The Atmosphere and Interior Structure of HAT-P-13b from Spitzer Secondary Eclipses

1.7 MB·

by  Ryan A. Hardy

PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
THEATMOSPHEREANDINTERIORSTRUCTUREOFHAT-P-13bFROMSPITZERSECONDARYECLIPSES
RYANA.HARDY1,2,JOSEPHHARRINGTON1,3,MATTHEWR.HARDIN1,NIKKUMADHUSUDHAN4,THOMASJ.LOREDO5,RYANC.
CHALLENER1,ANDREWS.D.FOSTER1,PATRICIOE.CUBILLOS1,6,ANDJASMINABLECIC1
1PlanetarySciencesGroup,DepartmentofPhysics,UniversityofCentralFlorida
Orlando,FL32816-2385
2DepartmentofAerospaceEngineeringSciences,UniversityofColoradoBoulder,Boulder,CO80309,USA
3Max-Planck-InstitutfürAstronomie
Königstuhl17,D-69117Heidelberg,Germany
7 4InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,CambridgeCB30HA,UK.
1 5DepartmentofAstronomy,CornellUniversity,IthacaNY14850,USAand
0 6SpaceResearchInstitute,AustrianAcademyofSciences,Schmiedlstrasse6,A-8042Graz,Austria.
2 ArXivPreprintJanuary5,20171:15
SubmittedtoApJ2015November523:30.
n
AcceptedforpublicationbyApJ2016December12.
a
J
ABSTRACT

3
WepresentSpitzersecondary-eclipseobservationsofthehotJupiterHAT-P-13binthe3.6µmand4.5µm

bands. HAT-P-13binhabitsatwo-planetsystemwithaconfigurationthatenablesconstraintsontheplanet’s
]
P second Love number, k2, from precise eccentricity measurements, which in turn constrains models of the
E planet’sinteriorstructure. Weexploitthedirectmeasurementsofecosω fromoursecondary-eclipsedataand
combinethemwithpreviouslypublishedradialvelocitydatatogeneratearefinedmodeloftheplanet’sorbit
.
h andthusanimprovedestimateonthepossibleintervalfork . Wereporteclipsephasesof0.49154 0.00080
2
p and0.49711 0.00083andcorrespondingecosωestimatesof- 0.0136 0.0013and- 0.0048 0.00±13.Under
- the assumpti±ons of previous work, our estimate of k of 0.81 0.10±is consistent with the±lower extremes
o 2
±
of possible core masses found by previous models, including models with no solid core. This anomalous
r
t resultchallengesbothinteriormodelsandthedynamicalassumptionsthatenablethem,includingtheessential
s
a assumptionofapsidalalignment. We also reporteclipse depthsof0.081% 0.008%in the 3.6µm channel
[ and 0.088% 0.028% in the 4.5 µm channel. These photometricresults±are non-uniquelyconsistentwith
solar-abundan±cecompositionwithoutanythermalinversion.
1
Subjectheadings:—eclipses—planetsandsatellites: atmospheres—planetsandsatellites: individual(HAT-
v
P-13b)—techniques:photometric
8
2
8
ablerangeofdampingcoefficients. Underthistheory,apre-
0
0 1. INTRODUCTION cise measurementofits eccentricitywoulddirectlyyieldthe
value of its second Love number, k , which describes how
. The G-type star HAT-P-13 hosts two planets, HAT-P-13 b 2b
1 theplanet’sgravitationalfieldchangesinresponsetoexternal
and HAT-P-13 c, the discovery of which were reported by
0 potentials(Ragozzine& Wolf 2009). Sucha solutionwould
Bakos et al. (2009). The smaller of the two, HAT-P-13 b,
7 provide constraints on the interior structure, particularly the
1 orbitsclosetoitshoststarwitha periodof2.91days. Ithas centralconcentrationoftheplanet’smass. Theseconstraints
v: (aWneinstnimetataeld.2m0a1s0s)oafn0d.8a5nMesJtiamndataendienqfluaitleibdrriuadmiutsemofp1e.r2a8tuRreJ willinformmodelsoftheplanet’sinteriorandformation.This
i parameter has been measured for bodies in the solar system
X of1626±42KassumingzeroBondalbedoanduniformheat usingradioscienceobservationsandforEarthusingsatellite
redistribution.Itsorbitwasfoundtohaveanon-negligibleec-
r laserranging(Rutkowska& Jagoda2010). Investigationsof
a centricityof0.013(Bakosetal.2009,Winnetal.2010). The thetidaldynamicsofeclipsingbinariesgobackasfarasthe
massiveouterplanet,HAT-P-13c,occupiesahighlyeccentric
late 19thcentury(Kreineretal. 2001). One wayto measure
orbit(e=0.66)withaperiodofabout446days.Theincreased
k for exoplanets and eclipsing binaries is to detect changes
separationofplanetcfromitshostmakesobservingatransit 2
in the occultationtiming. Forexample, Campo etal. (2011)
improbableandobservationwindowslongandinfrequent.To
unsuccessfullyattemptedtoobtaink forWASP-12bthrough
date,atransitofplanetchasnotbeenobserved. 2b
measurementoftheplanet’sapsidalprecessionrateusingsec-
TheHAT-P-13systemisuniqueinthatitstwo-planetcon-
ondaryeclipsesandradialvelocitydata.
figurationallowsforameasurementoftheinteriorstructureof
HAT-P-13b underequilibriumtide theoryassuminga fixed-
2. OBSERVATIONS
point eccentricity, i.e., assuming that all libration has been
Spitzer observed two secondary eclipses on 9 May 2010
dampedoutandtherateatwhichtheouterplanetpumpsthe
and 8 June 2010 (programID 60003). The first observation
inner planet’s eccentricity is balanced by the rate at which
wasperformedintheInfraredArrayCamera(IRAC)3.6µm
tidaldeformationdissipatesthisenergy.Thisrequiresthecir-
bandpass (Channel 1) and the second in the IRAC 4.5 µm
cularizationtimescaletobeconsiderablyshorterthanthees-
bandpass (Channel 2). Both observations were conducted
timated age of the system of 5 Gyr. Mardling(2010) calcu-
in sub-array mode and consisted of 68,608 frames, lasting
latesthatthistimescaleislikelylessthan1Gyrforareason-
8:09:06. TheChannel1observationstartedat23:55:32UTC
emailaddress:[email protected] andendedat8:04:37UTC.Thechannel2observationbegan
2 Hardyetal. 2016
at 4:03:15UTC and ended at 12:12:21. In an initial version differby∆BIC=BIC - BIC isapproximately
2 1
oftheChannel1data,analyzedwiththeinitialSpitzerreduc-
p
tionpipeline(versionS18.18.0),we founda discontinuityin 2 e∆BIC/2. (1)
thebackgroundlevelduetoseparatedarkcurrentcorrections p1 ∼
beingappliedmidwaythroughtheobservation.Thiswassub- After finding the best aperture size, we varied the BLISS
sequentlycorrectedintheSpitzerarchive. bin size until the BIC values for bilinearly interpolated in-
trapixel maps and nearest-neighbor-interpolated intra-pixel
3. DATAANALYSIS
mapswerecomparable(Stevensonetal.2012a).
