WASP-4b Transit Observations With GROND

2.1 MB·

by  Nikolay Nikolov

Astronomy&Astrophysicsmanuscriptno.nikolov-astro-ph c ESO2012
(cid:13)
January30,2012
⋆
WASP-4b Transit Observations With GROND
N.Nikolov1,Th.Henning1,J.Koppenhoefer2,3,M.Lendl4,G.Maciejewski5 andJ.Greiner3
1 Max-Planck-Institutfu¨rAstronomie,Ko¨nigstuhl17,69117Heidelberg,Germany
e-mail:[email protected]
2 Universita¨ts-SternwarteMu¨nchen,Scheinerstr.1,81679Munich,Germany
3 MaxPlanckInstituteforExtraterrestrialPhysics,Geissenbachstr.,85748Garching,Germany
4 ObservatoiredeGene`ve,Universite`deGene`ve,51chemindesMaillettes,1290Sauverny,Switzerland
5 Torun´ CentreforAstronomy,NicolausCopernicusUniversity,Gagarina11,PL87100Torun´ ,Poland
2 Preprintonlineversion:January30,2012
1
0 ABSTRACT
2
Context.Ground-basedsimultaneousmultibandtransitobservationsallowanaccuratesystemparametersdeterminationandmaylead
n
tothedetectionandcharacterizationofadditionalbodiesviathetransittimingvariations(TTVs)method.
a
Aims.Weaimedto(i)characterize theheavilybloated WASP-4bhot Jupiter anditsstar bymeasuring systemparametersandthe
J
dependenceoftheplanetaryradiusasafunctionoffour(Sloang′,r′,i′,z′)wavelengthsand(ii)searchforTTVs.
7 Methods.We recorded 987 images during three complete transitswith the GROND instrument, mounted on the MPG/ESO-2.2m
2
telescopeatLaSillaObservatory.Assumingaquadraticlawforthestellarlimbdarkeningwederivesystemparametersbyfittinga

compositetransitlightcurveoverallbandpassessimultaneously. Tocomputeuncertaintiesofthefittedparameters,weemploythe
] BootstrapMonteCarloMethod.
R
Results.Thethreecentraltransittimesaremeasuredwithprecisiondownto6s.WefindaplanetaryradiusR =1.413 0.020R ,an
S orbitalinclinationi=88. 57 0.45 andcalculateanewephemeris,aperiodP=1.33823144 0.00000032dapysandare±ferencetJruapnsit
◦ ◦
. epochT = 2454697.798311± 0.000046(BJD).Analysisofthenewtransitmid-timesinc±ombinationwithpreviousmeasurements
h 0 ±
shows no sign of a TTV signal greater than 20 s. We perform simplified numerical simulations to place upper-mass limits of a
p
hypotheticalperturberintheWASP-4bsystem.
-
o
Keywords.transitingplanets
r
t
s
a
[ 1. Introduction intervalbetween successive transitsto vary.The resulting tran-

sit timing variations (TTVs) allow the determination of the or-
1 Morethan 100extrasolarplanetshave beendetectedto pass in
v bitalperiodandmassoftheperturberdowntosub-Earthmasses
frontofthediskofitsparentstarssincethefirsttransitobserva-
7 (Miralda-Escude´ 2002,Holman& Murray2005,Holmanet al.
tionsreportednearlytwelveyearsago(Charbonneauetal.2000;
2 2010,Lissaueretal.2011).
Henryetal.2000;Mazehetal.2000).Theseclose-inplanetsor-
7 The transiting planet WASP-4b was discovered by Wilson
bittheirhoststarswithperiodstypicallysmallerthan 10days,
5 ∼ et al. (2008) within the Wide Angle Search for Planets in the
. probablyformedat greater orbital distances and later migrated
1 southernhemisphere(WASP-S,Pollaccoetal.2006).Theplanet
inwardgovernedbyprocesseswhicharestillunderdebate.The
0 is a 1.12 M hot Jupiter orbiting a G7V star with a period
discoveryofeachtransitingextrasolarplanetisofgreatinterest Jup
2 of 1.34 day. WASP-4b was found to have a heavily irradiated
forplanetaryscienceastheseobjectsprovideauniqueaccessto
1 atmosphere and inflated radius. Refined planetary orbital and
an accurate determinationof radii(down to a few percent)and
: physicalparameters,basedontransitphotometrywerepresented
v massesviatransitphotometryandradialvelocitymeasurements
Xi of the host star (Henry et al. 2000; Charbonneau et al. 2000). by Gillon et al. (2009), who used the Very Large Telescope
(VLT) to observe one transit, Winn et al. (2009), who mea-
Moreovertheyallow oneto plotthermalmapsof theplanetary
r suredtwotransitswiththeMagellan(Baade)6.5mtelescopeat
a surfaceviainfraredspectra(Richardsonetal.2007;Grillmairet
Las CampanasObservatory,Southworthet al. (2009),who ob-
al. 2007, Knutson et al 2007),determine the planetary temper-
served four transits using the 1.54m Danish Telescope at ESO
ature profiles and permit studies of the stellar spin-orbit align-
La Silla Observatoryand Sanchis-Ojeda et al. (2011),who ob-
ment(Quelozetal. 2000,Triaudet al. 2010,Winn etal. 2011,
servedfourtransitsusingtheMagellan(Baade)6.5mtelescope.
