A cautionary tale: limitations of a brightness-based spectroscopic approach to chromatic exoplanet radii

0.12 MB·

by  H. M. Cegla

Astronomy&Astrophysicsmanuscriptno.Chrom_RM_sim_letter_ref_nobold (cid:13)cESO2017
January6,2017
A cautionary tale: limitations of a brightness-based spectroscopic
approach to chromatic exoplanet radii
H.M.Cegla1,2,3,C.Lovis2,V.Bourrier2,C.A.Watson1,andA.Wyttenbach2
1 AstrophysicsResearchCentre,SchoolofMathematics&Physics,Queen’sUniversityBelfast,UniversityRoad,BelfastBT71NN,
UnitedKingdom
2 ObservatoiredeGenève,UniversitédeGenève,51chemindesMaillettes,1290Versoix,Switzerland
3 SwissNationalScienceFoundationNCCR-PlanetSCHEOPSFellow
7 Received31102016/Accepted23122016
1
0
2 ABSTRACT

n Determiningwavelength-dependent exoplanetradiimeasurementsisanexcellentwaytoprobethecompositionofexoplanetatmo-
a spheres.Inlightofthis,Borsaetal.(2016)soughttodevelopatechniquetoobtainsuchmeasurementsbycomparingground-based
J transmissionspectratotheexpectedbrightnessvariationsduringanexoplanettransit.However,wedemonstratehereinthatthisisnot

5 possibleduetothetransitlightcurvenormalisationnecessarytoremovetheeffectsoftheEarth’satmosphereontheground-based
observations.Thisisbecausetherecoverableexoplanetradiusissetbytheplanet-to-starradiusratiowithinthetransitlightcurve;we

] demonstratethisbothanalyticallyandwithsimulatedplanettransits,aswellasthroughareanalysisoftheHD189733bdata.
P
E Keywords. Methods:dataanalysis–Planetsandsatellites:atmospheres–Planetsandsatellites:fundamentalparameters–Planets
andsatellites:HD189733b–Techniques:radialvelocities–Techniques:spectroscopic
.
h
p
-
o1. Introduction curve to allow one to study the local, occulted stellar profiles
r directly by subtracting the in- from out-of-transit observations
tTransmission spectroscopy is an essential tool for charac-
s (see,e.g.Ceglaetal.2016a).Sincethetransitlightcurveisde-
aterising the atmospheres of transiting exoplanets (see e.g. pendentontheplanet-to-starradiusratio,itsetstheplanetradius
[Charbonneauetal. 2002; Pontetal. 2013; Madhusudhanetal.
thatisrecoverablewhenexaminingthebrightnessratiobetween
2014; Singetal. 2016, and references therein). Snellen (2004)
1 thelocalandout-of-transitprofiles(meaningonecannotrecover
demonstratedthat narrowbandexoplanetfeatures(e.g. sodium)
v newradiusvariationsfollowingB16).
1could be probed by analysing the shape of the stellar absorp- In this study,we first breakdown the physicalimplications
5tion lines as a planet occults its host star, that is, by studying of the B16 technique, and then simulate the planet transit of
2the chromaticRossiter-McLaughlin(RM) effect;more recently HD189733b to illustrate the impact of the technique’s short-
1DiGloriaetal. (2015) have shown that this effect can also be
comingsonthemeasuredplanetradius;wealsoreapplytheB16
0used to probe broadband signatures (e.g. Rayleigh scattering).
techniqueto HARPSdata,with a morerigorouserrorpropaga-
.Recently, Borsaetal. (2016, hereafter B16) presented a new
1 tion. In Sect. 2, we demonstrate how the choice of the transit
0techniqueusing(aversionof)line-profiletomography,withthe lightcurvenormalisationsetstherecoverableplanetradius.We
7intent of studying chromatic changes in planetary radii. How- present the simulated planet transits, and our reanalysis of the
1ever,we demonstratein thisLetterthatthe techniquein B16 is
HARPSdatainSect.3,andshowhowanunderestimationofthe
:unfortunatelyflawed.
v errorscanleadtospuriousclaimsofplanetaryradiusvariations.
i In principle, the application of line-profile tomography is Finally,wesummariseourconclusionsinSect.4.