3.1. Photometry Gaussianpriorswereplacedontheeclipseduration(0.1345
The data were analyzed using the Photometry of Orbits, 0.0017d)andingressandegresstime(0.018 0.0018d)
± ±
EclipsesandTransits(POET)pipeline(Stevensonetal.2010, forbothchannelsbasedonthecorrespondingtransitvaluesby
Campo et al. 2011, Nymeyer et al. 2011, Stevenson et al. Bakosetal.(2009).Thisimplicitlyassumesthatthegeometry
2012a,b, Cubillos et al. 2013, 2014). We used basic cali- ofthetransitisidenticaltothatoftheeclipse,anassumption
brateddata(BCD)framesprocessedthroughSpitzerpipeline that requires a negligible eccentricity. For comparison, we
S18.18.0forthe4.5µmbandandS19.1.0forthe3.6µmdata. calculated the eclipse duration and ingress and egress times
Photometry apertures were tested with radii in quarter-pixel from the known system parameters. These agree with their
incrementsfrom1.5to4.0pixelsforthe4.5µmdataand1.75 counterparttransitparameterstowithintheuncertaintyofthe
pixelsto4.0pixelsforthe3.6µmdata. Theskyannulusfor transitduration.Otherpriorswereflatwithintheirbounds.
allapertureshadinnerandouterradiiof7and15pixels,re-
3.3. Results
spectively.
3.3.1. Channel1-3.6µm
3.2. LightcurveModeling For the 3.6 µm channel, we tested nine apertures ranging
POET simultaneously models the combined effects of the between 2.0 and 4.0 pixels in increments of 0.25 pixels. In
eclipse, temporal sensitivity variations (the “ramp”), and eachaperture,wetestedfourtemporalsensitivitymodels:flat,
intra-pixel position sensitivity. POET models these effects linear,quadratic,andrisingexponential.Acrossallfourmod-
separately and combines them in a simultaneous fit, where elsandnineapertures,theapertureradiusyieldingthe mini-
the measured flux is simply the productof these three mod- mumSDNRwas2.25pixels. ThisisshowninFigure1. Af-
els. TheeclipsemodelfollowsthatofMandel&Agol(2002). terdeterminingtheSDNR-optimalaperture,weperformeda
Wechosefourrampmodelsforcomparison: noramp,linear, comparisonof the BIC valuesfor each model. As shown in
quadratic,andrisingexponential.Noothermodelswerecon- Table1, thelinearramphadthelowestBICvalueandthere-
sidered. POETmapsandremovesintra-pixelgainvariations fore best described the data (the BIC value is relative to the
usingthebilinearly-interpolatedsubpixelsensitivity(BLISS) lowest one). The quadratic ramp is the next most plausible
mappingtechniquedescribedbyStevensonetal.(2012a).We modelwithaprobabilityratioof 180:1,accordingtoEqua-
∼
removedthefirst20%ofthedata(13,721points)becausethey tion1. Figure2showsadependencyoftheeclipsedepthon
weretakenwhenthetelescopepointinghadnotyetsettledand aperturesizethatwouldchangeoureclipsedepthbylessthan
whentheramphasitsgreatestimpact.Thisisthe“preclip”re- 1σ. Figure6showstheRMSoftheresidualsvs. binsizefor
ferredtoinTable3. Thepointingsettlingresultedinapoorly thesedata.
calibratedportionoftheBLISSmap,whichprovidedlittlein-
formationonintra-pixelgainduringtheeclipseandthuscould
Table1
notbeusedtoconstraintheeclipsemodel.
Channel1ModelComparisonatAperture2.25withPreclip
We modeledlightcurvesforeachaperturesize. Atthebe-
ginningofeachfit,weminimizedχ2tofindthebestfittingset RampModel SDNR ∆BIC EclipseDepth[%]
ofparameters.Theuncertaintiesforthedataarethenrescaled Linear 0.0083845 0.0 0.0823
suchthatthereducedχ2=1. Thesamescalingfactorisused Quadratic 0.0083846 10.4 0.0779
for all models in a given aperture to allow model compari- RisingExponential 0.0083844 11.1 0.0835
NoRamp 0.0083909 69.3 0.0787
son(seebelow);thedifferencesinscalingfactorsfordifferent
modelsaregenerallysmall. Thefitisthenre-run.Thisproce-
dureaccountsforuncertaintyover/underestimatesinSpitzer’s
3.3.2. Channel2-4.5µm
pipelineduetoassumptionsthatdonotapplytoallanalyses.
Thisapproachalsoaccountsforaglobalaverageofcorrelated Inthischannel,wetested11aperturesrangingbetween1.5
noise,inthesensethattheuncertaintieswillbelargerthanthe and 4.0 pixels in incrementsof 0.25 pixels. As with the 3.6
point-to-pointscatterifrednoiseisimportant. Uncertainties µmchannel,ineachaperture,wetestedfourtemporalsensi-
associated with the best-fit parameters are then found using tivity models: flat, linear, quadratic, and rising exponential.
the differential-evolutionMetropolis-HastingsMarkov-chain Across all four modelsand 11 apertures, the aperture radius
MonteCarlo (MCMC) algorithm(ter Braak2006). We then yielding the minimum SDNR was 2.00 pixels, as shown in
comparedtheresultsacrossapertures,usingthestandardde- Figure3.AsshowninTable2,BICdeterminedthatthemodel
viationofnormalizedresiduals(SDNR)ofeachlightcurveto withnotemporalvariationbestdescribesthedata. Thelinear
find which aperture gives the best fit. We compared mod- rampisalsoplausible.Ourchoiceofaperturedoesnotimpact
els using the Bayesian Information Criterion (BIC, Liddle the eclipse beyondthe 1σ level(Figure4), exceptatthe im-
2007), which penalizes complex models and overfitting, re- plausiblysmallapertureradiusof1.5pixels,whichproduces
wardingsimplermodelswithgoodfitsandfewerparameters. ananomalouslyhighdepth.
AsmallerBICvaluesindicateshigherprobabilityofamodel. TheRMSasafunctionofbinsizeforthischannelisshown
The probability ratio of any two models whose BIC values inFigure6. Iftheredlineiswithintheblackregion,thereis
SecondaryEclipsesofHAT-P-13b 3
0.0105
Gaussian centering, No ramp certaintybythisratio,2.453,resultinginaneclipsedepthof
Gaussian centering, Linear ramp 0.0880% 0.0280%.