Johnson et a. 2011). All of these form a set of astrophysically
Duringtwoofthetransits,Sanchis-Ojedaetal.(2011)observed
preciousparameters,whicharecriticalforconstrainingthefor-
ashort-lived,low-amplitudeanomalythattheauthorsinterpreted
mationand evolutionof these interesting objects. Furthermore,
as the occultationof a starspotby the planet.Southworthet al.
the time intervals between successive transits are strictly con-
(2009) also noted similar anomalies in their light curves and
stant if the system consists of a planet moving on a circular
the possibility that they were caused by starspot occultations.
orbit around the parent star. If a third body is present in the
Sanchis-Ojedaetal.(2011),combinedtheirdatasetwiththatof
system, it would perturb the transiting planet causing the time
Southworthetal.(2009)andfoundthateachofthemisconsis-
⋆ Based on observations collected with the Gamma Ray Burst tent with a single spot and a star that is well-aligned with the
OpticalandNear-InfraredDetector(GROND)attheMPG/ESO-2.2m orbit.Trackingthisstarspot,itwaspossibletomeasuretherota-
telescopeatLaSillaObservatory,Chile.Programme083.A-9010. tionperiodofthehoststar.Anewpossiblestarspothasbeenre-
1
Nikolovetal.:WASP-4bTransitObservationsWithGROND
centlydetectedintwocloselyspacedtransitsofWASP-4bythe transittimes.Theexposuretimeswereintherange8–14s,de-
MiNDSTEp collaborationwith the Danish Telescope (Mancini pendingontheweatherconditions(i.e.seeingandtransparency).
2011,privatecommunication).Furthermore,Beereretal.(2011) Duringeachrunweusedthefastreadoutmode( 10s),achiev-
∼
performedspace-basedsecondaryeclipsephotometry,usingthe ing a cadence ranging from 18 to 24 s. To minimize system-
IRAC instrumenton the Warm Spitzer Space Telescope,of the aticeffectsinthephotometryassociatedwithpixel-to-pixelgain
planet WASP-4b in the 3.6 and 4.5 µm bands. Their data sug- variationswekeptthetelescopepointingstable.However,dueto
gest that WASP-4b’s atmosphere lacks a strong thermal inver- technicalissuescausedbytheguidingcamera 35%ofthetotal
∼
sion on the day-side of the planet, which is an unexpected re- numberofimageswere acquiredwithoutguiding,thatresulted
sult for an highly irradiated atmosphere. Ca´ceres et al. (2011) in 10-12pixeldriftsperobservingrun( 3.5hr).
∼ ∼
analyzedhigh-cadencenear-infraredground-basedphotometry, In the Near-Infrared (NIR) channels we obtained images
detectedtheplanet’sthermalemissionat2.2µmandconcluded withintegrationtimeof10s.Longerexposuresarenotallowed
thatWASP-4bshowsinhomogeneousredistributionofheatfrom due to technical constrains in the GROND instrument. It was
its day- to night-side. Finally, Triaud et al. (2010) investigated foundduringthe analysis that the JHK-imageswere of insuffi-
the spin-orbitalignment(β) of the WASP-4 system by measur- cientsignal-to-noiseratio(SNR)to beabletodetectthetransit
ing the parent star radial velocity during a transit of its planet andto allowaccurate system parameterderivationfromthe re-
(Rossiter-McLaughlineffect)andfoundβ = 4◦+4334◦,excludinga sulting light curves. In addition, the pixel scale in the NIR de-
projectedretrogradeorbit. − ◦ tectorsis0.6px 1,whichresultedinapoorlysampledstarpsfs
−
InthispaperwepresentthreenewtransitsofWASP-4bob- (typically4-5pixels).As we carriedoutallobservationsin the
servedinAugustandOctober2009withtheGRONDinstrument NIR without dithering to increase the cadence and to improve
(Greineretal.2008),attachedtotheMPG/ESO2.2mtelescope thetimesamplingandthephotometryprecision,itishardlypos-
at La Silla Observatory. We recorded each transit in four opti- sibletostackgroupsofNIRimageswithpriorbackgroundsub-
calg,r ,i andz (Sloan)channelssimultaneously.Usingthese traction.Therefore,weexcludedtheNIRdatainthefurtheranal-
′ ′ ′ ′
newdatasetswemeasuretheplanetorbitalandphysicalparam- ysis.
eters and constrain its ephemeris by fitting a new photometric AtthebeginningoftheobservationsonUT2009August26
data set over four pass-bands simultaneously. Unlike all previ- and30,WASP-4wassettingfromanair-massof1.02and1.05,
ousobservationalstudiesrelatedtotheWASP-4bexoplanet,that respectivelywhichincreasedmonotonicallyto1.5and1.6atthe
fit datain a singlebandpass,we modela transitlightcurveus- endoftheruns.DuringtheOctober8observations,theair-mass
ing the four bandpasses simultaneously.As pointed out by Jha decreasedfrom1.06to1.02andthenincreasedto1.15attheend
etal.(2000),thisapproachpermitsoneto breakafundamental oftherun.
