Broad-band transmission spectrum and K-band thermal emission of WASP-43b as observed from the ground

1.5 MB·

by  Guo Chen

Astronomy&Astrophysicsmanuscriptno.GChen_wasp43_R1 cESO2014
(cid:13)
January15,2014
Broad-band transmission spectrum and K-band thermal emission
⋆
of WASP-43b as observed from the ground
G.Chen1,2,3,R.vanBoekel3,H.Wang1,N.Nikolov3,4,J.J.Fortney5,U.Seemann6,W.Wang7,L.Mancini3,andTh.
Henning3
1 Purple Mountain Observatory, & Key Laboratory for Radio Astronomy, Chinese Academy of Sciences, 2 West Beijing Road,
Nanjing210008,China
e-mail:[email protected]
2 UniversityofChineseAcademyofSciences,19AYuquanRoad,Beijing100049,China
4
3 MaxPlanckInstituteforAstronomy,Königstuhl17,69117Heidelberg,Germany
1
4 AstrophysicsGroup,UniversityofExeter,StockerRoad,EX44QL,Exeter,UK
0
5 DepartmentofAstronomyandAstrophysics,UniversityofCalifornia,SantaCruz,CA95064,USA
2
6 InstitutfürAstrophysik,Friedrich-Hund-Platz1,37077Göttingen,Germany

n 7 Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012,
a China
J
3 Received24September2013;accepted8January2014
1

ABSTRACT
]
P
Aims.WASP-43bistheclosest-orbitinghotJupiter,andhasahighbulkdensity.Itcausesdeepeclipsedepthsinthesystemlightcurve
E
inbothtransitandoccultationattributedtothecooltemperatureandsmallradiusofitshoststar. Weaimatsecuringabroad-band
h. transmissionspectrumanddetectingitsnear-infraredthermalemissioninordertocharacteriseitsatmosphere.
p Methods. Weobservedonetransitandoneoccultationevent simultaneouslyintheg′, r′, i′,z′, J, H, K bandsusingtheGROND
- instrumentontheMPG/ESO2.2-metertelescope,inwhichthetelescopewasheavilydefocussedinstaringmode.Aftermodelingthe
o lightcurves,wederivedwavelength-dependenttransitdepthsandfluxratios,andcomparedthemtoatmosphericmodels.
r Results.Fromthetransitevent,wehaveindependentlyderivedWASP-43’ssystemparameterswithhighprecision,andimprovedthe
t
s periodtobe0.81347437(13)daysbasedonalltheavailabletimings. Nosignificantvariationintransitdepthsisdetected, withthe
a largestdeviationscomingfromthei-,H-,andK-bands.Giventheobservationaluncertainties,thebroad-bandtransmissionspectrum
′
[ canbeexplainedbyeitheraflatfeaturelessstraightlinethatindicatesthickclouds, syntheticspectrawithabsorptionsignaturesof