Gaussian centering, Quadratic ramp ±
0.0100
Gaussian centering, Rising exp. ramp
Table2
0.0095 Channel2ModelComparisonatAperture2.00withPreclip
R
DN RampModel SDNR ∆BIC EclipseDepth[%]
S
0.0090 NoRamp 0.0115917 0.0 0.0877
Linear 0.0115912 5.8 0.0867
Quadratic 0.0115903 15.8 0.1038
0.0085 RisingExponential 0.0115909 17.4 0.0947
0.0080
2.0 2.5 3.0 3.5 4.0 0.0145
Aperture size (pixels) Gaussian centering, No ramp
Gaussian centering, Linear ramp
0.0140 Gaussian centering, Quadratic ramp
Figure1. ComparisonofSDNRacrossallapertureradiiandmodelsexam- Gaussian centering, Rising exp. ramp
inedinthe3.6µmband,showingaminimumat2.25pixels.
0.0135
0.14 Linear ramp DNR0.0130
S
0.12
0.0125
%)0.10
h ( 0.0120
pt
e
Eclipse d0.08 0.0115 1.5 2.0 Ap2e.r5ture size (p3ix.e0ls) 3.5 4.0
0.06
Figure3. ComparisonofSDNRacrossallapertureradiiandmodelsexam-
0.04 inedinthe4.5µmband,showingaminimumat2.00pixels.
2.0 2.5 3.0 3.5 4.0
Aperture (pixels)
0.20
No ramp
Figure2. The3.6µmeclipsedepthforeachaperture.Thedepthcorrespond-
ingtotheapertureradiuswiththelowestSDNR(2.25pixels)ishighlighted
inred.
%)0.15
nosignificantdetectionofrednoiseatthatscale.Theblueand h (
green lines indicate the eclipse duration and ingress/egress ept
d
tsitmroen,grleyspcoecrrteivlaetleyd. fNoorttehitshtaytpteheofbclaaclckurlaantigoens. are inherently Eclipse 0.10
Cubillosetal.(2016)hasexaminedthisandotherred-noise
tests,andfindsthattheassumptionsofthisstandardtestbreak
downatpreciselythemostinterestingscale: Theeclipsedu- 0.05
rationisroughlyhalfthelengthofthedata,butthetestisonly
validforbinsizesmuchsmallerthanthelengthofthedata. 1.5 2.0 2.5 3.0 3.5 4.0
Aperture (pixels)
A standard red-noise adjustment based on this (question-
able)testistoscaletheeclipse-depthuncertaintiesbythera-
tioofthemeasuredtotheoreticalRMS(blacktored,inFigure Figure4. The4.5µm eclipse depthforeach aperture. Thedepthcorre-
spondingtotheapertureradiuswiththelowestSDNR(2.00pixels)ishigh-
6). However, our uncertainties already account for a global
lightedinred.Wenotethattheextremelysmallapertureradiusof1.5pixels
average of red noise, being calculated as the RMS residuals producesananomalouslyhighdepth.
from the best-fit model over the entire fit. The standard ad-
justmentistouseuncertaintiescalculatedfromashortrunof
datachosenfromaregionthatlookslikeithaslittlerednoise, 3.3.3. JointFit
orbytakingtheRMSof1/√2timesthedifferencebetween The final results we report here come from a simultane-
adjacent flux values, which assumes that the model changes ousfittobotheclipsesandaresummarizedinTable3. Both
littlebetweenadjacentpointsandthatsmall-scalerednoiseis eclipsessharedeclipsedurationandlimbcrossingtimetoim-
small. provetheaccuracyoftheseparameters.Theeclipsemidpoints
At 4.5 µm we take our photometric uncertainties to be were kept independentto enable future study of their varia-
1/√2 of the point-to-point variation RMS, 539.7 µJy. We tionintime. TheGelman-Rubinconvergencetestissatisfied
then fit the model to the data with these uncertainties, com- to within 1%. In pairwise parameter plots, all distributions
pare the measured residual RMS to the theoretical RMS at appear Gaussian with low correlation coefficients. Individ-
the eclipse scale (Figure 6), and scale the eclipse-depth un- ualparameterhistogramsallappearsymmetricandGaussian.
4 Hardyetal. 2016
Parametertraceplotsindicatethoroughexplorationofthefull 5. ORBITANDINTERIORSTRUCTURE
range of each parameter. The final photometry and best-fit
5.1. Orbit
modelsareshowninFigure5.
Thephasesoftheobservedsecondaryeclipsesprovidead-
ditionalconstraintsontheorbitofHAT-P-13b. The3.6µm
4. ATMOSPHERE
event occurs at a phase of 0.49154 0.00080 and the 4.5
HAT-P-13bisexpectedtohaveanequilibriumtemperature µmeventoccursataphaseof0.4971±1 0.00083. We note
of1626 42Kbasedonitsproximitytoitshoststar andan thatthephasesarewidelyseparated,wit±hthe4.5µmeclipse
±
assumedBondalbedoofzeroandefficientenergyredistribu- occurring 23 4 minutes later than the 3.6 µm eclipse.
tion. Itsscale heightforasolar-abundancehydrogen-helium One possibility±is that the difference is a result of differen-
compositionis expectedto be 500 km. The predictedadia- tial brightness across the planet’s surface in each of these
baticlapserateis 1.5Kkm-1. bands. However, the timing difference is comparable to the
Our secondary eclipse observations enabled modeling of best-fitingressand egresstime of the eclipses(26 2 min-
±
the dayside atmosphere of HAT-P-13 b. The 3.6 µm band utes),whichcarriestheimplausibleimplicationofthebright-
is particularly sensitive to the spectral signature of methane ness centersin the two bandsbeing on opposite sides of the
(CH )whilethe4.5µmbandcapturesspectralfeaturesasso- planet. Secularapsidalprecessionisalsotoosmalltoexplain
4
ciated with CO and CO . Whether these chemical species thisdifferenceoveraone-monthtimescale.
2
show up as emission or absorption signatures depends on Asapreliminaryestimate,wecanassesstheimpactofour
whether temperature increases or decreases with altitude at eclipse-phasemeasurementsonthesolutionthroughcompar-
the depths we are probing. This allows us to model the ison with orbital parameters from prior work. After a first-
pressure-temperature,T(p),profileofHAT-P-13b,albeitwith orderlight-timecorrectionof42.5s, theseeclipsephasesre-
somedegeneracy. spectively indicate ecosω values of -0.0135 0.0013 and
±
TomodelthedaysidespectrumandatmosphereofHAT-P- -0.0048 0.0013. These are in rough agreement with the
13b,weusethemethoddescribedbyMadhusudhan&Seager radial-ve±locity value of ecosω = - 0.0099 0.0036 (Winn
±
(2010,2009),withtheadditionofMarkov-chainMonteCarlo et al. 2010). To predict the effect of our ecosω observa-
and Bayesian analysisas describedin the supplementaryin- tion on the orbital solution before joint modeling, we took
formation of Stevenson et al. (2010). This model performs theirweightedmeansindividuallywiththeWinnetal.(2010)
one-dimensional, line-by-line, radiative-transfercalculations data, yielding -0.0132 0.0012 and -0.0054 0.0012, re-
± ±
foraplane-parallelatmosphere,assumingglobalenergybal- spectively. Substituting these averages and combining them
ance,hydrostaticequilibrium,andlocalthermodynamicequi- with the original Winn et al. (2010) esinω value of 0.0060
librium.Thespectrumofthestarisinterpolatedfromagridof 0.0069, we find values of e = 0.0145 0.0031 and ω =
Kuruczmodels(Castelli&Kurucz2004).Havingfewerspec- ±(155 12)o for the 3.6 µm event and e±= 0.0081 0.0052
tral samples of this planet’s atmosphere (2) than free model andω±=(132 37)oforthe4.5µmevent.Because±ofthe5σ
±
parameters(10),itisimpossibletodetermineauniquemodel separationbetweenthesetwoevents,weelectnottotaketheir
of the planet’s atmosphere. However, certain chemical con- weightedaverage. Thecalculationsinsteadtuneourexpecta-
figurations can be ruled out by modeling deviations from a tionsformoresophisticatedjointmodeling.