Xwellmotivatedforexoplanetatmospherecharacterisationifcor- 2. Limitationsofabrightness-basedapproachto
rrectlyimplemented.Thistechniqueisolatesthestarlightbehind
a chromaticexoplanetradii
the planet during transit (CollierCameronetal. 2010), and the
ratio of the integrated flux within the local profile (behind the In B16, the authors attempted to study passband-dependent
planet) to the out-of-transitprofile is equalto the brightnessof planet radius variations by averaging together the cross-
theoccultedstarlight.Inturn,theratioofthe occultedstarlight correlationfunctions(CCFs)forsubsetsofHARPSspectralor-
is dependent on the planet-to-star radius ratio. As such, if one ders. All of these CCFs, regardless of passband, were contin-
had space-based spectra then the planet radius could be recov- uumnormalisedandthenfurtherscaledusingaMandel&Agol
ered fromthe spectra alone, anddoingso in variouspassbands (2002)transitlightcurvebasedonthesystemparametersdeter-
wouldcharacterisetheplanetaryradiuswavelengthdependency. minedinthefullHARPSpassband,exceptforpassbanddepen-
For ground-basedspectra this is notpossible due to, for exam- dentlimbdarkeningcoefficients.
ple, transparency variations of the Earth’s atmosphere. To re- For each passband,theycreatedmaster out-of-transitCCFs
move these effects, ground-based spectra must first be contin- byaveragingtogetheralltheindividualout-of-transitCCFsina
uum normalised; they can then be multiplied by a transit light givennight,andthensubtractingtheout-fromthein-transitdata
toobtainCCFsforthestarlightoccultedbytheplanet.Theau-
Sendoffprintrequeststo:H.M.Cegla,e-mail:[email protected] thorsthenfittedGaussianfunctionstotherespectiveCCFs,pre-
Articlenumber,page1of5
A&Aproofs:manuscriptno.Chrom_RM_sim_letter_ref_nobold
sumablytoactasaproxyfortheintegratedfluxwithin,andar- (Borsa,PrivateComm.),suchthat
guedthattheratiobetweentheareas(determinedfromtheGaus-
CCFB16 =−CCFC16+β , (6)
sianfits)ofthelocaltotheout-of-transitCCFscouldserveasa loc loc lc
measure of the brightnessof the missing starlight, β, occulted
whereCCFC16 is thelocalCCF obtainedfollowingC16.Since
duringthein-transitobservations. loc
thecontinuumisa freeparameterintheGaussianfits,theratio
Theauthorsthencomparedthisempiricalβtotheexpected
oftheareasisstillequaltothatinEq.4.
brightness ratio based on an approximation to the solution for
Assuch,thetechniqueimplementedbyB16representsacir-
integratingthestarlightbehindtheplanetgiventheparticularge-
cularargument.Moreover,ifonehadthebroadbandphotometry
ometryofthesystem(andassumingaparticularfunctionforthe
necessaryforthecorrectspectralnormalisation,thentheplanet
limbdarkening).Sincethissolutionwasdependentontheplanet
radiicouldbedetermineddirectlyfromthelightcurvesalone.
radius, the authors argued that they were able to disentangle a
We stress that a solely brightness-based approach to trans-
planetradiusmeasurementforeachpassband.
missionspectroscopyusesonlytheequivalentwidth,andthere-
We demonstrate in Sect. 2.1 that the technique outlined by
foreprecludesanyretrievalofinformationonexoplanetradii.It
B16canonlyrecovertheplanetaryradiussetbythetransitlight
istheinclusionofthespectraldimensionthatisnecessarytode-
curveusedintheinitialnormalisation.However,weemphasise
termineR (i.e.utilisingtheDopplerinformation,asisdonein
p
that such a limitation is set due to a flux-based approach and
CollierCameronetal.2010;DiGloriaetal.2015).
would not be present in an RV-based approach,such as that in
3. Systematiceffectsonchromaticradius
DiGloriaetal.(2015)orthatintraditionallineprofiletomogra-
phy(i.e.followingtheCollierCameronetal.2010formulation). measurements
To try to understand how B16 obtained results mimicking
2.1.Transitlightcurvenormalisation
Rayleighscattering,wesimulatedthetransitofHD189733band
B16startedbydeterminingtheareaoftheirout-of-transitmaster applied their technique. To demonstrate that we could recover
CCFs, Aout, for each passband. Since the out-of-transit master ourmodelinputs,wealsopresentresultswhereinweappliedthe
CCFs (CCFout) were continuum normalised their area is equal normalisation from C16 with the correct planet radii for each
totheirequivalentwidth,EWout,thatis, passband;indoingsowediscoveredtheapproximationsforβin
B16underestimatedtheplanetradii,andthuswealsoexploreda
Aout = EWout. (1) numericalapproachforcalculatingthisbrightnessratiothatwas
moreaccuratethantheapproximationusedinB16.