atomicNa/KormolecularTiO/VOthatindicatecloud-freeatmosphere, oraRayleighscatteringprofilethatindicateshigh-altitude
1
hazes. Fromtheoccultationevent,wehavedetectedplanetarydaysidethermalemissionintheK-bandwithafluxratioof0.197
v ±
0.042%,whichconfirmspreviousdetectionsobtainedinthe2.09µmnarrowbandandK -band. TheK-bandbrightnesstemperature
7 S
1878+108 Kfavorsanatmospherewithpoorday-tonight-sideheatredistribution. Wealsohaveamarginaldetectioninthei-band
0 116 ′
(0.037−+0.023%), corresponding toT =2225 +139 K,whichiseitherafalsepositive, asignatureofnon-blackbody radiationatthis
0 0.021 B 225
wavelen−gth,oranindicationofreflectivehazes−athighaltitude.
3
1. Keywords. stars: planetarysystems–stars: individual: WASP-43–planetsandsatellites: atmospheres–planetsandsatellites:
0 fundamentalparameters–techniques:photometric
4
1
:1. Introduction (e.g.Guillot2005;Guillotetal.2006;Charbonneauetal.2007;
v
i Fortneyetal.2007).
XTransiting hot Jupiters are highly valuable in the characteriza-
rtionstudyofplanetaryorbits,structuresandatmospheres. They With high incident irradiation from the host stars, tran-
aorbit the host stars closely whilst they possess relatively large siting hot Jupiters also play a crucial role in planetary at-
sizesandmasses, therebyproducinglargetransitandradialve- mospheric characterization. Through observations of primary
locitysignals,whichtogetherresultinprecisedeterminationof transits, transmission spectrum can be constructed by measur-
the planetary system parameters, such as planetary mass, ra- ing the transit depths at different wavelengths, which carries
dius, surface gravity, orbital distance, stellar density etc (e.g. information of planetary atomic (e.g. Na, K) and molecu-
Seager&Mallén-Ornelas2003;Southworthetal.2007). Based lar (e.g. H O, CH , CO) absorption features when the stel-
2 4
onthesefundamentalparameters,theplanetarycompositionand lar lights are transmitted in the planetary day-night termina-
internalstructurecouldbe investigated,providingusaninsight tor region (Seager&Sasselov 2000; Fortneyetal. 2008, 2010,
viewoftheplanetaryformation,evolutionandmigrationhistory etc.). In a similar way, thermal emission spectrum can be
obtained by measuring the occultation depths (approximately
⋆ BasedonobservationscollectedwiththeGammaRayBurstOpti- the planet-to-star flux ratios) during secondary eclipses (i.e.
calandNear-InfraredDetector(GROND)ontheMPG/ESO2.2-meter occultations), which puts constraints on both chemical com-
telescopeatLaSillaObservatory, Chile. Programme088.A-9016(PI: position and temperature structure of the dayside atmosphere
Chen) (Burrowsetal. 1997; Burrows&Sharp 1999; Burrowsetal.
Articlenumber,page1of14
2006,2008a;Fortneyetal.2008;Madhusudhan&Seager2009, 2. ObservationsandDataReductions
etc.).
We observed one primary transit and one secondary eclipse
Abundantobservationshavebeenperformedtocharacterize eventsof WASP-43bwith the GROND instrumentmountedon
the atmospheresfordozensofhotJupitersin these twoaspects theMPG/ESO2.2-metertelescopeatLaSillainChile. GROND
(seethereviewbySeager&Deming2010). However,veryfew isanimaginginstrumentprimarilydesignedfortheinvestigation
hot Jupiters have been studied in both aspects which are com- of gamma-ray burst afterglows and other transients simultane-
plementary and could potentially constrain the origin of ther- ouslyinsevenbands: Sloang,r ,i, z andnear-infraredJ, H,
′ ′ ′ ′
mal inversions (e.g. Hubenyetal. 2003; Burrowsetal. 2007; K (Greineretal. 2008). The light goes through dichroics, and
Fortneyetal. 2008; Madhusudhan&Seager 2010), as the ab- issplitintoopticalandNIRarmsandfurtherintosevenbands.
sorbersthatcausethermalinversionsalso imprinttheirspectral Theopticalarmemploysbacksideilluminated2048 2048E2V
signatures on transmission spectra. This kind of studies have CCDs without anti-blooming structures, which hav×e a field of
started to emergeon some typicalcases of hotJupiters, forex- view(FOV)of5.4 5.4arcmin2andapixelscaleof0.158,and
ample,HD189733b(Pontetal.2013),WASP-12b(Swainetal. store data in FITS×file with fourextensions. The NIR′′armem-
2013)andWASP-19b(Beanetal.2013). ploys 1024 1024 Rockwell HAWAII-1 arrays, with an FOV
of10 10ar×cmin2andapixelscaleof0.60,whichplacedataof
WASP-43b is a hot Jupiter orbiting a K7V star every 0.81 × ′′
threebandssidebysideinasingleFITSfile. TheGRONDguide
days,firstdiscoveredbyHellieretal.(2011). Ithasthesmallest
camerais placed outsideof the main GROND vessel, resulting
orbital distance to its host star among the Jupiter-size planets.
in a guiding FOV which is 23 south of the scientific imaging
The host star is active as indicated by the presence of strong ′
FOV.TakingintoaccountthedifferentFOVscalesbetweenop-
Ca H+K emission. Gillonetal. (2012) significantly improved
tical and red arms, the orientation of guiding system, and the
the WASP-43 system parametersbased on20 transits observed
inclusionof asmanyreferencestars aspossible, a compromise
withthe60-cmroboticTRAPPISTtelescopeand3transitswith
betweenthesefactorsisnecessarywhendesigningtheobserving
the 1.2-m Euler Swiss telescope. The deduced planetary mass
strategy.Nevertheless,GRONDisstillapotentiallygoodinstru-
(2.034 0.052M )andradius(1.036 0.019R )indicatea
± Jup ± Jup ment for exoplanetobservations, since it has very few moving
highbulkdensitythatfavorsanoldageandamassivecore.They
parts and the capability of multi-band observations with large
also observed the occultations of WASP-43b at narrow bands
wavelengthcoverage.
withVLT/HAWK-I,resultinginathermalemissiondetectionat
2.09µm(F /F =0.156 0.014%)andatentativedetectionat Theobservingstrategiesforbothtransitandoccultationwere
p ⋆
1.19 µm (0.079 0.032%±). Blecicetal. (2013) performed at- thesame. Weheavilydefocussedthetelescopeduringbothob-
± servationsinordertospreadthelightofstarsontomorepixels,
mospheric modelingbased on their Warm Spitzer detectionsat
3.6µm(0.346 0.012%)and4.5µm(0.382 0.015%)incom- whichasaresultcouldreducethenoisearisingfromsmallnum-
± ± ber of pixels and avoid reaching the non-linear regime. When
bination with the two ground-basednear infrared (NIR) detec-
achievable,we didsky measurementsbothbeforeand afterthe
tionsofGillonetal.(2012),whichrulesoutastrongthermalin-
versioninthedaysideatmosphere,andsuggestsinefficientday- sciencetimeseries,whichweredesignedina20-positiondither
pattern around the scientific FOV. According to the experience
nightenergyredistribution.Recently,Wangetal.(2013)carried
thatwe hadin the observationsof WASP-5b(Chenetal. 2013,
out occultation observations with the WIRCam instrument on
the Canada-France-Hawaii telescope, and detected the thermal PaperI),staringmodeismorestableandintroduceslessinstru-
emissionintheH-band(0.103 0.017%)andK -band(0.194 mentalsystematiceffectsthannoddingmode.Therefore,forthe
S
0.029%).However,currentdat±aarestillinsufficienttoconstrai±n WASP-43b observations, we made the telescope staring on the
thechemicalcompositionofWASP-43b’satmosphere. targetduringthe3-hourlongscience timeseries. Theobserva-
tionswerecarriedoutinthegr iz JHK filterssimultaneously.
′ ′ ′ ′
In 2011, we started a project to characterize hot-Jupiter Thefinalobservingdutycycleisdeterminedbythecompromise
atmospheres using the GROND instrument (e.g. Paper I on between the integration times of optical arm and NIR arm, as
WASP-5b; Chenetal. 2013), which is capable of doing si- they are not fully independent in operation. The summary of
multaneous multi-band photometry. This technique now has bothtransitandoccultationobservationsarelistedinTable1.
been performed on several transiting planets to investigate
theiratmospheres(deMooijetal.2012;Southworthetal.2012;