degeneracy in the shape of the transit light curve. Each transit We employed standard IRAF1 procedures to perform bias
lightcurvecanbedescribedprimarilybyitsdepthandduration. and dark current subtraction as well as flat fielding. A median
For a single bandobservationsit is always possible to fit these combined bias was computed using 22 zero-second exposure
with a largerplanetif the stellar radiusis also increased and if framesand4darkframeswereusedtocomputethemasterdark.
the orbital inclination is decreased. The main advantage of the Asnonnegligiblefractionofthedatawasobtainedwithoutguid-
multi-bandtransitphotometryisthatitallowsthedetermination ing,itwascriticaltoperformthedatareductionwith flatfields
of the planet orbitalinclination unique, independentof any as- of high quality.A master flatfield was calculatedusing the fol-
sumptionsaboutthestellar andplanetaryradii.Finally,weadd lowingmethodology.Fromasetof12ditheredtwilightflatswe
the three new mid-transit times and search for TTVs. This pa- selected frames with median pixel counts in the range 10K to
perisorganizedasfollows.Insection2wepresentanoverview 35Kwhichiswell-insidethelinearregimeoftheGRONDopti-
ofthethreetransitobservationsofWASP-4bandthedatareduc- caldetectors.Finally,thereduced(bias-anddark-corrected)flat
tion.Insection3wediscussthelightcurveanalysisandtheerror framesweremediancombinedto producemasterflats foreach
estimation.Section4summarizesthemainresults. oftheg’,r’,i’andz’bands.
AperturephotometryofWASP-4andthereferencestarwas
performedoneachcalibratedimage.Toproducethedifferential
2. Observationsanddatareduction lightcurveofWASP-4, itsmagnitudewassubtractedfromthat
ofthecomparisonstar.Fortunately,thelaterwasofsimilarcolor
Three transits of WASP-4b were observed with the MPG/ESO andbrightness,whichreducedtheeffectofdifferentialcolorex-
2.2-mtelescopeatLaSillaObservatory(Chile)duringthreeruns tinction. For example, the instrumental magnitude differences
onUTAugust26and30andOctober82009(seeFig.1).Bad (comparison star minus WASP-4) measured on UT October 8
weatherconditionspreventeddatacollectionduringtheremain- 2009were∆g = 0.587mag,∆r = 0.669mag,∆i = 0.681mag,
′ ′ ′
ing two nights allocated for the project.To monitorthe flux of ∆z = 0.687mag.AspointedoutbyWinnetal.(2009)thecom-
′
WASP-4, we used the Gamma Ray Burst Optical and Near- parisonstarisslightlybluerthanWASP-4(∆(g i) = 0.094
′ ′
Infrared Detector (GROND). It is a gamma-ray burst follow- mag). − −
upinstrument,whichallowssimultaneousphotometricobserva-
To improve the light curves quality we experimented with
tionsin fouroptical(Sloan g, r , i, z) andthree near-infrared
′ ′ ′ ′ various aperture sizes and sky areas, aiming to minimize the
(JHK)bandpasses(Greineretal.2008).Intheopticalchannels
scatter of the out-of-transit (OOT) portions, measured by the
theinstrumentisequippedwithbacksideilluminatedE2VCCDs
magnituderoot-mean-square(r.m.s.).Bestresultswereobtained
(2048 2048,13.5µm). The field of view foreachof the four
with aperture radii of 16, 20.5 and 17.5 pixels for UT 2009
optical×channelsis5.4 5.4 withapixelscaleof0 .158pixel 1.
′ ′ ′′ − August26and30andOctober8,respectively.
×
During each observing run we verified that WASP-4 and a
nearbycomparisonstar were located within GROND’s field of 1 IRAF is distributed by the National Optical Astronomy
view.Thecomparisonstarwas 1.3′south-eastfromourtarget. Observatories, which are operated by the Association of Universities
∼
ForeachrunweobtainedrepeatedintegrationsofWASP-4and forResearchinAstronomy,Inc.,undercooperativeagreementwiththe
thecomparisonstarfor 3.5hr,bracketingthepredictedcentral NationalScienceFoundation.
∼
2
Nikolovetal.:WASP-4bTransitObservationsWithGROND
1.00
0.98
0.96
0.94
x
u
Fl 0.92
ggg’’’---fffiiilllttteeerrr rrr’’’---fffiiilllttteeerrr
e
v
ti 0.90
a

el
R 1.00
0.98
0.96
0.94
0.92
iii’’’---fffiiilllttteeerrr zzz’’’---fffiiilllttteeerrr
0.90
-0.05 0.00 0.05 -0.05 0.00 0.05
Time Since Midtransit (day)
Fig.1.Relativeg,r ,i andz -bandphotometryofWASP-4obtainedwithGROND.Thetransitsoccured(foreachpanelfromtop
′ ′ ′ ′
tobottom)onUT2009August26,August30andOctober8.Thetransitlightcurvesobtainedoneachsuccessiverunaredisplayed
withanoffsetof0.025inrelativefluxforabetterillustration.