solar-abundancespectrum. PastSpitzerobservationsofother InourdetailedMCMC model, we separatelyincorporated
planets have indicated methane deficiency (Stevenson et al. bothsecondary-eclipsemidpointtimesintoajointfitinclud-
2010) and an unexpectedly high C–O ratio (Madhusudhan ingradial-velocity(RV) data(see below),transitphotometry
etal.2011,Stevensonetal.2014,Lineetal.2014). (Southworthetal. 2012), andamateur(Poddanýetal. 2010)
FrommodelingtheatmosphereofHAT-P-13b,wefindthat and professionaltransit midpoints. We use HIRES RV data
it has efficient day-nightenergyredistribution. Our data are tabulatedbyKnutsonetal.(2014),whichincludeallprevious
consistent with a blackbody and with a wide range of com- measurementsbyWinnetal.(2010)andBakosetal.(2009).
positions,includingsolar. Giventhelargeuncertaintyonthe OneoutlierradialvelocitymeasurementintheKnutsonetal.
4.5 µm eclipse depth, our data can be explained by a wide (2014)datasetatBJD2455945wasdiscarded. Noneofthese
rangeof temperatureprofiles. For the altitudes probed(Fig- dataweretakenduringatransit,sotheRossiter-McLaughlin
ure7,rightinset),anisothermalatmosphereat1700Kwould effectwasnotmodeled.Alltimestampsonthedatawerecon-
yield a blackbodyspectrum consistent with the data (yellow vertedtoaconsistentBJD(TDB)timestandardasprescribed
dashed line in Figure 7). Alternately, the data are also con- byEastmanetal.(2010). Themid-transittimesandtheirori-
sistent with a fiducial solar-abundance composition with no gins are all listed in Table 5. Only ETD transit data with a
thermalinversion(blacklineinFigure7anditsleftinset).Fi- qualityratingof1–3wereused. Thelimb-darkeningparame-
nally,sincethebrightnesstemperatureinthe4.5µmchannel, terswerefixedtointerpolatedtabulatedvaluesfoundbyWinn
withinthe1σuncertainties,canbeslightlyhigherthanthatin etal.(2010).
the3.6µmchannel,wecannotrobustlyruleoutathermalin- The model we use for the orbit fit is briefly described in
version. However,astrongthermalinversionisstillunlikely. Stevenson et al. (2012b). The model uses 13 free parame-
Futureobservationsinthenear-infrared,e.g.,withtheHubble ters, and follows the formalism of Gillon et al. (2009). The
SpaceTelescope Wide Field Camera 3 (1.1-1.7µm) or from code, Photometry, Event Timing, and Radial-velocityAnaly-
thegroundinthe J, H,andK bands, couldprovidemorero- sis, PETRA, minimizes χ2 for the aforementioned data us-
bust constraintson the atmospherictemperature profile T(p) ingthetransitphotometrymodelsofMandel&Agol(2002),
andcompositionofthisplanet.Theuncertaintyat4.5µmwas radial velocity models described by Paddock (1913), and
increased to accountfor red noise, as presented in Figure 6. a linear ephemeris for transit and eclipse timing data with
AsdiscussedinSection3.3.2,thistesthasquestionablevalid- provisions for apsidal motion as described by Campo et al.
ity. Theoriginalunscaleduncertaintyof0.011%ruledouta (2011). The parameters for planet b are the reduced transit
blackbodyandathermalinversion. impactparameter(b′ =b1+esinω); the scaled semi-amplitude
1- e2
SecondaryEclipsesofHAT-P-13b 5
1.03
1.05 1.001
1.02
1.000
1.01
1.00
0.999
1.00
malized Flux0.95 malized Flux0.99 malized Flux0.998
Nor Nor Nor0.997
0.98
0.996
0.90 0.97
0.96 0.995
3.6 µm 3.6 µm 3.6 µm
4.5 µm 4.5 µm 4.5 µm
0.85 0.95 0.994
0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.42 0.44 0.46 0.48 0.50 0.52 0.54
Orbital Phase (2.916-day period) Orbital Phase (2.916-day period) Orbital Phase (2.916-day period)
Figure5. Secondary-eclipsephotometryforHAT-P-13bintheIRAC3.6µmand4.5µmbands. Correspondingbest-fitmodelsarerepresentedinorangeand
blue,respectively. Left: Rawphotometrywithbest-fitmodelshowingposition-andtime-dependentsensitivitycorrelatedwithinstrumentoscillation. Center:
Binnedphotometrywiththebest-fitmodel(coloredlines)andthebest-fitmodelwithoutaneclipse(blacklines). Right: Binnedphotometrywithtime-and
position-dependentsystematicsdividedout,leavingonlythesecondaryeclipseandbest-fiteclipsemodels.Errorbarsrepresent1σuncertainties.
10-3 10-3
S S
RM 10-4 RM 10-4
3.6 µm 4.5 µm
10-5 10-5
100 101 102 103 104 100 101 102 103 104
Bin Size (sec) Bin Size (sec)
Figure6. RMSnoisevs.binsizeforthe3.6and4.5µmchannelsinthejoint
fit. Thegreenandbluelinesindicatetheeclipsedurationandingress/egress
time,respectively.