Mancinietal.2013a,b,c;Nikolovetal.2013;Fukuietal.2013; 2.1.Transitobservation
Copperwheatetal. 2013; Nascimbenietal. 2013). Among our
The transit eventwas observedon January 8 2012, from05:24
targets, WASP-43b is favorable for observation because of
to 08:21UT, whichcovered 50 minutesbothbeforeexpected
its large transit depth 2.5% and high incident irradiation ∼
9.6 108 ergs 1cm 2 (G∼illonetal. 2012). If zero albedo and ingress and after expected egress (see Fig. 1). This night was
∼ × − − ofhighrelativehumidity,rangingfrom40%to60%. Themoon
zerodaytonightheatredistributionareassumed,anequilibrium
was illuminated by 99%, with a minimum distance of 65 to
temperatureof1712Kisderived. Weaimtoconstructabroad- ◦
WASP-43.Theairmasswaswellbelow1.30.Althoughthetele-
bandtransmissionspectrumforWASP-43bandalsotodetectits
scope was heavily defocussed, the radius of the donut-shaped
NIRthermalemission.
pointspreadfunction(PSF)ringvariedbyasmuchas1.0dur-
′′
This paper is organizedas follows: Sect. 2 summarises the ingtheobservation,indicatingthattheseeingwasnotverysta-
transit and occultation observations, as well as the data reduc- bleandhadevidentimpactonourPSF. Theobservationwasin
tion. Sect. 3 describes the process of transit and occultation a good auto-guiding status thanks to a bright star in the guid-
light curve modeling, including the re-analysis of light curves ingFOV.Wedidskymeasurementsonlybeforethesciencetime
obtainedbyamateurastronomers. Sect.4reportsthenewlyde- series as the morning twilight had begun at the end of the ob-
rived orbital ephemeris and fundamental physical parameters, servation. For the science time series, the optical bands were
andpresentsdiscussiononWASP-43b’satmosphericproperties. integratedfor90secondsinfastread-outmodesimultaneously,
Sect.5givestheoverallconclusions. and81frameswererecorded,resultinginadutycycleof 69%.
∼
Articlenumber,page2of14
G.Chenetal.:TransitandoccultationobservationsofWASP-43b
Table1.SummaryoftheWASP-43bObservationswiththeGRONDinstrument
Date Start/endtime Type Airmass Moon Filter N t Aperture N β σ
obs exp ref 120s
(UT) (UT) illum.(d) (sec) ( ) β β (ppm)
′′ χ r
2012-01-08 05:24 08:21 Tran. 1.29 1.06 1.07 99%(65 ) g 81 90 3.6,4.9,6.0 1 1.26 1.21 678
◦ ′
→ → →
r 81 90 5.5,8.4,9.0 1 1.40 1.00 504
′
i 81 90 6.2,9.0,9.6 1 1.23 1.00 645
′
z 81 90 4.7,7.6,8.4 1 1.57 1.00 798
′
J 244 3 8 6.3,11.1,15.6 3 0.59 1.97 1241
×
H 244 3 8 6.3,11.7,15.6 1 1.01 2.83 1269
×
K 244 3 8 5.1,9.9,14.4 2 0.64 1.50 1269
×
2012-03-03 02:52 05:59 Occ. 1.12 1.06 1.18 69%(63 ) g 98 90 5.4,7.3,8.1 2 1.57 1.00 673
◦ ′
→ → →
r 98 90 6.5,9.0,9.6 1 2.31 1.52 475
′
i 98 90 5.5,7.7,8.5 2 2.58 1.00 604
′
z 98 90 5.5,7.7,8.5 1 2.50 1.49 575
′
J 389 4.5 4 8.4,11.4,15.6 3 1.30 2.53 953
×
H 389 4.5 4 6.9,11.1,15.6 3 0.95 3.38 885
×
K 389 4.5 4 6.0,9.6,14.4 2 0.47 1.09 1425
×
Notes.Type"Tran."/"Occ."correspondstotransit/occultation,respectively. "Moonillum."isthefractionoftheMoonthatisilluminated,while
thebracketeddistheminimumdistancetotheMoon. N isthenumberofretrievedimages,whileN isthenumberofreferencestarstocreate
obs ref
acompositereferencelightcurve. t referstointegrationtimeforgriz,anddetectorintegrationtime(DIT)timesthenumberofDIT(N )
exp ′ ′′ ′ DIT
forJHK. Aperturesizesrefertotheoptimalaperture,inner/outerannuliradiiadoptedinthephotometry. β andβ aretheχ -rescalingandred
χ r ν
noiserescalingfactorsasdescribedinSect.3.1. σ referstothestandarddeviationoflight-curveO–Cresidualsbinnedinevery2minutes.
120s
Thelastthreecolumnsarecalculatedfromtheglobaljointanalysiswithwavelength-dependentradius(orfluxratios),i.e. Method3asdescribed
inSect.3.2.
TheNIRbandswereintegratedwith8sub-integrationsof3sec- through median combination as well, except that the sigma-
onds,whichwereaveragedtogetherbeforereadout. 244frames clippingfilterwasappliedifnecessary. Afterthedarkwascor-
wererecordedintheNIR,resultinginadutycycleof 56%. rected,eachimagewassmoothedwithamedianfilterandcom-
∼
pared to the unsmoothed one. The amplitudes of the readout
patternweredeterminedbydifferentiatingmedianvalueofeach
2.2.Occultationobservation
columnto the overallmedianlevel, and were then correctedin
The occultation event was observed on March 3 2012, from theoriginaldark-subtractedimages. Theflatfieldwascorrected
02:52to05:59UT,whichcovered 70minutesbeforeexpected aftertheremovalofthispattern.
∼
ingressand 40minutesafterexpectedegress(seeFig.2).Rela-
Accordingtoourexperienceonothertargets(e.g.Chenetal.
∼
tivehumidityforthisnightwasalsohigh( 45%),andthemoon
2013),skysubtractionmightresultinlightcurvesofslightlybet-
∼
was illuminated by 69%, with a minimum distance of 63 to
◦ terprecision. Inthisapproach,a skymodeliscreatedandsub-
WASP-43.Theairmasswasbelow1.20forthewholeevent.The
tractedforeach individualscience framebyoptimallycombin-
resultingPSFdonutringsizewasstableout-of-eclipse,whileit
ingthescaledbefore-andafter-scienceskymeasurements.This
variedalotduringtheeclipse,whichwascausedbythesudden
techniqueisnotcapableofremovingtemporalvariations,butis
jumpsofpoorseeing.Wedidskymeasurementsbothbeforeand
helpfulforremovingspatialvariationsinprinciple. However,it
afterthescienceobservation. Theopticalbandswereintegrated
isnotthe case forthisstudy. We foundnoimprovementin the
with90secondsinfastread-outmode,whiletheNIRbandswere
data set by applying the sky subtraction technique. Therefore,
integratedwith4sub-integrationsof4.5seconds.Intheend,we
we decidedto performouranalysison thedata setwithoutsky
collected98framesfortheopticaland389framesfortheNIR,
subtraction.
translatingintoadutycycleof78%and63%,respectively.
After these calibrations, we employed the IDL/DAOPHOT
package to perform aperture photometry on WASP-43 as well
2.3.Datareduction as nearby comparisonstars of similar brightness. The location
ofeachstarwasdeterminedbyIDL/FIND,whichcalculatesthe
Both sets of observationswere reducedin a standard way with
ourIDL1 codes,whichlargelymakeuseofNASAIDLAstron- centroidby fitting Gaussians to the marginalx, y distributions.
omy User’s Library2. Calibration for the optical data includes ThisfindingalgorithmwasappliedontheGaussian-filteredim-
agesthatwereoflowerresolution,inwhichtheirregulardonut-
bias subtraction and flat division. The master frames for both
shapedPSFs becamenearlyGaussianafter properconvolution.
were created from median combination of individual measure-
WerecordedtheFWHMofeachstarbymaskingoutthecentral
ments.Thetwilightskyflatmeasurementswerestar-maskedand
regionof the originaldonutandfitting a Gaussian to the donut
normalizedbeforemediancombination.
wing. Timeseriesofeachstarwasself-normalizedwithitsout-
FortheNIRdata,thecalibrationisalittlemorecomplicated
of-transitfluxlevel.Wethencarefullychosethebestcomparison
due to the presence of an electronic odd-even readout pattern
starensembleineachbandtocorrectthefirstorderatmospheric
along the X-axis. The calibration includes dark subtraction,
effect on the WASP-43 time series, in the following way: var-
readout pattern removal, and flat division. The master frames
iouscombinationof comparisonstars were experimented. The
for dark, twilight sky flat and sky measurements were created
ensemblewhichleavesWASP-43withtheleastlight-curveO–C
1 IDLisanacronymforInteractiveDataLanguage,fordetailsplease residuals was chosen. In order to find the optimalphotometry,
refertohttp://www.exelisvis.com/idl/ 40 apertureswere laid on the optical imagesin step of 1 pixel,
2 Seehttp://idlastro.gsfc.nasa.gov/ each with 10 sky annulus sizes in steps of 2 pixels, while 30
Articlenumber,page3of14
WASP-43b Jan-08-2012 transit WASP-43b Jan-08-2012 transit WASP-43b Jan-08-2012 transit
3