TheauthorsalsomeasuredtheareasofthelocalCCFsbehindthe
planet,A .Sincethein-transitCCFs(CCF )arenormalisedby 3.1.Analyticalbrightnessratioapproximation
loc in
thetransitlightcurve,theareaofthelocalCCF(CCF )is
loc Unfortunately,integrating the limb darkened brightness under-
A =(1− f )EW =β EW , (2) neath a planet lying off stellar disc centre is not straightfor-
loc lc loc lc loc
ward and even approximate analytical expressions are quite
where f is the flux from the light curve, EW is the equiva- complex(especially if considering ingress and egress regions).
lc loc
lent width of the local CCF, and β is the fraction of starlight For this reason, B16 used the β formalism presented in
lc
occultedbytheplanetundertheassumptionsofthetransitlight CollierCameronetal.(2010),whichwasbasedontheanalytical
curveusedinthenormalisation. approximationsofOhtaetal.(2005)fortheRMeffect.Therein
Inanidealcase,wherethelocalstellarphotosphericprofiles thebrightnessratioforafullyin-transitplanet(i.e.noingressor
can be represented by constant Gaussian functions (assumed egressregionswereconsidered)wasdefined,underthestandard
bothaboveandinB16),thentheonlydifferencebetweenthelo- linearlimbdarkeninglaw,as:
calanddisc-integratedout-of-transitCCFsisthebroadeningby
stellarrotationpresentinthedisc-integratedobservations.Since R 21−u +u ∗µ
therotationalbroadeningpreservestheequivalentwidth,then β≈ p 1 1 , (7)
R ! 1−u /3
⋆ 1
EW =EW = EW , (3)
out loc in whereR isthestellarradius,R istheplanetradius,u isthelin-
⋆ p 1
earlimbdarkeningcoefficient,andµisthecentre-to-limbplanet
wheretheEW andtheEW arenotonlyequaltoeachother
out loc
butarealsoequaltothein-transitequivalentwidth,EW (since position.Wenotethatµ=cos(θ)= 1−x2 −y2,whereθisthe
in p p
itissimplyasummationoflocalprofilesofequalEW),andthe centre-to-limbangle, and x ,y is tqhe centre of the planet (see
p p
ratiooftheareasbecomes: CollierCameronetal.2010;Ceglaetal.2016a,fordetails).We
alsonotethatOhtaetal.(2005)statethattheaccuracyofthisap-
A
loc =β . (4) proximationdiminisheswithincreasingR /R ,arguingthatthe
A lc p ⋆
out additionalterms in the analytical solution contribute to ∼1% if
R /R is≤0.1anduptofewpercentifR /R ∼0.3.Giventhat
Hence, under the above assumptions one can only recover p ⋆ p ⋆
R /R isonlypredictedtovaryafewprecentinwavelengthfor
the planetradiusinjected into the modeltransitlight curve,re- p ⋆
particularatmosphericcharacteristics,suchasRayleighscatter-
gardlessofwhichpassbandisstudied.Thisisbecausethetran-
ing, this approximationmay inject systematic errors that could
sit light curve normalisation effectively sets the area of the lo-
be misinterpreted as having a physical origin (even if the light
cal profile. We note, that the transit light curve normalisation
curvenormalisationisdonecorrectly).