Toassesstherednoiseatdifferentscales,wecalculatetheRMSoftheresid-
ualsfromthebest-fitmodelafteraveragingneighboringresidualsinbinsof
Figure7. Well-fittingmodelspectrumforHAT-P-13bwiththeSpitzerband-
increasingsizes.Theverticalblackbarsindicatethe3σrangeoftheRMSes-
passes(main)andthecorrespondingpressure-temperatureprofile(leftinset)
timateateachbinsize.Theredlineisthetheoreticalscalingoftheunbinned
andnormalizedcontributionfunctions(rightinset). Thedashedyellowline
RMSresidual.At3.6µmthereisnoindicationofsignificantrednoiseatthe
is the corresponding blackbody spectrum fora1700 K bodyand the blue
eclipse-durationscale.SeeSection3.3.2fordiscussionofthevalidityofthis
curvesshowothertheblackbodyspectraforthehighestandlowesttemper-
testandhowitappliestoourdata.
atures(1843Kand1100K,respectively)inthepressure-temperatureprofile
depictedintheinset. Notethelogarithmicscaleoftheabscissa,witheach
(K2 = K√1- e2P1/3); the planet-star radiusratio; the tran- tickdenotinga1µminterval.
sitduration;thetransitmidpointtimeT ;theperiodP ;and
0b b
theLaplacevectorcomponentse cosω ande sinω . Planet certainties.Pairwisemarginalizationoftheparametersshows
b b b b
c’s parametersare its scaled semi-amplitude; Laplace vector low correlations, except between three of the transit param-
components; predicted transit midpoint, and orbital period. eters and the period and transit midpoint time. Priors were
The fit also models the velocity and secular acceleration of uniformand bounded. Inspection of trace plots shows good
thestarHAT-P-13.Themodelusesthestellardensitycalibra- exploration within the bounds of each parameter. Posterior
tionofEnochetal.(2010)totakethesemodelingparameters histogramsoftheindividualparametersareroughlyGaussian
anddeterminethephysicalparametersofthesystem. Wees- anddescendtozerowithintheboundaries. Wherenecessary,
timate photometric and radial velocity jitter (0.25% of total we estimate 1σ confidenceintervalsby findinga 68%inter-
stellar flux and 4.2 m s- 1, respectively) from an initial best valcentered on the mode of each posterior distribution. For
fit to all available data and add these jitter estimates to the Rayleigh-distributedparameterslikeeccentricity,themedian
instrumentalerrorbars,accordingly. valuetends to be largerthan the mode, leading to asymmet-
We ran a Metropolis-Hastings Markov chain for one mil- ricuncertaintyestimates. Table4summarizesourfitresults.
lioniterationstoexploretheparameterspaceandestimateun- Figure 8 shows the best-fitting radial velocity model and its
6 Hardyetal. 2016
Table3
JointBest-FitLightCurveParameters
Parameter 3.6µm 4.5µm
Arrayposition(x¯,pix) 14.25 14.10
Arrayposition(y¯,pix) 14.88 14.92
Positionconsistencya(δx,pix) 0.008 0.012
Positionconsistencya(δy,pix) 0.008 0.010
Aperturesize(pix) 2.25 2.00
Skyannulusinnerradius(pix) 7.0 7.0
Skyannulusouterradius(pix) 15.0 15.0
Eclipsedepth(%) 0.0801(81) 0.088(28)
BrightnessTemperature(K) 1732(75) 1573(93)
Midpoint(orbits) 0.49154(80) 0.49711(83)
Eclipsemidpoint(BJDUTC-2,450,000) 5326.7020(23) 5355.8807(24)
Eclipsemidpoint(BJDTDB-2,450,000) 5326.7027(23) 5355.8815(24)
Eclipseduration(hr) 3.215(28) 3.215(28)
Ingress/Egresstime(hr) 0.439(28) 0.439(28)
Systemflux:Fs(µJy) 74635.7(3.5) 46330.3(2.8)
Ramp:R(t) Linear None
Ramplinearterm 0.0183(21) ···
BLISSmap(M(x,y)) Yes Yes
Minimumnumberofpointsperbin 4 4
Totalframes 68608 68608
Framesused 53250 54386
Rejectedframes(%) 1.48 0.09
Preclipframes(%) 20 20
Freeparameters 6 3
AICvalue 107644.9 107644.9
BICvalue 107731.1 107731.1
SDNR 0.0083616 0.0115475
Uncertaintyscalingfactor 0.951 0.531
aRMSframe-to-framepositiondifference.
residuals. Figure 9 shows the O-C (residualtiming) plotfor massoftheplanet,thelessofitsoutermassrespondstotides
transit and eclipse data. We find that the best-fitting eccen- andthelowerthevalueofk . Planetswithmoreuniformden-
2
tricityofplanetb’sorbitis0.0093+0.0044,andω =(202+12)◦. sity distributions are more responsive to tides and thus have
- 0.0016 - 46
Because the eccentricity is the Euclidean norm of two nor- a higher value of k2. Planets with some mechanicalrigidity
mally distributed components,its distributionhas a long tail tendtohavelowervalues. Thevalueofk2 rangesfrom0for
andamedianvalueof0.011,higherthanthemode. Thedif- highlycondensedplanets)to1.5foruniform-densityspheres
ifnecreonncseisitnenωtwbiethtwaepesnidpallaanliegtsnmbeanntd. c is ∆ω =(27+- 1446)o, not r(eRlaagtiovzezlyinpere&ciWseloylfth2r0o0u9g)h.sFaoterllEitaertlhas,ekr2rahnagsinbgeetnobmee0a.s3u0r1ed1
To further test whether the apsides are aligned, we com- (Rutkowska & Jagoda 2010). Larger and less rigid planets
putetheratioofthelikelihoodofalignedapsidestounaligned likeJupiterandSaturnhavevaluesof0.49and0.32,respec-
apsides, otherwise known as the Savage-Dickey density ra- tively(Ragozzine&Wolf2009).
tio, (Verdinelli& Wasserman 1995). We use the normalized Batyginetal.(2009)provideafourth-orderpolynomialre-
histograms of the distribution of the difference between the latingthemeasuredorbitaleccentricityofplanetbtok2b.This
twoω values,∆ω =ω - ω ,obtainedfromtheMCMCrun isfurtherconfirmedbyKrammetal.(2012)usingtheobser-
b c
to estimate a probability density function. We compare this vations of Winn et al. (2010) to limit k2b to 0.265 – 0.379.
probabilitydensity where ∆ω =0 andto the prior probabil- The Kramm et al. (2012) models have two layers: one con-
ity density given that the two apsides are randomlyoriented taining an envelope of hydrogen, helium and metals; and a
accordingto a uniformdistribution (1/2π). This test shows rocky core. Values of k2b above the upper limit found by
thatthealignedmodelis0.50timesaslikelyastheunaligned Kramm et al. (2012) correspond to interior models with no
model,sotheplanetsareaboutaslikelytohavetheirapsides rocky core. Our observations do not rule out apsidal align-
aligned as not. The uncertainty associated with e sinω — ment. Underthesameassumptions,75%ofourMCMCpos-
b b
nearlyanorderofmagnitudelargerthanthatofecsinωc—is teriordistributionofeb fallsbelowthecriticaleccentricityof
akeysourceofthisambiguity,andcanbereducedwithcon- 0.0145,belowwhichmodeledcoremassvanishes. The95%
tinuedradialvelocitymeasurements. upperlimit for the eccentricity is 0.021. This distribution is
illustratedinFigure10.