1.00 1.00 g’ 0 g’
g’

-3
0.99 r’ 0.99 r’ 3
r’
0.98 i’ 0.98 i’ 0

-3
0.97 z’ 0.97 z’ 3
i’
0

0.96 0.96 -3
3
0.95 0.95 z’
0
elative flux01..9040 elative flux01..9040 J -3esiduals (10)-306 J
R0.99 J R0.99 R
-6
H
0.98 H 0.98 6

0 H
0.97 0.97 K

-6
K
0.96 0.96 6

0.95 0.95 0 K

0.94 0.94 -6
-100 -50 0 50 100 -100 -50 0 50 100 -1 00 -5 0 0 5 0 10 0
Time from mid-transit [min] Time from mid-transit [min] Time from mid-transit [min]
Fig.1. PrimarytransitlightcurvesofWASP-43basobservedwiththeGRONDinstrumentmountedontheESO/MPG2.2mtelescope. Ineach
panel,shownfromtoptobottomaretransitlightcurvesofgrizJHK. Leftpanelshowslightcurvesthatarenormalizedbythereferencestars.
′ ′′ ′
Middlepanelshowsbaseline-correctedlightcurveswhicharebinnedinevery2minutesfordisplaypurpose(seeSect.3.1forbaselinecorrection).
Rightpanelsshowthebest-fitlight-curveresiduals,alsobinnedper2minute.Best-fitmodelsforallpanelsareoverlaidinsolidordashedlines.
Table2.Quadraticlimb-darkeningcoefficientsadoptedinthiswork (e.g.star’slocationonthedetector,seeingetc).Inordertomodel
theselightcurvesproperly,wechosetofitthedatawithmodels
Filter u1 u2 composedoftwocomponents:
g 0.867 0.022 0.042 0.020
′
± − ±
r′ 0.628±0.017 0.120±0.011 F(mod)= E(pi)B(x,y,z,s,t) (1)
i 0.486 0.010 0.166 0.005
′
z 0.398±0.008 0.184±0.004 The first component is the analytic light curve model
′
± ±
J 0.286 0.009 0.229 0.003 (Mandel&Agol 2002), representing the transit or occultation
± ±
H 0.135 0.005 0.330 0.003 signal itself. For the transit event, a quadratic limb darkening
± ±
K 0.120 0.003 0.275 0.003 lawisadopted:
± ±
I /I =1 u (1 µ) u (1 µ)2 (2)
µ 1 1 2
− − − −
apertureswerelaidontheNIRimagesinstepsof0.5pixel,each
with10skyannulussizesinstepof1pixel.Thisresultedin400 where I is the intensity and µ = cosθ (θ is the angle be-
and 300 datasets with differentaperture settings for the optical tween the emergentintensity and the line of sight). We calcu-
and NIR, respectively, of which the one that leaves WASP-43 late the two theoretical coefficients u1 and u2 by bilinearly in-
withtheleastlight-curveO–Cscatterwasadopted. Table1lists terpolatingin the Claret&Bloemen (2011) table, in which the
the number of reference stars in use and the final aperturesfor effective temperature Teff = 4520 120K, the surface gravity
±
photometry. logg⋆ = 4.645 0.011, the metallicity [Fe/H]= 0.01 0.12
± − ±
are taken from Gillonetal. (2012) while the microturbulence
Finally,weextractedtheobservationtimeofeachframe. In
ξ = 0.5 0.3 km s 1 from Hellieretal. (2011). Resulting
this process, we made the time of each frame centered based r −
±
values with uncertainties are set as Gaussian priors (GP; see
on its actual total integration. This UTC time was then con-
Equation 4) in the subsequent fitting process, and listed in Ta-
verted to Barycentric Julian Date in the Barycentric Dynami-
ble 2. Thus this theoretical model E(p) contains six free pa-
calTimestandard(BJD )usingtheIDLprocedurewrittenby i
TDB
rameters: theorbitalinclinationi,theplanet-to-starradiusratio
Eastmanetal.(2010).
R /R , the scaled semi-major axis a/R , the mid-transit point
p ⋆ ⋆
T ,thelimb-darkeningcoefficientsu andu ,whiletheperiod
mid 1 2
P is fixed at literature value (or updated ephemeris iteratively,
3. Lightcurveanalysis
seeSect.4.1). Theeccentricityeisfixedatzerosinceitcannot
3.1.Lightcurvemodeling bedeterminedbyasingletransit.
Fortheoccultationevent,E(p)becomes:
i
As shown in the left panels of Fig. 1 and 2, the reference-
corrected light curves still exhibit systematics which are cor- λ
E(T ,F /F )=1 e (3)
relatedwith instrumentalparametersor atmosphericconditions occ p ⋆ − 1+(F /F ) 1
p ⋆ −
Articlenumber,page4of14
G.Chenetal.:TransitandoccultationobservationsofWASP-43b
WASP-43b Mar-03-2012 occultation WASP-43b Mar-03-2012 occultation WASP-43b Mar-03-2012 occultation
1
g’
g’ 0
1.000 1.000 g’
-1
1
r’ r’
0.995 0.998 r’ 0