The light curves contain smooth trends, most likely due to Table 1. Lightcurvescatter differencemeasuredwiththe stan-
differential extinction. To improve its quality we decrease this darddeviationofthetimeseriespriorandafterdetrending.All
systematiceffectusingtheOOTportionsofourlightcurves.We quantitiesinmmag.
plot the magnitude vs. air-mass data for each run and channel
andfitalinearmodeloftheform: run g r i z
′ ′ ′ ′
Aug26 0.503 0.358 0.482 0.339
f(z)=a+bz, (1) Aug30 0.818 0.973 0.633 0.725
Oct10 0.733 0.614 0.430 0.495
where(a)and(b)areconstantsand(z)istheair-mass.Once
thecoefficientswerederived,we appliedthe correctionto both
Toillustratethelightcurvequalityimprovementwepresent
thetransitandtheOOTdata.Performingthiscorrectionweno-
the scatter decrease after the described detrending procedure
tice thatthe baselinemagnitudesof our targetand the compar-
(Table1).
ison star show slight, nearly linear correlations with the (x,y)
centerpositionsofthePSFcentroidsoneachCCDchip.Were-
move these near-linear trends from WASP-4 and the reference
3. Lightcurveanalysis
star by modelling the base-line of the light curve with a poly-
nomialthatincludesalineardependencyonthecentroidcenter TocomputetherelativefluxofWASP-4duringtransitasafunc-
positions(xandy)ofthestarsonthedetectorsusingthefunction tion ofthe projectedseparationof the planet,we employedthe
oftheform: modelsof Mandel& Agol(2002),which in additionto the or-
bitalperiodPandthetransitcentraltimeT areafunctionoffive
C
f(x,y)=1+k x+k y+k xy, (2) parameters,includingtheplanettostarsizeratio(R /R ,where
x y xy p
R and R are the absolute values of the planet and sta∗r radii),
p
where (k ), (k ) and (k ) are constants. We then subtracted the orbita∗l inclination i, the normalized semimajor-axis (a/R ,
x y xy
thefitfromthetotaltransitphotometryobtainedforeachchan- whereaistheabsolutevalueoftheplanetsemimajoraxis)an∗d
nel during the three runs. No other significant trends that were twolimbdarkeningcoefficients(u andu ).Becausetheparam-
1 2
correlatedwithinstrumentalparameterswerefound. etersa/R ,R /R andiaredegenerateinthetransitlightcurve,
p
∗ ∗
3
Nikolovetal.:WASP-4bTransitObservationsWithGROND
1.00
0.99
0.98
g’-filter r’-filter
0.97
0.96
x
u
Fl 0.95

e
v
ti 0.94
a
el
R 1.00
0.99
0.98
0.97 i’-filter z’-filter
0.96
0.95
0.94
-0.05 0.00 0.05 -0.05 0.00 0.05
Time Since Midtransit (day)
Fig.2.ThecompositelightcurvesofWASP-4 obtainedduringthreerunsonUT2009August26,August30andOctober8.The
best-fittransitmodelsaresuperimposedwithcontinuouslinesandtheobservedminusmodeledresidualsareshowncenteredatflux
level0.95oneachpanelalongaconstantline.
we assume fixed values for M = 0.92 0.06M from Winn Table 2. Theoretical Limb-Darkening Coefficients (Quadratic
et al. (2009)and R = 0.907 0∗.013R from±Sanchis⊙-Ojedaet al. Law).
−+0.014
(2011)tobreakthis∗degeneracy.Ide∗allywewouldliketofitfor
allparametershowever,onlythefirstthreedeterminethebest-fit LDcoefficient g r i z
′ ′ ′ ′
radiusofthestar,theradiusoftheplanet,itssemimajoraxisand wavelength(nm) 455 627 763 893
inclinationrelativetotheobserver. u (linear) 0.623 0.413 0.314 0.248
1
u (quadratic) 0.183 0.290 0.303 0.308
Thevaluesforthetwo limbdarkeningcoefficientswerein- 2
cludedinourfittingalgorithmtocomputethetheoreticaltransit
models of Mandel & Agol (2002). We assume the stellar limb
To derive the best fit parameters we constructed a fitting
darkeninglawtobequadratic,
statisticoftheform:
Iµ =1 u (1 µ) u (1 µ)2, (3) χ2 = Nf fi(observed)−fi(predicted) 2, (4)
1 2 " σ #
I1 − − − − Xi=1 i
where f(observed)isthefluxofthestarobservedatthei-th
i
where I is theintensity andµ is thecosine ofthe anglebe- moment(withthemedianoftheOOTpointnormalizedtounity),
tween the line of sight and the normal to the stellar surface. σ controls the weights of the data points and f(computed) is
i i
We fixed (initially) the limb darkening coefficients (u and u ) thepredictedvalueforthefluxfromthetheoreticaltransitlight
1 2
to their theoretical values (see Table 2), which we obtained curve. We assume the orbital eccentricity to be zero and mini-
fromthecalculatedandtabulatedATLASmodels(Claret2004). mizethe χ2 statistic usingthe downhillsimplexroutine,asim-
Specifically, we performed a linear interpolation for WASP-4 plemented in the IDL AMOEBA function (Press et al. 1992).
stellarparametersT =5500 100K,log g=4.4813 0.0080 The minimization method evaluates iteratively the χ2 statistic,
eff
cgs,[Fe/H]= 0.03 0.09an±dv =2.0 1.0kms 1,w±hichwe yet avoiding derivative estimation until the function converges
t −
− ± ±
adoptedfromWinnetal.(2009). totheglobalminimum.
4
Nikolovetal.:WASP-4bTransitObservationsWithGROND
In the entire analysis we derive uncertainties for the fitted Table4.Summaryoftheresidualr.m.s.(observedminuscalcu-
parametersusingthebootstrapMonteCarlomethod(Pressetal. latedflux)oftheunbinnedandbinneddata.