5.2. Interior This constraint on k is calculated from the best-fit ec-
2b
Confirmationofapsidalalignmentandmeasurementsofthe centricity from the MCMC run, the distribution of which is
eccentricity of the inner planet enable study of the planet’s skewedbytherelativelylargeuncertaintyinebsinωb. Italso
interior. Batygin et al. (2009) outline a method for recov- dependsontheassumptionofapsidalalignment. Onlyabout
beryinKgrapmlamnetetb’asl.L(o2v0e12n)umanbderB,ekc2kbe.rT&hiBsaistyfguirnth(e2r01ex3p).loFreodr ω2%c ionftthheeMvaalurkeosvofchωabinf,alwlhinictho tshpeanfsul1l.r5a◦n.geTohfevdailsuterisbouf-
planetsdescribableasfluids,themorecentrallycondensedthe tion of the aligned subset of eccentricity values is narrower
SecondaryEclipsesofHAT-P-13b 7
An alternative interpretation can stem from forcing the
assumption that ω = ω , where ω is comparatively well
b c c
20 known.Fromoureclipse-derivedmeasurementofe cosω =
b b
1)− 10 - 0.00946 0.00088,wefindthateb =0.0095 0.0009and
als (m s−100 rtheseumltasjuogrgi±teystosfakv2bervyallouwescaorreelmaragsesr.than 0.379±. Again, this
du−20
Resi−30 6. CONCLUSIONS
−40 OurobservationsofHAT-P-13b’ssecondaryeclipsetiming
54500 55000 55500 56000 56500 57000
BJD -2400000 haveallowedustorefineitseccentricityandinformmodelsof
150 itsinteriorstructurebetterthanwithradialvelocityandtran-
) 100 sitobservationsalone. Thepressure-temperatureprofilefrom
1−
m s 50 ouratmosphericmodelfitsprovidesaconstraintontheenve-
b ( 0 lope density of HAT-P-13 b, which can also inform interior
net −50 structure models and further be used to constrain k . Our
a 2b
Pl−100 lowered best-fit eccentricity suggests a higher range of k
2b
−150 valuesand low probabilityof HAT-P-13b havinga substan-
0.0 0.2 0.4 0.6 0.8 1.0
tialcoremass.
200 This conclusion rests on the assumption that all libration
) 0 betweenplanetsb andc hasdampedoutandthe apsidesare
1−
m s−200 aligned. While our data are not inconsistent with apsidal
et c (−400 alignment, the uncertainties of the measurements of ∆ω do
n allowseparationoftensofdegrees. Bayesiancomparisonof
a
Pl−600 thealignedandnon-alignedhypothesesisinconclusive.
−800 If we force apsidal alignment, the measured eccentric-
0.0 0.2 0.4 0.6 0.8 1.0
Orbital phase (orbits) ity and its uncertainty become consistent with the value of
e cosω measured with eclipse phases. This eccentricity
b b
value( 0.009)is consistentwith the best-fit valueandcon-
Figure8. Residualsofincludedradialvelocitydata(top,bluepoints)against ∼
thebest-fittingorbitmodel.Themiddleandbottomplotsshowthebest-fitting sistentwithveryhighvaluesofk2b.
radial-velocity predictions (black lines) foreach planet shown withfolded Iftheconditionsforthemeasurementofk areindeedsat-
2b
RVdata. Theshaded grayregion around the residual zero line shows the isfied and the measurement of the eccentricity can be taken
1σmodelpredictionuncertainty(nottheper-pointuncertainty). Thesingle
atfacevalue,thentheimplausibilityofalowcoremassmay
excluded point (orange) does notdramatically alter the best-fit parameters
whenincluded,butincreasestheestimatedjitterby∼20%. requireadjustmentoftheinteriormodels.
The less tantalizing possibility is that the central assump-
tionisinvalid:HAT-P-13bandcmaysimplynotbeapsidally
20
alignedandtheirmutuallibrationhasnotdampedout. Inthis
10 case,thissystemmaybeaninappropriatecandidateforprob-
ing exoplanet interiors in this manner. Our measurement of
0
O-C (Minutes)−−2100 esthptseacmeecaocyefnneotbrtiacrnietdpier∆sesωaenndntetahcreegsfiusmaxreeydnttposoioinnffteporefkrli2iabbp.rsaIiftsitohfnoisrinibstohttheheppchlaaasnsee-,
Transit Model then our measurement of these parameters represents a sin-
Eclipse Model
−30 Transits gle snapshot of the evolution of these parameters about the
Eclipses
−5450000 55500 56000 56500 57000 57500 fixedpoint. Asthelibrationalperiodofthissystemis 105
Midpoint Time − 2400000 BJD years(Mardling2007),itisunlikelythatthisevolution∼canbe
Figure9. Timingresidual(observedminuscalculated,O-C)plotsfortransit observedwithina humanlifetimewithpresentmeasurement
andeclipsemidpointtimingdata. Thisfigureshowstheresidualsoftiming
precision. Whilethefixed-pointeccentricitymaybecloseto
datarelative topredictions foracircular orbit. Thebest-fitting modelsfor
transit and eclipse data are shown bysolid and dashed lines, respectively. ourmeasuredvalue(e.g.,within 0.01),thesensitivityofk2b
∼
Theshadedgrayregionsaroundeachmodelshowthe1σmodelprediction to errors in e is too high for us to produce any meaningful
b
uncertainty. estimatesofk forthenon-alignedcase.
2b
One of the major caveats of our timing measurements
andmoresymmetric,withameanof0.0088 0.0009. Un- is the significant difference in secondary eclipse times be-
±
der the relation of Batygin et al. (2009), this correspondsto tween channels. The two eclipse midpoints differ by 23
±
k = 0.81 0.10. Since Kramm et al. (2012) find that val- 4minutes,whichisapproximatelythesameasHAT-P-13b’s
2b
±
uesabove0.379correspondtovanishingcoremass,thisresult limb crossing time. If this difference is due to wavelength-
mayindicatethatHAT-P-13bhasasmallornonexistentrocky dependentasymmetricbrightnessdistributions,itrequireshot
core.Thisunexpectedlyhighestimateisbelowthetheoretical spotstobeextremelyfarfromthesub-stellarpointandinop-
maximumvalueofk ,1.5,whichcorrespondstoauniform- positedirectionsforthetwochannels. Onepossibleexplana-
2b
densitysphere. Becausetheinteriorstructureofplanetsmust tionforthedifferenceiscorrelatednoise. Ourprocedurefor
obey both hydrostatic equilibrium and the equation of state estimatinguncertaintiesalreadyconsidersaglobalaverageof
ofitscomponentmatter,atrueuniform-densitysphereofthis correlated noise. Secular apsidal precession is too small to
sizeishighlyimplausible.Forann=1polytropewithavan- explainthisdifferenceoverthemonthseparatingtheseobser-
ishing core, the maximum value of k is 0.52 (Storch & vations. Eclipse-timingvariationsonthescaleofthetransit-
2b
∼
Lai2015). Ourestimateiswithin3σofthislimit. timingvariationsmaybepossible,butthedifferencebetween
8 Hardyetal. 2016
0.030
160
0.025 Batygin et al. (2009) constraint 140
120
Mcore>0 Mcore<0 (forbidden) ty
0.020 si
100n
e
d

y
eb t
80 bili
a
0.015 b
o
60 Pr
40
0.010
Best-fit e
b
20
0.005 0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
k
2b
Figure10. Ourbest-fiteccentricity,witha1σconfidenceinterval(solidanddashedorangelines,respectively),anditsMCMC-generatedposteriorprobability
densitydistribution(blackshading). Thebluelineisthemodelrelatingk2btotheeccentricityofBatyginetal.(2009)andtheupperlimitofk2bcorresponding
tomodelsofHAT-P-13bwithzerocoremassderivedbyKrammetal.(2012,verticaldashedline,k2b<0.379).