-1
1
0.990 i’ 0.996 i’ 0 i’

-1
0.985 z’ 0.994 z’ 01 z’
elative flux 1.00 J elative flux1.000 J -3esiduals (10)-102 J
R R R
-2

2
0.98 H 0.995 H H
0

-2

0.96 K 0.990 K 2
K
0

-2
0.94
-100 -50 0 50 -100 -50 0 50 -1 00 -5 0 0 5 0
Time from mid-eclipse [min] Time from mid-eclipse [min] Time from mid-eclipse [min]
Fig.2. OccultationlightcurvesofWASP-43basobservedwithGROND.Ineachpanel,shownfromtoptobottomareoccultationlightcurvesof
griz JHK. Leftpanelshowslightcurvesthatarenormalizedbythereferencestars. Middlepanelshowsbaseline-correctedlightcurveswhich
′ ′′ ′
arebinnedinevery8minutesfordisplaypurpose(seeSect.3.1forbaselinecorrection). Rightpanelsshowthebest-fitlight-curveresiduals,also
binnedper8minute. Best-fitmodelsforallpanelsareoverlaidinsolidordashedlines. TheoccultationdepthisdetectedintheK-band(0.197
0.042%),andmarginallydetectedinthei-band(0.037+0.023%). ±
′ 0.021
−
where λ refers to the Equation 1 in Mandel&Agol (2002) in resultant χ2 is less than the previous χ2, this jump is directly
e
thecaseofuniformsourcewithoutlimbdarkening. Thismodel accepted. However,if it’s larger,we stillacceptitwith a prob-
has two free parameters: the mid-occultationtime T and the abilityof exp( ∆χ2/2). Beforea chainstarts, we optimizethe
occ
−
planet-to-starfluxratioF /F ,whileotherparametersarefixed stepscaleusingthemethodproposedbyFord(2006)sothatthe
p ⋆
atvaluesinheritedfromthetransitevent. acceptance rate is 0.44. After several chains are completed,
∼
The second component is the baseline correction function, wedoGelman&Rubin(1992)statistics to checkwhetherthey
which is used to correctthe instrumentaland atmospheric sys- are well mixed and converged. In the end, we discard the first
tematics,includingtheeffectsofthestar’slocationonthedetec- 10%linksofeachchainandcalculatethemedianvalue,andthe
tor (x, y), PSF donutring size s, airmass z, and time sequence 15.865%and84.135%levelofthemarginalizeddistributionof
t. We searchfor the best-fitparametersbyminimizingthe chi- the remaininglinks, which are recordedas the best-fit parame-
square: tersand1-σlowerandupperuncertainties.
Since the photometric uncertainties sometimes do not re-
N [F(obs) F(mod)]2 flect the actual properties of the light curve data points, either
χ2 = i − i +GP (4) duetounder-/over-estimationofnoiseorduetotime-correlated
σ2 (obs)
Xi=1 F,i noise,weperformedrescalingontheuncertaintiesintwosteps.
ForeachMCMCfittingprocess,wealwaysinitiallyranseveral
We select the best baseline model for each band based on the chains of 105 links on the data with original photometric un-
BayesianInformationCriterions(BICs,Schwarz 1978): BIC = certainties. In the first step of rescaling, we calculated the re-
χ2 +klog(N), wherek is the numberof freeparametersand N duced χ2 for the best-fit model, and recorded the first rescal-
ν
is the number of data points. The chosen baselines with their
ing factor β = χ2 in order to force the best fit to have a
derivedcoefficientsforbothnightsarelistedinAppendixA. χ ν
reduced chi-squarepequal to unity. In the second step, we fol-
Todeterminetheprobabilitydistributionfunction(PDF)for
lowedtheapproachofWinnetal. (2008) to accountfortheef-
each parameter, we employ the Markov Chain Monte Carlo
fectoftime-correlatedrednoise,inwhichtwomethodswereuti-
(MCMC)techniqueutilizingtheMetropolis-Hastingsalgorithm
lized. Inthe"time-averaging"(TA)method(see e.g.Pontetal.
with Gibbs sampling (see e.g. Ford 2005, 2006). Instead of
2006), red noise remains unchanged while white noise scales
perturbingthe baseline coefficients, we follow the approach of
down with larger binning (see Fig. 3). Standard deviations for
Gillonetal. (2010), in which these coefficients are solved by
thebest-fitresidualswithoutbinningandwithbinningindiffer-
the SingularValueDecompositionalgorithm(SVD, Pressetal.
enttimeresolutions,rangingfrom10minutesuptotheduration
1992). At each MCMC step, a jump parameter is randomly
ofingress/egress,werecalculatedtoestimatethisfactor:
picked out, and the analytic light curve model E(p) is divided
i
from the light curve. The baseline coefficients are then deter- σ N(M 1)
mined by linear least square minimization using SVD. If the βTA,N = σN r M− (5)
1
Articlenumber,page5of14
0.164 0.164
0.162 0.162
1000
0.160 0.160
R* 0.158 R* 0.158
100 R/p 0.156 R/p 0.156
g1 r1 i1 0.154 0.154
transit transit transit
0.152 0.152
pm] 10 0.150 0.150
uals [p 1000 4. 4 4. 6 4 .8a/R5. 0 5. 2 5. 4 81.0 82.0i [d eg8]3.0 84.0
d *
esi 0.164 5.4
d r 0.162
e 100 5.2
nn z1 J1 H1 0.160
MS of bi 10 transit transit transit R/Rp* 00..115568 a/R* 45..80
R 0.154
1000 0.152 4.6
0.150 4.4
-4 0 -2 0 0 2 0 4 0 -40 -20 0 20 40
100
K1 i2 K2 tmid [sec] tmid [sec]
transit occultation occultation
84.0 8844..00
10
83.5 8833..55
1 10 1 10 1 10
Number of individual points binned g] 83.0 g] 8833..00
de 82.5 de 8822..55
Fig. 3. Standard deviation of light-curve O–C residuals binned in i [ 82.0 i [ 8822..00
different time resolutions, showing the level of time-correlated noise.
81.5 8811..55
ReddashedlineindicatestheexpectedPoisson-likenoise,i.e.standard
81.0 8811..00
deviation of unbinned O–C residuals over square-root of N. Vertical
dottedlineshowscorresponding ingress/egress duration. Thenumber -40 -20 0 20 40 4.4 4.6 4.8 5.0 5.2 5.4
t [sec] a/R
followingfilternameindicateseitherprimarytransit(1)oroccultation mid *
(2).
Fig.4. Correlationsbetweenpairsofjumpparametersforthetransit
lightcurves.Blackcircleswitherrorbarsaretheresultsfromindividual
analysis(Method1)ontheseven-bandlightcurves,whilecontoursin-
whereσ isthestandarddeviationofresidualsbinnedinevery
N dicatethejointprobabilitydistributionfunction(PDF)fromglobaljoint
N points, and M is the number of bins. The final β is taken
TA analysiswithcommonradius(Method2). Bothmethodshaveconsis-
tobethemedianvalueofseverallargestβTA,N,ofwhichoutliers tentcorrelation.
could be removed while the information of red noise compo-
nentremainsunchanged.Inthe"prayer-bead"(PB)method(see
e.g. Southworth 2008), the shape of time-correlated noise was – Method3: globaljointanalysiswithwavelength-dependent
preserved. The best-fit residuals were shifted cyclicly from ith radius. Theseven transitlightcurveswerejointly fitted, in
to i+1th positions, and added back to the best-fit model, while whichallthelightcurvessharedthesamei,a/R andT ,
⋆ mid
off-positiondatapointsattheendwerewrappedbacktothebe- whileR /R wasallowedtovaryfromfiltertofilter.
p ⋆
ginning. Thiswasrepeatedin an oppositedirectionaswell, so
that2N 1syntheticlightcurveswerecreatedandmodeled.The In Method 1, we tried to characterize the light curves indi-
−
ratio between uncertaintiesderived from this process and orig- vidually, so that the variation of derived parameters from filter
inal MCMC process was recordedas β . Finally, we adopted tofiltercanbeinvestigated. Overall,thederivedparametersare
PB
therednoisefactorasβ = max(β ,β ,1). We thenrescaled consistentwitheachother.Thestandarddeviationsofindividual
r TA PB
theoriginaluncertaintiesbyβ β (seecorrespondingentriesin ianda/R arewellbelowtheiraverageuncertainties,whilethat
χ r ⋆
×
Table1and3),andranseveralmorechainsof106 linkstofind ofRp/R⋆andTmidarelessthantwiceoftheiraverageuncertain-
thefinalbest-fitparameters. ties. Strongcorrelationbetweenianda/R⋆canbeseen(seethe
datapointswitherrorbarsinFig.4),andbothofthemarecorre-
latedwithR /R . OnlyT isindependentofotherparameters.
p ⋆ mid
3.2.Fittingoftransitlightcurves
Most red noise factors come from the time-averaging method,
Our seven-band transit light curves were obtained simultane- exceptin the g′- and H-bands. These factors are very close to
ously,andcoveredalargewavelengthrangefromtheopticalto unityintheoptical,indicatingthatthelevelofrednoiseislow.
theNIR.Whilemostinferredphysicalpropertiesshouldbeprin- Itcouldalsobearesultofrelativelylongexposuretime(90sec)
cipally the same in different bands, the probed apparent plan- thatmakesthecadencenotfrequentenoughtoreflectthefeature
etary "radius" could be wavelength-dependent. Therefore we ofrednoise.Theleveloftime-correlatednoiseintheNIRseems
adoptedthreemethodsofMCMCanalysistodeterminethesys- obviousevenwithvisualinspection,especiallythedipbetween
temparametersandtoinvestigatetheirdeviations: +50and+80minutesasshowninFig.1,thusresultinginlarger
rescalingfactors.Weestimatedthestandarddeviationofbest-fit
– Method1:individualanalysis.Theseventransitlightcurves residualsper2 minuteintervalsto showthe qualityof thelight
were fitted individually, in which i, a/R⋆, Rp/R⋆ and Tmid curve, which can be directly compared to Gillonetal. (2012).
wereobtainedforeachlightcurve. Weachievedascatterof 0.05–0.08%intheoptical,and 0.11–
∼ ∼
– Method 2: global joint analysis with common radius. The 0.13%intheNIRper2minuteintervals,whichcorrespondtoa
seventransitlightcurveswerejointlyfitted,inwhichallthe range of 2.1–4.5 and 6.2–8.7 times the photon noise limit,
∼ ∼
lightcurvessharedthesamei,a/R ,R /R andT . respectively. For comparison, Gillonetal. (2012) reachedac-
⋆ p ⋆ mid
Articlenumber,page6of14
G.Chenetal.:TransitandoccultationobservationsofWASP-43b
Table3.ResultsoftheanalysisontheJan-08-2012transitlightcurves
Filter i a/R R /R T b O–Cc βd σ d
⋆ p ⋆ mid 120s
( ) indi.analysis jointanalysisa (BJD 2450000) (min) β β (ppm)
◦ TDB− χ r
Thiswork:Method1–individualanalysis ................................................................................
g 82.33+0.49 4.88+0.12 0.1588+0.0022 0.15750+0.00108 5934.791927+0.000089 -0.45+0.13 1.18 1.00 639
′ 0.45 0.11 0.0023 0.00109 0.000089 0.13
r 82.88+−0.39 5.03+−0.10 0.1567+−0.0014 0.15741+−0.00083 5934.792132+−0.000069 -0.15+−0.10 1.38 1.00 499
′ 0.37 0.09 0.0014 0.00083 0.000069 0.10
i 82.35+−0.36 4.90+−0.10 0.1594+−0.0012 0.15847+−0.00077 5934.792233+−0.000086 -0.01+−0.12 1.22 1.00 641
′ 0.36 0.09 0.0012 0.00078 0.000087 0.12
z 83.43+−0.57 5.17+−0.15 0.1553+−0.0014 0.15720+−0.00088 5934.792386+−0.000103 0.21+−0.15 1.52 1.00 768
′ 0.56 0.15 0.0014 0.00089 0.000103 0.15
J 81.84+−0.86 4.69+−0.22 0.1596+−0.0029 0.15715+−0.00251 5934.792530+−0.000214 0.42+−0.31 0.56 1.76 1123
0.77 0.19 0.0029 0.00254 0.000213 0.31
H 82.83+−1.19 5.00+−0.31 0.1533+−0.0024 0.15396+−0.00245 5934.792508+−0.000241 0.39+−0.35 1.00 2.00 1234
1.04 0.27 0.0025 0.00248 0.000238 0.34
K 82.42+−0.84 4.92+−0.22 0.1549+−0.0022 0.15465+−0.00181 5934.792226+−0.000233 -0.02+−0.34 0.64 1.52 1270
0.71 0.19 0.0022 0.00184 0.000232 0.33
− − − − − −
(Weighted) 82.61+0.20 4.954+0.051 0.15714+0.00064 ... 5934.792178+0.000040 -0.09+0.06 ... ...
0.19 0.048 0.00065 0.000040 0.06
− − − − −
Thiswork:Method2–globaljointanalysiswithcommonradius ............................................................
82.69+0.18 4.979+0.048 ... 0.15739+0.00065 5934.792190+0.000043 -0.07+0.06 ... ...
0.18 0.048 0.00064 0.000043 0.06
− − − − −
Thiswork:Method3–globaljointanalysiswithwavelength-dependentradius(adoptedasthefinalresults) ...................
82.64+0.20 4.967+0.051 ... 0.15743+0.00041a 5934.792193+0.000043 -0.07+0.06 ... ...
0.19 0.050 0.00041 0.000043 0.06
− − − − −
Gillonetal.(2012) .....................................................................................................
82.33+0.20 4.918+0.053 ... 0.15945+0.00076 5726.54336+0.00012 0.80+0.17 ... ...
0.20 0.051 0.00077 0.00012 0.17
− − − − −
Notes. (a) In the global joint analysis with wavelength-dependent radius (i.e. Method 3), R /R is allowed to vary from filter to filter
p ⋆
similar to Method 1. They are listed together with Method 1 for direct comparison. The final R /R from Method 3 is a weighted
p ⋆
mean of seven filters. (b) T is a jump parameter in the MCMC analysis. (c) The O–C values are calculated from comparison to:
mid
T(N)=2455934.792239(40)+N 0.81347437(13),whereN =0forthisworkandN = 256forGillonetal.(2012).(d) Thelastthreecolumns
inthistablearecalculatedfromthe×individualanalysis,whicharedifferentfromthoseinT−able1.

