8M . ⋆
⊙ rived from theoretical stellar tracks with the exception of the
9
FaediF.:ThreenewexoplanetsfromWASP
Teramo models. The latter give a lower stellar mass value of 3.2.Planetaryparameters
0.87 0.04 M which is more than 1–σ away from our best-
fit res±ult (altho⊙ugh within 2–σ). The stellar masses of planet The planetary properties were determined using a simultane-
ous Markov-Chain Monte Carlo analysis including the WASP
host stars are usually derived by comparing measurable stel-
photometry, the follow up TRAPPIST and Euler photom-
lar properties to theoretical evolutionary models, or from em-
etry, together with SOPHIE and CORALIE radial velocity
pirical calibrations. Of the latter, the most widely used is the
measurements (as appropriate see Table 2 and Tables 6, 7,
Torresetal.(2010)calibration,whichisderivedfromeclipsing
and 8). A detailed description of the method is given in
binary stars, and relates logg and T to the stellar mass and
eff
CollierCameronetal.(2007)andPollaccoetal.(2008).Ourit-
radius.However,while T canbe determinedwith highpreci-
eff
erativefittingmethoduses thefollowingparameters:theepoch
sion,loggisusuallypoorlyconstrained,andthusstellarmasses
of mid transit T , the orbitalperiod P, the fractionalchangeof
derived from the spectroscopic logg can have large uncertain- 0
ties and can suffer from systematics. For example the masses flux proportional to the ratio of stellar to planet surface areas
∆F = R2/R2, the transitdurationT , the impactparameterb,
of 1000 single stars, derived by Valentietal. (1998) via spec- pl ⋆ 14
tral analysis, were found to be systematically 10% larger than theradialvelocitysemi-amplitude K1, the stellar effectivetem-
those derived from theoretical isochrones. A similar discrep- perature Teff and metallicity [Fe/H], the Lagrangian elements
ancywasalso foundintheanalysisofthe stellarparametersof √ecosω and √esinω (where e is the eccentricity and ω the
WASP-37 (Simpsonetal. 2011), WASP-39 (Faedietal. 2011), longitude of periastron), and the systematic offset velocity γ.
andWASP-21(Bouchyetal. 2010).Additionally,differentsets For WASP-54 and WASP-57 we fitted the two systematic ve-
oftheoreticalmodelsmightnotperfectlyagreewitheachother locities γCORALIE and γSOPHIE to allow for instrumental offsets
(Southworth 2010), and moreover at younger ages isochrones betweenthe two data sets. The sum ofthe χ2 forall inputdata
are closely packedand a small changein T or ρ can havea curves with respect to the models was used as the goodness-
eff ⋆
significanteffectonthederivedstellarage.Foreachplanethost of-fit statistic. For each planetary system four different sets of
starweshowaplotwithonesetofstellartracksandisochrones, solutionswereconsidered:withandwithoutthemain-sequence
while we give a comprehensivelist of the four models’ results mass-radius constraint in the case of circular orbits and orbits
inTable9.Usingthemetallicityof[Fe/H]= 0.27dexourbest- withfloatingeccentricity.
−
fit stellar properties from the Padova isochrones (Marigoetal. AninitialMCMCsolutionwithalineartrendinthesystemic
2008 and Girardietal. 2010) for WASP-54 yield a mass of velocity as a free parameter, was explored for the three plane-
1.1+0.1M andastellarageof6.3+1.6Gyr,inagreementwiththe tary systems, however no significant variation was found. For
1.0 2.4
gyrochro⊙nologicalageandamore−accurateestimate.ThePadova thetreatmentofthestellarlimb-darkening,themodelsofClaret
isochrones together with the stellar mass tracks and WASP-54 (2000,2004)wereusedinther-band,forbothWASPandEuler
resultsareshownInFigure13.Accordingtothestellarmodels, photometry,andinthez-bandforTRAPPISTphotometry.