theeclipsetimesisnoticeablylargerthanthescatteroftransit Batygin,K.,Bodenheimer,P.,&Laughlin,G.2009,ApJ,704,L49
times shown in Figure 9. Follow-up eclipse observationsof Becker,J.C.&Batygin,K.2013,ApJ,778,100
HAT-P-13bwouldresolvethistimingdiscrepancy. Campo,C.J.,Harrington,J.,Hardy,R.A.,Stevenson,K.B.,Nymeyer,S.,
Ragozzine,D.,Lust,N.B.,Anderson,D.R.,Collier-Cameron,A.,Blecic,
The depths of our eclipses have shown HAT-P-13 b’s at-
J.,Britt,C.B.T.,Bowman,W.C.,Wheatley,P.J.,Loredo,T.J.,Deming,
mospheretobeconsistentwithsolar-abundancecomposition,
D.,Hebb,L.,Hellier,C.,Maxted,P.F.L.,Pollaco,D.,&West,R.G.
efficient day-night redistribution, and no thermal inversion 2011,ApJ,727,125
layer. However,wehaveobservedeclipsesinonlytwowave- Castelli,F.&Kurucz,R.L.2004,ArXive-prints,astro-ph/0405087
lengths, so further observations in other infrared passbands Cubillos,P.,Harrington,J.,Loredo,T.J.,Lust,N.B.,Blecic,J.,&Stemm,
M.2016,SubmittedtoApJ
mayindicatemoreinterestingchemistry.
Cubillos,P.,Harrington,J.,Madhusudhan,N.,Foster,A.S.D.,Lust,N.B.,
Wethanktheamateurobserverswhocontributeddatatothe Hardy,R.A.,&Bowman,M.O.2014,ApJ,797,42
ExoplanetTransitDatabase(Table5). Wethankcontributors Cubillos,P.,Harrington,J.,Madhusudhan,N.,Stevenson,K.B.,Hardy,
toSciPy,Matplotlib,andthePythonProgrammingLanguage, R.A.,Blecic,J.,Anderson,D.R.,Hardin,M.,&Campo,C.J.2013,ApJ,
thefreeandopen-sourcecommunity,theNASAAstrophysics 768,42
Eastman,J.,Siverd,R.,&Gaudi,B.S.2010,PASP,122,935
DataSystem,andtheJPLSolarSystemDynamicsgroupfor
Enoch,B.,CollierCameron,A.,Parley,N.R.,&Hebb,L.2010,A&A,516,
software and services. This work is based on observations A33
madewiththeSpitzerSpaceTelescope,whichisoperatedby Fulton,B.J.,Shporer,A.,Winn,J.N.,Holman,M.J.,Pál,A.,&Gazak,
theJetPropulsionLaboratory,CaliforniaInstituteofTechnol- J.Z.2011,AJ,142,84
ogyundera contractwith NASA. Supportforthisworkwas Gillon,M.,Demory,B.-O.,Triaud,A.H.M.J.,Barman,T.,Hebb,L.,
Montalbán,J.,Maxted,P.F.L.,Queloz,D.,Deleuil,M.,&Magain,P.
providedbyNASA throughan awardissued byJPL/Caltech
2009,A&A,506,359
andthroughtheNASAScienceMissionDirectorate’sAstro- Knutson,H.A.,Fulton,B.J.,Montet,B.T.,Kao,M.,Ngo,H.,Howard,
physics Data Analysis Program, grant NNX13AF38G, and A.W.,Crepp,J.R.,Hinkley,S.,Bakos,G.Ã.,Batygin,K.,Johnson,J.A.,
PlanetaryAtmospheresProgram,grantNNX12AI69G. Morton,T.D.,&Muirhead,P.S.2014,ApJ,785,126
Kramm,U.,Nettelmann,N.,Fortney,J.J.,Neuhäuser,R.,&Redmer,R.
2012,A&A,538,A146
REFERENCES Kreiner,J.M.,Kim,C.-H.,&Nha,I.-S.2001,AnAtlasofO-CDiagramsof
EclipsingBinaryStars
Bakos,G.Á.,Howard,A.W.,Noyes,R.W.,Hartman,J.,Torres,G., Liddle,A.R.2007,MNRAS,377,L74
Kovács,G.,Fischer,D.A.,Latham,D.W.,Johnson,J.A.,Marcy,G.W., Line,M.R.,Knutson,H.,Wolf,A.S.,&Yung,Y.L.2014,ApJ,783,70
Sasselov,D.D.,Stefanik,R.P.,Sipo˝cz,B.,Kovács,G.,Esquerdo,G.A.,
Pál,A.,Lázár,J.,Papp,I.,&Sári,P.2009,ApJ,707,446
SecondaryEclipsesofHAT-P-13b 9
Table4
JointOrbitalFitMCMCParameters
MCMCParameters
Planet-to-starradiusratio 0.0860±0.001
Scaledimpactparameter 0.729±0.030
Transitduration(d) 0.13942±0.0024
Transitmidpoint(BJDTDB) 2454779.93106±0.00030
Planetborbitalperiod(d) 2.91624039±0.00000081
Linearlimb-darkeningterm 0.306800
Quadraticlimb-darkeningterm 0.325100
ebsinωb -0.0035±0.0080
ebcosωb -0.0087±0.0009
Scaledplanetbsemi-amplitude(ms-1d1/3) 151.7±1.0
SystemRVoffset(ms-1) -67.0±0.8
RVaccelerationterm(ms-1a-1) 19.3±0.4
Planetctransitmidpoint(BJDTDB) 2455757.69±0.19
Planetcorbitalperiod(d) 445.81±0.10
Planetcscaledsemi-amplitude(ms-1d1/3) 2466.4±6.4
ecsinωc 0.0528±0.0023
eccosωc -0.6536±0.0020
χ2 3972.9
DegreesofFreedom 3810
χ2 1.04
rd
NumberofDataPointsinFit 3825
BIC 4096.6
DerivedParameters
eb 0.0093+- 00..00004146
ωb(◦) 202+- 1426
Planetbsemi-amplitude(ms-1) 106.2+- 01..32
Transitimpactparameter 0.732+- 00..003240
Planetbsemi-majoraxis(AU) 0.04313+- 00..0000003236
Inclination(degrees) 82.2+- 00..68
Stellarmass(solarmasses) 1.261+- 00..002293
Stellarradius(solarradii) 1.73+- 00..1009