curacies 0.11–0.15%intheir opticaltransitlightcurvesusing 0.0035 0.0014
60-cman∼d1.2-mtelescopes,and 0.04–0.05%intheirNIRoc- K 0.0012 i’
0.0030
∼
cultationlightcurvesusingan8.2-mtelescope. 0.0010
0.0025
fromInaMgelothboadlsvi2ewan,din3w, whiechtrwieed ctoanobatvaoiindtrinantrsoidtupcairnagmeextetrras F/Fp*0.0020 F/Fp*00..00000068
0.0015
variation from the correlation between parameter pairs (e.g. i 0.0004
0.0010
and a/R⋆). The differences between Methods 2 and 3 depend 0.0002
0.0005
mainlyonwhethertheapparentplanetaryradiusiswavelength-
dependent. We also calculated the weighted average of R /R 0. 48 0. 49 0. 50 0. 51 0.4 8 0.4 9 0.5 0 0.5 1 0.5 2
p ⋆ Phase Phase
forMethod3inthesamewayaswedidinMethod1.
Fig.5. Correlationbetweenmid-occultationtime(convertedtophase
Resultsfromthesethreemethodsagreeverywellwitheach
fordisplaypurpose)andfluxratiofortheK-andi-bandsderivedfrom
′
otherwithintheirerrorbars. Sincephysicallytheprobedatmo- the MCMC analysis. Three contour levels indicate the 68.3% (1-σ),
sphericdepthcouldbedifferentindifferentbandsduetoeither 95.4%(2-σ)and99.7%(3-σ)confidencelevels,respectively.
clouds/hazes or atomic/molecular absorption, we decide to re-
port results from Method 3 as our final results. Note that the
rednoisefactorsarelargerinthecasesofglobaljointanalysis,
The flux ratios detected in the K- and i-bands are 0.197
which is expected since time-correlated noise is coupled with 0.042%and0.037+0.023%,respectively.Our′i-banddetectioni±s
light curves and individual analysis has more flexibility in the 0.021 ′
marginalwith1.8-−σsignificance. Our K-banddetectionagrees
modeling. The red noise factorsofMethod3 are shownin Ta-
within 1-σ with the value of 0.156 0.014% obtained with
ble1whilethoseofMethod1areshowninTable3. ±
VLT/HAWK-Iin the 2.09µm narrowband(Gillonetal. 2012),
andagreeswellwiththevalueof0.194 0.029%obtainedwith
±
CFHT/WIRCam in the K -band(Wangetal. 2013). The time-
3.3.Fittingofoccultationlightcurves S
correlatednoiselevelis lowforboth K- andi-bandsasshown
′
inFig.3. We achieveda scatterof1425ppmand604ppmper
Giventhemodestlight-curvequality,wefittedthesevenoccul-
2 minute intervals for the K- and i-bands, with corresponding
tation light curves by fixing the mid-occultation time T and ′
occ estimatedphotonnoiselimitsof2.1 10 4and1.9 10 4,respec-
common transit parameters at known values, and only setting × − × −
tively.
F /F asthefreeparameter. Valuesofa/R ,R /R andiwere
p ⋆ ⋆ p ⋆
obtainedfromtheglobaljointanalysisonourtransitlightcurves WealsotriedfreelyfittingTocc inadditionto Fp/F⋆ forthe
(Method 3). Tocc was calculated from Tocc = T0 + (N +φ)P, K- and i′-bands, so as to test the dependence of flux ratio on
where N = 67 and φ = 0.5002 0.0004. The mid-occultation mid-occultationtime. ThisresultedinFp/F⋆=0.203 0.036%
phaseφwastakenfromBlecicet±al.(2013),whichwasprecisely and F /F = 0.037 +0.023%, respectively. As shown±in Fig. 5,
p ⋆ 0.021
determinedbythejointanalysisofSpitzer3.6µmand4.5µmoc- while the i-band T − is not well constrained, the K-band T
′ occ occ
cultationlightcurves. We onlydetectedormarginallydetected occursonanoffsetphasearoundφ=0.4907+0.0036(i.e.anoffset
0.0027
theoccultationsignalsintheK-andi-bands. of -10.9 minutesto φ = 0.5002). Since bot−h Spitzer and high-
′
Articlenumber,page7of14
precisionground-basedoccultationobservationshaveruledout Weperformedanotherindividualanalysisontheseventran-
aneccentricorbitforWASP-43b(Gillonetal.2012;Blecicetal. sit light curves in order to investigate the central transit times
2013;Wangetal.2013),wespeculatetheoffsetofourT aris- underthecontrolofcommonsystemparameters. Weadoptedi,
occ
ing from contaminationof instrumentalsystematics. However, a/R andR /R determinedintheglobaljointanalysis(Method
⋆ p ⋆
we note that the occultation depths do not strongly depend on 3),andimportedthemasGaussianpriorsinthisanalysis. Only
phase. Themeasureddepthsremainnearlyconstantwithin1-σ T wasallowedtofreelyfloatthroughoutthismodeling. This
mid
whenT variesfromphase0.48to0.51. resultsinsevenmeasurementsonthesameepoch. Asshownin
occ
Fig.6,thesevencentraltimesarenotexactlythesame.Thestan-
darddeviationoftheirbest-fitvaluesis 1.3timesoftheirmean
3.4.Fittingofmid-transittimes uncertainties. Compared to the uncert∼ainty-weighted average,
the r -, i-, H-, K-bands deviate less than 1σ, the z-, J-bands
′ ′ ′
deviate less than 2σ, while the g-band deviates 2.2σ. We
′
Table4.Transittimingdatausedinthiswork repeated this analysis with different baseline mode∼ls to exam-
inewhetherthisdeviationwascausedbydetrending. However,
Epoch [TBtrJanD−T2DB45]0000 O[m–Cina] Referenceb epvleesntwmhoednelw(neofromrcaeldizaatlilotnhefalcigtohrtpcluursveasstloophea,vie.et.hces+amcet)siwme-
...c 5528.868227+0.000078 ... Gillonetal.(2012) 0 1
-2 5933.16500+0−.00.0000305078 -0.42+0.50 1 couldseeasimilartrend.Therefore,ifthisdeviationcomesfrom
000 555999333444...777999212291333−1220++−+−.0000000..000....0000000300000030000001100881177584620 ---000...410451+−−+−+0000000.......11411116780023 TTThhhiiissswwwooorrrkkk(((gri′′′))) iboamlaflspttehehleriesnfeeetcimccteolininrgtrgrheasctltcditoueimnvrv.ieaesAtesanhrfoaertpohsemet,irlwltphueoenscdsaaivenbrenierlosiatttgyicmeiosbartryteehdcma.ttuiCttchohbenyulseinisdncseterrtroihtndaaguinncttih2ineaσgst
0 5934.792407−+00..000000110170 0.24−+00..1156 Thiswork(z′) (exceptg),thisdeviationisnotsignificant.
0 5934.792551−+0.000247 0.45−+0.36 Thiswork(J) ′
0.000257 0.37 Wealsore-analyzedtheamateurtransitlightcurvesobtained
0 5934.792508−+00..000000334441 0.39−+00..4499 Thiswork(H) fromtheTRESCAProject3(Poddanýetal.2010),whichwillbe
0 5934.792228+−0.000229 -0.02+−0.33 Thiswork(K)
0.000230 0.33 usedintheinvestigationoftransittimingvariations(TTVs)ef-
6 5939.67471+00−..0000008820 2.34−+11..1185 2 fectinSect.4.1.Wediscarded15outof42availablelightcurves
7 5940.48713+−00..0000007601 0.82+−10..0818 3 todate (August2013),becauseofeither partialtransitsorvery
12 5944.55336+−00..0000129022 -0.82+−22..7961 4 poordataquality(witha scatter in best-fitresidualslargerthan
55 5979.53402+−00..0000009930 1.00−+11..3340 5 1%)orasymmetrictransitshapecausedbystrongvisibletime-
55 5979.53352+−0.00055 0.28+−0.79 6 correlated noise. Since most of these data lack the instrumen-
0.00058 0.84
61 5984.41454+−0.00106 0.53+−1.53 7 tal parameters while some of them even do not have measure-
0.00088 1.27
61 5984.41457+−0.00151 0.57+−2.17 8 ment uncertainties, the instrumental systematics that might af-
0.00147 2.12