1992). It uses the original data sets (from each run and pass-
band), with their N data points to generate synthetic data sets run band σ β σ
sys
alsowiththesamenumberofpointswithreplacements.Wethen [mag] [mag]
fit each data set to derive parameters. The process is repeated Aug26 g′ 0.0025 1.41 0.0035
untilwegetanapproximatelyGaussiandistributionforeachpa- Aug26 r′ 0.0025 1.38 0.0035
rameter and take the standard deviation of each distribution as Aug26 i′ 0.0028 1.45 0.0041
Aug26 z 0.0028 1.49 0.0042
theerrorofthecorrespondingfittedparameter. ′
Aug30 g 0.0023 1.19 0.0027
Ground-based time series data are often proned with time- ′
Aug30 r 0.0017 1.10 0.0019
correlatednoise(e.g.“rednoise”;seePontetal.2006)andthere- ′
Aug30 i 0.0025 1.23 0.0031
′
forethedataweightsσ needaspecialtreatment,i.e.theuncer-
i Aug30 z′ 0.0022 1.29 0.0028
taintiesmustbecalculatedaccuratelyinordertoobtainreliable Oct08 g 0.0018 1.22 0.0022
′
estimatesofthefittedparameters.Itisacommonpracticetouse Oct08 r 0.0018 1.17 0.0021
′
thecalculatedPoissonnoise,ortheobservedstandarddeviation Oct08 i 0.0019 1.29 0.0025
′
oftheout-of-transitdatafortheweights.Ourexperienceshows Oct08 z′ 0.0020 1.33 0.0027
that these methods often result in underestimated uncertainties
Notes.σrepresentstheresidualscatterovertheentireobservingtime
of the modeled parameters. To estimate realistic parameter un-
interval on each run; σ is the rescaled value for the photometric
certaintieswe employtwo methods.First we rescaled the pho- sys
weights,reflectingthepresenceofrednoise.
tometricweightsσ sothatthebest-fittingmodelforeachband
j
andrunresultsinareducedχ2 =1,whichthereforerequiresthe
initial values for the photometricuncertaintiesto be multiplied we assume that the inclination and the semimajor axis of the
bythe factorsχ2red = 1.396,χ2red = 1.058andχ2red = 1.179,for planetary orbit should not depend on the observed pass-band.
theUTAugust26and30andOctober82009runs,respectively. Therefore, we constrained these parameters to a single univer-
Second,wetakeintoaccountthe“rednoise”inourdataby sal value. Following this procedurefor the radiusof the planet
followingthe “time-averaging”approachthatwas proposedby we found 1.413 0.020 R and the best-fit value for the or-
Jup
Pontetal.(2006)andusedinthetransitdataanalysisofvarious bital inclination±and semimajor axis i = 88.57 0.45 and
◦ ◦
authorsincludingGillonetal. (2006),Winnetal.(2007,2008, a = 0.02300 0.00036 AU, respectively. For co±mparison of
2009)andGibsonetal.(2008).Themainideaofthemethodisto the key parame±ter, R , Wilson et al. (2008) derived 1.416+0.068
computethestandarddeviation(scatter)oftheunbinnedresidu- R , Gillon et al. (2p008) derived 1.304+0.054 R , Winn e−t0.0a4l3.
alsbetweentheobservedandcalculatedfluxes,σ andalsothe Jup 0.042 Jup
1 (2009)derived1.365 0.021R ,South−worthetal.(2009)de-
standarddeviationofthetime-averagedresiduals,σN,wherethe rived 1.371+0.032 R ±and SancJhupis-Ojeda et al. (2011) derived
flux of each N data points where averaged creating M bins. In 0.035 Jup
1.363 0.02−0R . OurvalueforR isslightlyhigherthanthe
theabsenceofrednoiseonewouldexpect ± Jup p
citedradiusintheliteratureandisdominatedbytheuncertainty
of the stellar radius R . The value for the orbital inclination,
σ M
σ = 1 . (5) fromouranalysisisina∗goodagreementwithearlierresults.For
N √N rM 1 example, Winn et al. (2009) found 88.56 0.46, Sanchis-Ojeda
− ◦−+0.98
However, in reality σN is larger than σ1 by some factor β, et al. (2011) found 88.80◦−+00..4631, while Gillon et al. (2009) and
which,aspointedoutbyWinn etal. (2007),is specificto each Soutworthet al. (2009)found89.35◦+00..6449 and88.80◦ −90.00◦,
parameterofthefittedmodel.Forsimplicityweassumethatthe respectively. The results for the fitted−parameters of the transit
valuesofβarethesameforallparametersandfinditsvalueby lightcurvemodellingallowustoderiveasetofphysicalproper-
averagingβoverarangeofbinswithtimescalesconsistentwith tiesfortheWASP-4 system.Table3exhibitsacompletelistof
thedurationofthetransitingressoregress.ie.10 30min.The thesequantities.