fortheabovefollowsCeglaetal.(2016a,hereafterC16),where
CCF =CCF − f ∗CCF ;whereas,thetransitlightcurve
loc out lc in 3.2.Numericalbrightnessratioapproximation
normalisationinB16was
ToinvestigatetheimpactoftheaccuracyofEq.7,wedecidedto
CCFB16 =CCF f −CCF +(1− f ) (5) calculateβnumerically.Forthisapproach,thein-transitstarlight
loc in lc out lc
Articlenumber,page2of5
Ceglaetal.:Limitationsofabrightness-basedapproachtochromaticexoplanetradii
Simulated Data HARPS Data
1 in 4 pts
Oversampled
Borsa
0.158 0.158
d
e
er
v
co 0.156 R*0.156
R/R Re*p R/p 0.160 Nightly (1 in 4 pts)
0.158
0.154 0.154 0.156
0.154
CB1166 TTeecchhnniiqquuee 00..115502 AJSuuelgp ‘0 ‘‘00776
Simulated R
p
0.152 0.152 400 500 600 700
400 450 500 550 600 650 400 500 600 700
Wavelength (nm) Wavelength (nm)
Fig. 1. Recovered average planet radius, R , from the simulated data Fig. 2. Recovered average planet radius, R , for each passband as a
p p
foreachpassbandasafunctionofwavelength(plottedusingthemid- functionofwavelengthfortheobservedHARPSdata.ResultsfromB16
dlewavelengthinthepassband).Filledcirclesrepresentwhenthesim- areshowningreen(wherethewavelengtherrorbarsrepresentthepass-
ulated R was constant, and hollow circles represent when the simu- band wavelength region), and those from our reanalysis are shown in
p
latedR varied;inbothcasestheseareshowninredwiththeerrorbars red when using the oversampled CCF and in black when using only
p
reported byB16 for comparison purposes only. Resultsfromthe B16 everyoneinfourpointsintheCCF.Subplot:thenightlyrecoveredR
p
procedureareshowninblack,whilethosefromthenumericalapproxi- whenusingonlyeveryoneinfourpointsintheCCF(nightindicatedby
mationhereinandtheC16formulationareinblue.Thelinesrepresent colour).ThehorizontaldashedlinesshowthemeanR recoveredbythe
p
linearfitstothesimulatedR shownforviewingease. B16methodonthesimulateddata(i.e.thesolidblackpointsinFig.1).
p
blocked by the planet is still defined as β = Floc/F⋆, with F⋆ 3.3.Simulatedstar-planetsystem
andF definedasthefluxesofthetotalstellardiscandthestel-
loc
lardiscundertheplanet,respectively.Notetheobservedbright- WeusedthesimulatedstellargridofCeglaetal.(2015,2016b)
ness of the un-occulted star can be analytically determined by and injected into each grid cell a Gaussian profile with a full-
integratingagivenlimbdarkeninglawovertheprojectedstellar width half-maximum(FWHM) of 5 km s−1 (note this width is
disc;foralinearlimbdarkeningthisis similartotheexpectedvalueforthestellarphotosphere).Inthe
simulatedstarwedidnotconsideranyastrophysicaleffects(i.e.
granulationor starspots etc.) other than rigid body stellar rota-
tion,whichwas set to the valueobtainedbyC16, 3.25kms−1.
F =R2 2π 1I(µ)µdµdφ=πR2 1− u1 , (8) Wealsoassumedanedge-on(i⋆ =90◦)alignedorbit.
⋆ ⋆Z Z ⋆ 3 ! The transit was sampled in 21 equal steps in phase from
0 0
−0.02−0.02,centredaboutmid-transit,withanadditionalsam-
whereφistheazimuthalangle.Aspreviouslystated,calculating ple at phase = 0.03 to serve as a completely out-of-transitref-
the flux behind the planet analytically is not trivial. Hence, we erence. We simulated a transit for each of the seven passbands
calculatedF numericallybyconstructingasquarestellargrid (from400−700nm)usedinB16,andappliedalinearlimbdark-
loc
with a width of 2R centred about the planet position (x ,y ), ening using the coefficients (for each passband) these authors
p p p
withnequalstepsintheverticalandhorizontaldirection.Con- provided.Foreachofthesevenpassbandtransitswe injecteda
tributionsfromstepsthatdidnotliebeneaththeplanetand/oron planetwithaconstantradiusequaltothevalueassumedbyB16
the stellar disc were excluded.Thus, we approximatedthe flux for the whole HARPS passband (Rp = 0.1581R⋆, hereafterre-
behindtheplanetas ferred to as the broadband Rp), but varied the limb darkening
accordingly.
2R 2 Forthissetoftransits,wetestedtheimpactofthetransitlight
F ≈ I p , (9) curvenormalisation.Inthefirstcase,wefollowedtheprocedure
loc xy
X n ! in B16, and in the second case we normalised the data follow-
ing C16 and used the numerical approximation in Sect. 3.2 to
whereIxyisthelimbdarkenedintensityatagivenpositioninthe estimateRp.Examiningthefirstcaseallowedustoexamineany
aforementionedgridand(2R /n)2isthecorrespondingarea. errorsintroducedusingtheβapproximationand/ortheB16nor-
p
OuraimwastotrytorecoverR asafunctionofwavelength, malisation.Ontheotherhand,thesecondcaseofferedatestcase
p
wherein the injected R was only used to construct the correct toensurewecouldrecoverthemodelinputs.