61 5984.41489+−0.00057 1.03+−0.82 9 fect the transit shape can hardly be corrected. In order to de-
0.00059 0.85
61 5984.41443+−0.00115 0.37+−1.66 8 terminethecentraltransittimesmorerobustly,wereplacedour
0.00109 1.57
77 5997.43061+−0.00078 1.22+−1.12 10 fittingstatistic (i.e. χ2)withthewavelet-basedlikelihoodfunc-
0.00082 1.18
77 5997.43015+−0.00086 0.55+−1.24 5 tion proposed by Carter&Winn (2009), in which we assume
0.00090 1.30
77 5997.42948+−0.00105 -0.41+−1.51 6 the time-correlatednoise to vary with a power spectral density
0.00104 1.50
77 5997.42957+−0.00105 -0.28+−1.51 6 of1/f atfrequency f. Thejumpruleisthesame,exceptthatthe
0.00111 1.60
82 6001.49842+−0.00183 1.85−+2.64 11 likelihood increases with higher probability. We convertedthe
0.00247 3.56
82 6001.49691+−0.00062 -0.33+−0.89 12 timestampsofTRESCAlightcurvesintoBJDTDBandadoptedi,
88 6006.37954+−00..0000104700 2.24−+12..0012 8 a/R⋆andRp/R⋆asGaussianpriorsfromouranalysisdescribed
99 6015.32727+−00..0000018499 1.54+−12..2185 13 inSect.3.2. ThisresultedinuncertaintiesfortheTRESCAcen-
412294 66208335..7676146823++−−0000....00000000201159003841 -12..6515++−−3111....64544105 1154 ttrhaalnttrhaonsseitotrimigeinsatlhlyatliastreed∼in20t–h2e7T0R%ES(oCnAawveerbasgiete.80T%he)nlaerwgleyr
435 6288.65335+−00..0000123254 -0.34+−13..9243 16 determined central transit times for the TRESCA light curves
0.00211 3.04 areshowninTable4. Asacomparison,thetimingsofourseven
482 6326.88704+−0.00088 0.23−+1.27 17
0.00094 1.35 transit light curveswould have been enlarged 10% using this
484 6328.51416+−0.00080 0.47+−1.15 18 ∼
0.00075 1.08 wavelet-basedanalysis. However,inordertohaveadirectcom-
493 6335.83414+−00..0000211980 -1.38+−32..1744 17 parisonwithGillonetal.(2012),forourtransitlightcurves,we
533 6368.37418+−00..0000112324 0.15−+11..7963 19 choosethetimingsfromtheχ2-basedanalysisasthefinalvalues.
557 6387.89805+−0.00062 0.85+−1.89 17
0.00065 0.94
622 6440.77245+−0.00044 -1.22+−0.63 17
0.00042 0.60
− −
4. Resultsanddiscussion
Notes. (a) The O–C values are calculated from comparison to lin-
ear regression: T(N)=2455934.792239(40)+N 0.81347437(13). 4.1.Perioddetermination
(b) The numbers in the reference column indica×te the source au-
thors of the TRESCA project, which provides data at the website: Inadditiontoourseventimingmeasurementsononetransitand
http://var2.astro.cz/EN/index.php. TRESCAtimingslistedherearede- 27re-analyzedtimingsfromTRESCA,wealsocollectedthe23
rivedfromahomogeneous fitusingourowncodes.(c) Thisephemeris timingslistedinTable6ofGillonetal.(2012).Wefittedalinear
entryreferstothe23transitslistedintheTable6ofGillonetal.(2012). functiontothese57timingsbyminimizingχ2:
References.(1)Starr,P.;(2)Naves,R.;(3)Ayiomamitis,A.;(4)René,
R.; (5) Nicolas, E.; (6) Gonzalez, J.; (7) Horta, F.G.; (8) Lomoz, F.; T (E)=T (0)+EP (6)
c c
(9)Martineli,F.;(10)Garcia,F.;(11)Carreño,A.;(12)Schteinman,G.
M.;(13)Zibar,M.;(14)Hall,G.;(15)Chapman,A&Díaz,N.D.;(16) 3 TRESCA is an acronym from words TRansiting ExoplanetS and
Lopesino,J.;(17)Evans,P.;(18)HaroJ.L.;(19)Büchner,A.; CAndidates,seehttp://var2.astro.cz/EN/tresca
Articlenumber,page8of14
G.Chenetal.:TransitandoccultationobservationsofWASP-43b
300
200 0.85
ec] 100
C [s 0
O - -100 0.60MO •
-200 0.80 10Gyr
-300
-400 -200 0 200 400 600
Epoch 4Gyr
300 0.80MO •
ec] 120000 ρ-1/3 0.75 1Gyr
C [s 0
O - --210000
-300 0.70MO •
0.70
0 20 40 60 80 100 120 450 500 550 600
Ep och E poch
60 0.50MO •
c] 40
C [se 200 0.655000 4800 4600 4400 4200
O - -20 T*,eff [K]
-40
g′ r′ i′ z′ J H K Fig.7. StellarevolutionarytracksobtainedfromMowlavietal.(2012)
to derive the stellar mass and age for WASP-43. Solid lines labeled
Fig.6. TransittimingO–CresidualsforWASP-43b.Inthetoppanel,
with numbers show the basic tracks at solar abundance, while dotted
green circles show timings from Gillonetal. (2012) (with epoch less
linesshowtheinterpolatedtracks.Dashedlinesindicatetheisochrones.
than-200),bluesquaresshowtimingsfromTRESCA(withepochlarger
Contours overlaid on the distribution density map show the posterior
than-10,seeSect.3.4forthere-analysisprocess),whileredstarshows
distributionoflinksinourMCMCprocess,inwhichthosewithdifferent
ourweightedaveragetimingvalue(atepoch0),theerrorbarofwhich
metallicitiesarealsoincluded.
indicatesthestandarddeviationofoursevenfilters.Middlepanelshows
azoom-inviewofthetransittimingsobtainedafterepoch-10. Bottom
panel shows our seven-filter timings. Dashed line refersto the linear 0.00000022 days and δP = ( 2.2 1.1) 10 9 days orbit 2.
regression,whiledottedlinerepresentsaquadraticfit. This δP translates into a P˙ = 0−.09 ±0.04×s ye−ar 1, which is−7
−
±
times smaller than that of Blecicetal. (2013). This quadratic
in which E is the epoch, and the epoch number of our obser- fit has a BIC of 147.36, which is almost the same as that of
vation was set as 0. From the fitting we obtained a new tran- the linearfit ( BIC=147.69). Thereforewe canconcludethata
sitephemerisofT (0)=2455934.792239 0.000040(BJD ) quadraticmodeldoesnotimprovethefitofephemeris.
c TDB
and an improved orbital period of P± = 0.81347437 Asaconclusion,weprefernoevidenceforsignificantTTV
0.00000013days. Thisnewperiodis4timesmoreprecisetha±n withincurrentdataset. The currentTTV rmsof 52.6s roughly
thatofGillonetal.(2012).WeshowtheO–CdiagramsinFig.6, correspondsto a timing deviationcaused by a perturberwith a
andlistallthenewlydeterminedtimingdatainTable4. massof2.17 M inthe2:1resonanceaccordingtotherelation-
Thisfithasaχ2 =139.68with55degreesoffreedom(DOF), shipderivedby⊕Agoletal.(2005).
resulting in a reduced chi-square χ2 = 2.59. This indicates a
ν
poorfitbylinearfunction. However,thestandarddeviationfor
4.2.Physicalparameters
thebest-fitresidualsis52.6s, whilethemedianuncertaintyfor
individualtimingsis30.2s. Fromthisview,thesignificanceof InordertodeterminethephysicalparametersfortheWASP-43
TTV is low. We examinedall the timings, and found that four system,wemadeuseoftheoutputPDFsfromourMCMCanaly-
epochs ( 375, 347, 288 and 256) deviating more than 3σ sisonthetransitlightcurves,stellarevolutionarytracks,aswell
levellead−to thi−s large−χ2, all of−which come from Gillonetal. astheRV semi-amplitude. We firstderiveda setofparameters
ν
(2012). Discardingthese fourepochswouldresultin a smaller thatsimplydependedonthelightcurve,suchastransitduration,
valueχ2=1.62.Wealsonotethat,intheexperimentofSect.3.4, ingress/egressduration and mean stellar density, using the for-
ν
thewavelet-basedanalysisproducesonaverage10%largerun- mulae from Seager&Mallén-Ornelas(2003). By adoptingthe