resultingvaluesforβarethenusedtorescaleσ in−theχ2bythis To completethe lightcurveanalysiswe furtherfit the light
j
value(seeTable4) curvesallowingthelinearandthequadraticlimbdarkeningcoef-
To derivetransitmid-times(T )we fixedtheorbitalperiod ficients(u andu )ineachpass-bandtobetreatedasfreeparam-
C 1 2
PtoaninitialvaluetakenfromSanchis-Ojedaetal.(2011)and eters. We aim to compare the shapes of the transit light curves
fitted the light curves from each run for the best T , planet to andthefittedsystemparametersfromthisfitandthecurvesde-
C
star size ratio, inclination and normalized semimajor axis. We rived using theoretically predicted limb darkening coefficients.
thenfindthebestorbitalperiodPandT usingthemethoddis- Inordertominimizetheχ2-statisticusingallofthe11parame-
C
cussedin4.2.ThenwetakethenewvaluesfortheT andPand ters,including8limbdarkeningcoefficientsweagainemployed
C
repeatthefitforthebestplanettostarsizeratio,inclinationand the downhillsimplex algorithm and the bootstrap method.The
normalizedsemimajor axis. This procedureis iterated until we new parameter values we find R = 1.409 0.020R , i =
p Jup
±
obtainaconsistentsolution. 88.75 0.40 , a = 0.02298 0.00033AU result in a slightly
◦ ◦
smaller±valueoftheχ2 functi±on(1.001),asthefitisabletore-
red
movesometrendsinthedata.However,wereporttheparameter
4. Results
valuesderivedusingthe theoreticallypredictedlimb darkening
coefficientasfinalresultsbecausethenewfitisalsomoresensi-
4.1.Systemparameters
tivetosystematicsinthelightcurvephotometry.
We setthemassandradiusofthe starequalto0.92 0.06 M A set of multi-band transit light curves also allows one to
and0.907−+00..001134R ,respectively,anddeterminethebes±t-fitradiu⊙s search for a dependence of the planetary radius, Rp as a func-
for WASP-4b, R∗by minimizing the χ2 function over the four tion of the wavelength. Variations of R in some of the pass-
p p
band-passes and the three runs simultaneously. Furthermore, bandscouldbe producedby absorptionlines such as water va-
5
Nikolovetal.:WASP-4bTransitObservationsWithGROND
Table3.SystemparametersoftheWASP-4systemderivedfromthelightcurveanalysis.
Parameter Value 68.3%Conf.Limits Unit Comment
–Lightcurvefit–
Planet-to-starsizeratio p=R /R 0.15655 0.00028 – 1
p
Orbitalinclination i ∗ 88.57 0.45 deg 1
Normalizedsemimajoraxis a/R 5.455 0.031 – 1
Transitimpactparameter b=(a/R∗)cosi 0.136 0.043 – 1
Reducedchi-square χ2∗ 1.005 – – 1
red
–Planetaryparameters–
Radius R 1.413 0.020 R 2
p Jup
Semimajoraxis a 0.02300 0.00036 AU 2
Meandensity ρ 0.582 0.036 ρ 2
p Jup
Surfacegravity g 15.36 0.91 ms 2 2
p −
Transitduration t 2.1696 0.0047 hour 1
D
Ingress/egress t 0.3014 0.0039 hour 1
ing/egr
–Stellarparameters–
Meandensity ρ 1.715 0.029 gcm 3 1
−
g Linearlimb-darkeningcoefficient u∗ 0.616 0.046 – 1
′ 1
g Quadraticlimb-darkeningcoefficient u 0.211 0.060 – 1
′ 2
r Linearlimb-darkeningcoefficient u 0.427 0.044 – 1
′ 1
r Quadraticlimb-darkeningcoefficient u 0.303 0.064 – 1
′ 2
i Linearlimb-darkeningcoefficient u 0.292 0.047 – 1
′ 1
i Quadraticlimb-darkeningcoefficient u 0.304 0.060 – 1
′ 2
z Linearlimb-darkeningcoefficient u 0.241 0.045 – 1
′ 1
z Quadraticlimb-darkeningcoefficient u 0.386 0.063 – 1
′ 2
Notes. (1)Basedontheanalysisofthemulti-bandlightcurvespresentedinthiswork;(2)Valuesobtainedusing(1)andresultsforthe M ,R ,
T andM fromWinnetal.(2009)andSanchis-Ojedaetal.(2011). ∗ ∗
eff p
Table5.Best-fitradiusineachband. bitalperiodPandthereferencetransitepochT byplottingthe
0
transitmid-timesasafunctionoftheobservedepoch(E)
band λ Radius
(nm) RJup TC(E)=T0+E P. (6)
g 455 1.409 0.021 ×
′
±
r 627 1.415 0.020
′ ± Inthis linear fit the constantcoefficientis the best-fit refer-
i 763 1.407 0.021
z′ 893 1.420±0.021 encetransitepoch(T0)andtheslopeofthelineistheplanetary
′ ± period, P. We then use the new values for the period and the
Notes.Thebest-fitradiiwerederivedafterfixingtheorbitalinclination reference epoch to repeat our fitting procedure for the system
andnormalizedsemimajoraxistotheirbest-fitvaluesfromTable3. parameters until we arrive at a point of convergence.We used
the on-line converter developed by Eastman et al. (2010) and
transformedthetransitmid-timesfromJDbasedonUTCtoBJD
por, methane, etc. in the planetary atmosphere. As a check for based on the BarycentricDynamicalTime (TDB). We derive a
this assumption we fitted the data originating from each pass- Period = 1.33823144 0.00000032 day and a reference tran-
bandindividually.InsteadoffixingRp/R ,ianda/R toaasin- sittimeTC = 2454697±.798311 0.000046BJD. Theresultfor
gleuniversalvaluewesettheplanettost∗arradiusrat∗ioasafree thebest-fitperiodisconsistentw±iththeonefromSanchis-Ojeda
parameterandkeeptheremainingquantitiesasfreeparameters. et al. (2011), who found P = 1.33823187 0.00000025 day,
Table5displaysthebest-fitradiiasafunctionofthewavelength and reporteda smaller error as they measure±d the periodusing
withnoindicationsofvariationswithinthemeasurederrorbars. allavailabletransittimes,includingthefouradditionalmeasure-
mentsreportedbySouthworthetal.(2009).