Stellardensity(solardensity) 0.243+- 00..0024
ab/R∗ 5.36+- 00..2310
Madhusudhan,N.,Harrington,J.,Stevenson,K.B.,Nymeyer,S.,Campo, Stevenson,K.B.,Bean,J.L.,Madhusudhan,N.,&Harrington,J.2014,
C.J.,Wheatley,P.J.,Deming,D.,Blecic,J.,Hardy,R.A.,Lust,N.B., ApJ,791,36
Anderson,D.R.,Collier-Cameron,A.,Britt,C.B.T.,Bowman,W.C., Stevenson,K.B.,Harrington,J.,Fortney,J.,Loredo,T.J.,Hardy,R.A.,
Hebb,L.,Hellier,C.,Maxted,P.F.L.,Pollacco,D.,&West,R.G.2011, Nymeyer,S.,Bowman,W.C.,Cubillos,P.,Bowman,M.O.,&Hardin,
Nature,469,64 M.2012a,ApJ,754,136
Madhusudhan,N.&Seager,S.2009,ApJ,707,24 Stevenson,K.B.,Harrington,J.,Lust,N.B.,Lewis,N.K.,Montagnier,G.,
—.2010,ApJ,725,261 Moses,J.I.,Visscher,C.,Blecic,J.,Hardy,R.A.,Cubillos,P.,&Campo,
Mandel,K.&Agol,E.2002,ApJ,580,L171 C.J.2012b,ApJ,755,9
Mardling,R.A.2007,MNRAS,382,1768 Stevenson,K.B.,Harrington,J.,Nymeyer,S.,Madhusudhan,N.,Seager,S.,
—.2010,MNRAS,407,1048 Bowman,W.C.,Hardy,R.A.,Deming,D.,Rauscher,E.,&Lust,N.B.
Nascimbeni,V.,Piotto,G.,Bedin,L.R.,Damasso,M.,Malavolta,L.,& 2010,Nature,464,1161
Borsato,L.2011,A&A,532,A24 Storch,N.I.&Lai,D.2015,MonthlyNoticesoftheRoyalAstronomical
Nymeyer,S.,Harrington,J.,Hardy,R.A.,Stevenson,K.B.,Campo,C.J., Society,450,3952
Madhusudhan,N.,Collier-Cameron,A.,Loredo,T.J.,Blecic,J., Szabo,G.M.,Kiss,L.L.,Benko,J.M.,Mezo,G.,Nuspl,J.,Regaly,Z.,
Bowman,W.C.,Britt,C.B.T.,Cubillos,P.,Hellier,C.,Gillon,M., Sarneczky,K.,Simon,A.E.,Leto,G.,ZanmarSanchez,R.,Ngeow,
Maxted,P.F.L.,Hebb,L.,Wheatley,P.J.,Pollacco,D.,&Anderson, C.-C.,Kovari,Z.,&Szabo,R.2010,VizieROnlineDataCatalog,352,
D.R.2011,ApJ,742,35 39084
Paddock,G.F.1913,PASP,25,208 terBraak,C.2006,StatisticsandComputing,16,239,
Pál,A.,Sárneczky,K.,Szabó,G.M.,Szing,A.,Kiss,L.L.,Mezo˝,G.,& 10.1007/s11222-006-8769-1
Regály,Z.2011,MNRAS,413,L43 Verdinelli,I.&Wasserman,L.1995,J.Amer.Statist.Assoc.,90,614
Poddaný,S.,Brát,L.,&Pejcha,O.2010,NewA,15,297 Winn,J.N.,Johnson,J.A.,Howard,A.W.,Marcy,G.W.,Bakos,G.Á.,
Ragozzine,D.&Wolf,A.S.2009,ApJ,698,1778 Hartman,J.,Torres,G.,Albrecht,S.,&Narita,N.2010,ApJ,718,575
Rutkowska,M.&Jagoda,M.2010,ActaGeophysica,58,705
Southworth,J.,Bruni,I.,Mancini,L.,&Gregorio,J.2012,MNRAS,420,
2580
10 Hardyetal. 2016
Table5
TransitTimingData.
Mid-TransitTime Uncertainty Source
(BJDTDB)
2457063.35092 0.00125 Brettona
2457045.84957 0.00122 Bennia
2456713.39949 0.00172 Dittlera
2456663.82395 0.00147 Garlitza
2456634.65866 0.00125 Navesa
2456622.99501 0.00076 Shadicka
2456593.8322 0.00099 Bennia
2456331.36740 0.00199 Gaitana
2456039.74601 0.002 Shadicka
2456013.50595 0.0013 Carrea
2455978.50697 0.00145 Poddanýa
2455978.50418 0.00097 Garciaa
2455969.75398 0.00119 Shadicka
2455943.51402 0.00173 Gonzaleza
2455934.76136 0.00187 Emeringa
2455657.71276 0.00217 Shadicka
2455628.55433 0.00125 Sergisona
2455602.31426 0.00139 Poddanýa
2455584.81496 0.00153 Dvoraka
2455511.90502 0.00134 Shadicka
2455476.91775 0.00105 Shadicka
2455613.97390 0.00225 Fultonetal.(2011)
2455616.89290 0.00152 Fultonetal.(2011)
2455619.80786 0.00134 Fultonetal.(2011)
2455622.72351 0.00166 Fultonetal.(2011)
2455564.39916 0.0018 Nascimbenietal.(2011)
2455593.56187 0.00115 Nascimbenietal.(2011)
2455596.47702 0.00305 Nascimbenietal.(2011)
2455599.39307 0.00076 Nascimbenietal.(2011)
2455602.31108 0.00167 Nascimbenietal.(2011)
2455558.56342 0.00098 Páletal.(2011)
2455561.48456 0.004 Páletal.(2011)
2455590.64563 0.00179 Páletal.(2011)
2455141.55297 0.001 Szaboetal.(2010)
2455249.45157 0.002 Szaboetal.(2010)
2455593.56147 0.00115 Southworthetal.(2012)
2455596.47327 0.00202 Southworthetal.(2012)
2455599.39446 0.001 Southworthetal.(2012)
2455669.38140 0.00126 Southworthetal.(2012)
aThe Transiting ExoplanetS and Candidates group (TRESCA,
http://var2.astro.cz/EN/tresca/index.php) supply their data to the Exo-
planet Transit Database (ETD), http://var2.astro.cz/ETD/) which per-
forms theuniform transit analysis described byPoddaný etal. (2010).
TheETDwebsiteprovidedthenumbersinthistable,whichwerecon-
vertedfromHJD(UTC)toBJD(TDB).