certainties than our time-averaging and prayer-bead methods. RV semi-amplitudevalue (in the form of K = K√1 e2P1/3)
2
ConsideringthatGillonetal.(2012)performedasimilaranaly- −
from Gillonetal. (2012), we were able to derive the planetary
sistoourswhichisbasedonthetiming-averagingmethodonly,
surfacegravity(Southworthetal.2007).
it is likely that this poor fit arises from underestimated timing
We then determined the stellar mass and age by interpo-
uncertainties.
lating in the stellar evolutionary tracks using the MCMC pro-
Blecicetal. (2013) tried to fit all the available timings and
cess. Sincephotometricmeasurementsareindependentofspec-
to estimate the decay rate using an quadratic ephemeris model
toscopicmeasurementsthatprovideusstellareffectivetempera-
(Adamsetal.2010):
tureT and metallicity [Fe/H],it is a goodcomplementto the
eff
determinationofstellarmass. Tohaveadirectcomparisonwith
T (E)=T (0)+EP+δP E(E 1)/2 (7)
c c ∗ − Gillonetal. (2012), we adopted the Geneva stellar evolution-
arytracks(Mowlavietal.2012),andinterpolatedthemintofiner
They obtained a result strongly favoring this model over the
linear one. Since their results were based on the original grids. Themassinterpolationwasperformedinthe[ρ−1/3,Teff]
TRESCA timings with underestimated uncertainties, we de- planebyMCMC,inwhich,Teff and[Fe/H]wereobtai∗nedfrom
cided to repeat the same quadratic fit, which had a result Gillonetal. (2012), and were randomly generated from Gaus-
of Tc(0) = 2455934.792262 0.000041, P = 0.81347399 sian distributions, while ρ−1/3 was taken from the a/R⋆ chains
± ± ∗
Articlenumber,page9of14
Table5.SystemparametersoftheWASP-43system
Parameter Symbol Value Note
TransitParameters
Orbitalperiod[days]........................ P 0.81347437 0.00000013 A
±
Mid-transittime[BJD ].................. T 2455934.792239 0.000040 A
Planet/starradiusratioT.D.B.................... R0/R 0.15743 0.0004±1 B
p ⋆ ±
Orbitalinclination[deg]..................... i 82.64 0.19 B
±
Scaledsemi-majoraxis..................... a/R 4.967 0.050 B
⋆ ±
Transitduration[days]...................... T 0.05115 0.00022 D
Ingress/egressduration[days]............... T14=T 0.01103±0.00025 D
Transitimpactfactor........................ b1=2 ac3o4si/R 0.636+0.0±10 D
⋆ 0.011
OccultationParameters −
Mid-occultationtime[BJD ].............. T 2455989.6943+0.0029 C
TDB occ 0.0022
Planet-to-starfluxratioinK-band[%]........ F /F 0.197 0.042 − C
Planet-to-starfluxratioini-band[%]........ Fp/F⋆ 0.037+±0.023 C
′ p ⋆ 0.021
OtherOrbitalParameters −
Orbitaleccentricity......................... e 0.(fixed) G
Argumentofperiastron[ ].................. ω 0.(fixed) G
◦
Orbitalsemi-majoraxis[AU]................ a 0.01524 0.00025 F
±
Rochelimit[AU]........................... a 0.00749 0.00012 F
R ±
StellarParameters
Mass[M ]................................. M 0.713+0.018 E
Radius[R⊙ ]................................ R⋆ 0.660−+00..002018 F
Density[ρ⊙]............................... ρ⋆ 2.482+−00..007079 D
Surfacegra⊙vity[cgs]........................ lo⋆gg 4.652−0.007.3006 F
Effectivetemperature[K]................... T ⋆ 4536+±98 E
eff 85
Metallicity[dex]........................... [Fe/H] 0.01+−0.10 E
0.09
Age[Gyr]................................. t 4.4+3−.7 E
age 2.4
PlanetaryParameters −
Mass[M ]............................... M 2.029+0.035 F
Jup p 0.040
Radius[R ]............................... R 1.034− 0.014 F
Density[gJucpm 3]........................... ρp 2.434+±0.067 F
− p 0.065
Surfacegravity[cgs]........................ logg 3.692− 0.009 D
Equilibriumtemperature(A =0, f=1/4)[K] .. T p 1439+±31 D
B eq 28
Equilibriumtemperature(A =0, f=1/2)[K] .. T 1712−+37 D
B eq 33
Equilibriumtemperature(A =0, f=2/3)[K] .. T 1839−+40 D
B eq 36
BrightnesstemperatureinK-band[K]........ T 1878−+108 D
B,K 116
Brightnesstemperatureini-band[K]........ T 2225−+139 D
Incidentflux[109ergs 1cm′ 2].............. FB,i′ 0.973−+202.5088 D
SafronovNumber....−.....−................. hΘi 0.0873−0+.007.0316 D
0.015
−
Notes. A: Determined fromlinear regression of timingdata listedinTable4; B: Determinedfrom our global joint analysis of theseven-band
transitlightcurves(fordetail,seeTable3);C:DeterminedfromouranalysisoftheK-ori-bandoccultationlightcurves; D:Derivedfromthe
′
PDFofgroupBorCusingtheoreticalformulae;E:DerivedfromtheevolutionarytracksanalysisusingPDFfromgroupB;F:Derivedfromthe
PDFofgroupBandEusingtheoreticalformulae;G:Botharefixedas0inouranalysisoftransitlightcurves.
derivedin our previousglobaljointanalysis. At each step, the relationshipsareparameterizedbyage, coremassandeffective
link [ρ−1/3, Teff] was put onto the tracks according to [Fe/H]. orbital distance. Assuming that WASP-43b is a hypothetical
Interpo∗lation was bilinearly performedamong mass tracks and planetmovingaround the Sun which receives the same flux as
isochrones. Linksthatwereofftracksorolderthan12Gyrwere the actual planet, the effective orbital distance is calculated as
discarded. AfterthisMCMCprocess,wederivedastellarmass a = a(L⋆/L )−1/2 = 0.0376AU. Accordingto the theoretical
of 0.713+0.018 M and a poorlyconstrainedage of 4.4+3.7Gyr pr⊕ediction, on⊙ly models with an old age could explain current
0.021 2.4
for WASP−-43. T⊙he posterior distributions of T (4536−+98K) data. After interpolating in the theoretical models with a solar
eff 85 compositionat 4.5 Gyr, we obtained theoreticalplanetaryradii
and[Fe/H](0.01+0.10)remainsimilartoinput,thebest-fitv−alues
0.09 of1.13R , 1.07R , and1.01R in thecasesofcorefree,
of which only sh−ift slightly since our a/R is slightly different Jup Jup Jup
⋆ a 50 M core, and a 100 M core, respectively. Therefore,the
fromGillonetal.(2012). Fig.7showstheposteriordistribution
current⊕massandradiusfor⊕WASP-43bindicatea massive core
ofthisMCMCprocess.Withthisrefinedstellarmassvalue,new
insidethisplanet,andfavoranoldagethatisconsistentwiththe
stellarradius,orbitalsemi-majoraxis,andplanetaryradiuswere
derivedagefromstellarevolutionarytracks.
derived. Finally,theplanetarymasswasderivedbysolvingthe
Equation25ofWinn(2010).
Weobtainedamassof2.029+0.035M andaradiusof1.034
0.014R forWASP-43b,whi−c0h.04c0orreJsuppondtoabulkdensity 4.3.Atmosphericproperties
Jup
±
of 2.434 +0.067 g cm 3. This puts WASP-43b in the top list of
0.065 −
densehot−Jupiters. Fortneyetal.(2007)calculatedgroupsofgi- Oneofourprimarygoalsobservingbothtransitandoccultation
ant planet thermal evolution models, in which the mass-radius eventsistoprobetheatmosphereofWASP-43binacomplemen-
Articlenumber,page10of14