Wefurtherinvestigatedtheobservedminuscalculated(O
4.2.Derivingthetransitephemeris −
C) residuals of our data and the reported transit mid-times at
One of our primary goals is to measure an accurate value for thetimeofwritingforanydeparturesfromthepredictedvalues
the transitephemeris(T and P). We include allavailable light estimated usingour ephemeris.As it was shownby Holman&
0
curvesfromthethreerunsandfitforthelocationsofminimum Murray(2005)and Agoletal. (2005)a deviationin the O C
−
lightusingthebest-fitplanetaryradius,inclinationandsemima- valuescanpotentiallyrevealthepresenceofmoonsoradditional
joraxisfromSect.(4.1.).Weminimizetheχ2asdefinedinSect. planetsinthesystem.WelistandplottheO Cvaluesfromour
−
(4)overthefour-banddataofeachrunbyfittingsimultaneously analysisinTable5andFigure3,respectively.Ananalysisofthe
for the T . After the best-fit transit mid-times are derived we O C valuesshowsnosignofa TTVsignalgreaterthan20s,
C
−
add them to all reportedtransit mid-timesavailable at the time exceptthe two big outliers at epochs300 and 305. We put up-
of writing in the literature2 (Table 5). We furtherfit for the or- per constraintsonthe mass of an aditionalperturbingplanetin
2 Southwortetal.(2009)measuredmid-timesduringfourtransitsof asunreliableduetotechnicalissuesassociatedwiththecomputerclock
WASP-4b.Weexcludethesetimesinouranalysis,astheywerereported atthetimeofobservations(Southworth2011,privatecommunication)
6
Nikolovetal.:WASP-4bTransitObservationsWithGROND
Table6.Literaturetransitmid-timesofWASP-4andtheirresid-
ualsinadditiontotheephemerisderivedinthiswork. 1
0
Epoch Transitmidtime O C Reference
(BJD) (d−ay) min) -1
3000 22445543396643..51706954+−+0000....0000000032223115 -00..0000021213 11 O-C ( -2
303 2454368.59341−+0.00025 0.00003 1
305 2454371.26813+−00..0000009277 -0.00171 1 -3
0.00087
324 2454396.69623+−00..0000002165 -0.00001 1 -4
549 2454697.798228−+00..000000005555 -0.00008 2 0 200 400 600 800
587 2454748.651228+−0.000072 0.00012 2 Epoch
0.000072
809 2455045.738643+−0.000054 0.00016 3
0.000054
812 2455049.753274+−0.000066 0.00010 3
0.000066
815 2455053.767816+−0.000053 -0.00006 3 20
0.000053
827 2455069.826637+−0.000086 -0.00001 4
0.000086 10
830 2455073.841103+−0.000070 -0.00024 4
0.000070
850 2455100.605928+−0.000061 -0.00005 3 c) 0
0.000061 e
859 2455112.650002+−00..000000007744 -0.00005 4 C (s -10
− O-
Notes.(1)Gillonetal.(2009);(2)Winnetal.(2009);(3)Sanchis-Ojeda -20
etal.(2011);(4)Thiswork;Theepochofthefirstobservedtransitof
-30
WASP-4bwastakenasequaltozero.
-40
550 600 650 700 750 800 850
Epoch
thesystemasafunctionofitsorbitalparameters.Wesimplified
Fig.3. ThetransittimingresidualsforWASP-4balongwiththe
thethree-bodyproblembyassumimgthatthesystemiscoplanar
onesigmaerrorbars.Toppanel:Theobservedtransitmid-times
andinitialorbitsofbothplanetsarecircular.Theorbitalperiod
based on this work and others in the literature were subtracted
of the perturber was varied in a range between 0.1 and 10 or-
from the calculated times produced by our ephemeris. Lower
bitalperiodsofWASP-4b.We generated1000syntheticO C
diagrams based on calculations done with the Mercury pa−ck- panel:Acloserviewoftheavailabletransitmid-timesfrom2009
and2010.