a late-F star with [Fe/H]= 0.27 dex, of this radius and mass From the parameters mentioned above, we calculate the
−
has evolved off the zero-age main sequence and is in the shell massM,radiusR,densityρ,andsurfacegravityloggofthestar
hydrogenburningphaseofevolutionwithanageof6.3+1.6Gyr. (which we denote with subscript ) and the planet (which we
2.4 ⋆
Thebest-fitstellaragesfromthe othersets ofstellarm−odelsof denotewithsubscript ),aswellastheequilibriumtemperature
pl
WASP-54alsoagreewithourconclusion.InFigure13thelarge of the planet assuming it to be a black-body (T ) and that
pl,A=0
uncertaintyon the minimum stellar mass estimated from inter- energy is efficiently redistributed from the planet’s day-side to
polationofthePadovaisochronesislikelyduetotheproximity its night-side.We alsocalculate thetransitingress/egresstimes
totheendofthemainsequencekink.ThePadovaevolutionary T /T , and the orbital semi-major axis a. These calculated
12 34
models were selected nevertheless, because they show clearly values and their 1–σ uncertainties from our MCMC analysis
theevolvedstatusofWASP-54. are presented in Tables 4 and 5 for WASP-54, WASP-56 and
WASP-57. The corresponding best-fitting transit light curves
areshowninFigures1,2,and3andinFigures10,11,and12.
Thebest-fittingRVcurvesarepresentedinFigures4,6,and8.
– For WASP-54 the MCMC solution imposing the main
InFigures14,and15weshowthebest-fitYonsei-Yalestellar sequencemass-radiusconstraintgivesunrealisticvaluesforthe
evolutionmodelsandmasstracks(Demarqueetal.2004)forthe best-fit stellar temperature and metallicity, as we expected for
planet host stars WASP-56 and WASP-57, respectively. Using an evolved star. We then relaxed the main sequence constraint
themetallicity of[Fe/H]= 0.12dexforWASP-56 ourfit ofthe and explored two solutions: one for a circular and one for an
YY-isochronesgivesastellarmassof1.01+0.03M andastellar eccentric orbit. In the case of a non-circular orbit we obtain
0.04
age of 6.2+3.0 Gyr. This is in agreementw−ith the⊙Li abundance a best-fit value for e of 0.067+0.033. This is less than a 3–σ
2.1 0.025
measured−in the spectral synthesis (see Table 3), and supports detection,andassuggestedbyL−ucy&Sweeney(1971),Eq.22,
the conclusion that WASP-56 is indeed an old system. Using it could be spurious. From our analysis we obtain a best-fit χ2
themetallicity of[Fe/H]= 0.25dexderivedfromourspectral statistic of χ2 = 24.3fora circularorbit,andχ2 = 18.6for
− circ ecc
analysisofWASP-57,weinterpolatetheYY-modelsandweob- aneccentricorbit.Thecircularmodelisparameterisedbythree
tainabest-fitstellarmassof0.89+0.04M andageof2.6+2.2Gyr. parameters:K,γ andγ ,whiletheeccentricmodel
0.03 1.8 SOPHIE CORALIE
Theseresultsalsoagreewithour−results⊙fromspectrals−ynthesis additionally constrains ecosω and esinω. We used the 23 RV
andshowsthatWASP-57isarelativelyyoungsystem.Foreach measurementsavailableandweperformedtheLucy&Sweeney
systemtheuncertaintiesinthederivedstellardensities,temper- F-test (Eq. 27 of Lucy&Sweeney 1971), to investigate the
atures and metallicities were included in the error calculations probabilityofatrulyeccentricorbitforWASP-54b.Weobtained
forthestellaragesandmasses,howeversystematicerrorsdueto aprobabilityof9%thattheimprovementinthefitproducedby
differencesbetweenvariousevolutionarymodelswerenotcon- the best-fitting eccentricity could have arisen by chance if the
sidered. orbit were real circular. Lucy&Sweeney (1971) suggest a 5%
10