age(Chambers1999).WeappliedtheBulirsch–Stoeralgorithm
tointegratetheequationsofmotion.Calculationscovered1150
days,i.e.860periodsofthetransitingplanet,thatarecoveredby
observations.TheresultsofsimulationsarepresentedinFig.4. 103
OuranalysisallowsustoexcludeadditionalEarth-massplanets 100
closetolow-orderperiodcommensurabilitieswithWASP-4b. 102
andFpoerritohdecPaseanodfaatprearntsuirtbininggplpalnaentetwwithithasseemmii--mmaajjoorraaxxiissaa1 )Earth 10-1)upiter
&onManuroruatyer20o10rb5itd(eir.iev.ead2t≥heaa1p)p,rpoexriiomdatPe2foanrmdumlaass M2 Holman2 M (Mp 101 10-2M (MpJ
100
∆t 45π M2 P α3(1 √2α3/2) 2 (7) 10-3
≃ 16 M ! 1 e − e − 10-1
∗
0.2 0.5 2.0 5.0
a P /P
α = 1 (8) p b
e
a (1 e )
2 2 Fig.4.Theupper-masslimitofahypotheticaladditionalplanet
−
thatcouldperturbtheorbitalmotionofWASP-4basafunction
for the magnitude of the variation (in seconds) of the time of ratio of orbital periods of transiting planet, P , and the per-
b
interval(∆t)betweensuccessivetransits.Onecouldimaginean turber,P .Orbitslocatedinagreyareawerefoundtobeunsta-
p
exterior perturbing planet on a circular coplanar orbit twice as ble.
farasWASP-4b (periodP 3.75daynotin meanmotionres-
≈
onance with the transiting planet). If such an imaginary planet
hadamassof0.1M ,itwouldhaveinduced 5secvariations
Jup 5. Concludingremarks
∼
inthepredictedtransitmid-timesofWASP-4b.Furthermore,the
perturbercouldcauseradialvelocityvariationsoftheparentstar We have used the GROND multi-channelinstrument to obtain
13.78 m/s, which is below the radial velocity r.m.s. of the four-bandsimultaneouslightcurvesoftheWASP-4systemdur-
∼
WASP-4 residual equal to 15.16 m/s, presented in the analysis ingthreetransits(atotalof12lightcurves)withthe aimtore-
ofTriaudetal.(2010).Although,afewoutliersarevisibleinthe finetheplanetandstarparametersandtosearchfortransittim-
O C diagramweconsiderthepredictionofsuchanimaginary ing variations.We derivedthe final valuesforthe planetaryra-
−
planetintheWASP-4systemasimmature,becausetheweights dius R and the orbital inclination i by fixing the stellar radius
p
oftheO C pointsmightstillrequireanadditionaltermtoac- R and mass M to the independently derived values of Winn
countfor−systematicsofunknownorigin. et∗al. (2009) an∗d Sanchis-Ojeda et al. (2011). We include the
7
Nikolovetal.:WASP-4bTransitObservationsWithGROND
time-correlated“red-noise”inthephotometricuncertaintiesus- Triaud,A.H.M.J.,CollierCameron,A.,Queloz,D.,etal.2010,A&A,524,25
ingthe“time-averaging”methodologyandandbyrescalingthe Winn,J.N.Holman,M.J.andHenry,G.W.,etal.2007,AJ,133,1828
weightstoproducevaluefortheχ2 equaltounity.Wefurther Winn,J.N.,Holman,M.J.,Torres,G.,etal.2008,ApJ,683,1076
red Winn,J.N.,Holman,M.J.,Carter,J.A.,etal.2009,AJ,137,3826
performthelightcurvesanalysisbyminimizingtheχ2 function Winn,J.N.,Howard,A.W.,Johnson,J.A.,etal.2011,AJ,141,63
overallpassbandsandrunssimultaneouslyviatwoapproaches. Wilson,D.M.,Gillon,M.,Hellier,C.,etal.2008,ApJ,675,L113
First we modeled the data using theoretically predicted limb-
darkeningcoefficientsfor the quadratic law. Second, we fit the
lightcurvesforthelimb-darkening.Bothmethodsresultincon-
sistentsystemparameterswithin<1%.Thesecondmethodpro-
ducedlimbdarkeningparameterscompatiblewith the theoreti-
cal predictions within the one-sigma errorbarsof the fitted pa-
rameters.
Weaddedthreenewtransitmid-timesforWASP-4b,derived
a new ephemeris and investigated the O C diagram for out-
−
lierpoints.Wehavenotfoundcompellingevidencesforoutliers
thatcouldbeproducedbythepresenceofasecondplanetinthe
system.Wedidnotdetectanyshort-livedphotometricanomalies
suchasoccultationsofstarspotsbytheplanet,whichwherede-
tectedbySanchis-Ojedaetal.(2011).Atthetransitr.m.s.level
ofourlightcurves( 2.2mmag)itwouldbechallengingtode-
∼
tectsimilaranomalies.Howeverwenotethatduetothebright-
nessoftheparentstar,theshortplanetaryorbitalperiodandthe
significant transit depth, the WASP-4 system is well suited for
follow-upobservations.
Acknowledgements. PartofthefundingforGROND(bothhardwareaswellas
personnel)wasgenerouslygrantedfromtheLeibniz-PrizetoProf.G.Hasinger
(DFG grant HA 1850/28-1). N.N. acknowledges the Klaus Tschira Stiftung
(KTS)andtheHeidelbergGraduateSchoolofFundamentalPhysics(HGSFP)
forthefinancial supportofhisPhDresearch. GMacknowledges thefinancial
supportfromthePolishMinistryofScienceandHigherEducationthroughthe
Iuventus Plus grant IP2010 023070. The authors would like to acknowledge
LuigiMancini,JohnSouthworthandtheanonymousrefereebytheirusefulcom-
mentsandsuggestions.
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