p
lightcurves(actingasifwehadsimultaneousmulti-colourpho- For a secondtest, we repeatedthe above,butvariedthe ra-
tometry).Hence,whentryingtorecoverR ,westartedwiththe diusofthesimulatedplanet;forthisweselectedR equaltothe
p p
broadbandplanetradiusandthen allowedit to varyby upto ± valuesreportedbyB16foreachpassband.Againwetestedtwo
0.005R instepsof0.0001R .Therecoveredplanetradiusthen cases: first followingthe B16 procedure(where the lightcurve
⋆ ⋆
corresponded to the planet radii that minimised the difference limb darkeningvaries in each passband, but the light curve ra-
betweenβandA /A . dius remains fixed at the broadbandR ), and the second using
loc out p
Articlenumber,page3of5
A&Aproofs:manuscriptno.Chrom_RM_sim_letter_ref_nobold
theC16normalisation(wenotetheassumedlightcurvehasthe Table1.Bestfitstoobserveddata
correctR here)andthenumericalapproximationinSect.3.2.
p Data Function BIC χ2 Function BIC χ2
r r
3.3.1. Obtainingtheplanetradiusandsystematicerrors 1in4pts Flat 13.9 2.0 Linear 11.7 1.6
Oversamp. Flat 65.4 10.6 Linear 29.1 5.0
WeexaminedtherecoveredR asafunctionofstellardiscposi-
p B16 Flat 13.1 1.9 Linear 5.2 0.3
tion,andfoundonlyaslightdependanceondiscpositionwhen
following B16. However, if one point each at the ingress and planetradii(inblack)areconsistentwithaflatline(within1−3σ
egressregionswereincludedthenthedependenceondiscposi- of the mean R recovered in the simulated data, i.e. the solid
p
tion was strong, and including such data would systematically blackpointsinFig.1),asexpectedfromSect.2.Webelievethe
decrease the recovered Rp (as the β formulationis not valid in reason B16 report a trend with wavelength, and we do not, is
theseregions). largelyduetodifferencesinourerroranalysisandGaussianfit-
Moreover,wefoundthat,regardlessoftheB16orC16nor- tingtechniques.
malisation, using the β approximation always underestimated
InB16,therecoveredR foreachstellardiscpositionandall
p
the limb darkeningbehind the planet and thereforealso under-
threetransitswereaveragedtogethertoprovideoneR foreach
p
estimated the true planet radius. This is because the analytical
passband, and the reported errors came from the rms of these
approximationassumesthelimbdarkeningbehindtheplanetis
individualplanetradii(i.e.thestandarddeviationdividedbythe
constant,andequaltothevaluebehindthecentreoftheplanet.In
squarerootofthetotalnumberinthepassband).Inouranalysis,
reality,thestellarphotospherebehindtheplanetexhibitsarange
wereporttheweightedmeanforeachpassband,withtheweights
oflimbdarkening.ThisiswhythenumericalmodelinSect.3.2
being the inverse square of the error for each individualplanet
isnecessarytorecovertheR injectedintothesimulateddata.
p radii(wheretheerrorwascalculatedbypropagatingtheerrorson
The Rp reportedin B16 comesfromaveragingtogetherthe theCCFareasasreportedfromtheGaussianfitsfollowingC16,
planet radii recovered across the stellar disc. If the limb dark- andassumingnegligibleerroronthelimbdarkeningandstellar
ening effects are sufficiently removed(and the stellar profile is discpositions).Theerrorontheweightedmeanthenwassimply
constant), then this providesa goodmeans to boost the signal- thesquarerootoftheinversesumoftheweightssquared.Ifthe
to-noise in the reported Rp. In Fig. 1, we present the average errors on individual Rp were all exactly equal to the standard
recoveredRp asafunctionofwavelengthfromthesimulations, deviation,thenthetwoapproacheswouldyieldthesameresult.
forbothtests(whenR wasconstantandwhenitvaried).Asex-
p In addition to this slight difference in error analysis, B16
pectedfromSect.2.1,theB16procedurealwaysresultsinnearly
also applied their Gaussian fits to the oversampled CCF grid
thesameR ,regardlessofwhetherthetrueR variedornot.
p p provided by the HARPS pipeline (Borsa, Private Comm.). We
For ournumericalapproachand the C16 normalisation,we cautionagainstsuchanapproach,astheoversamplingwilllead
demonstrate accurate recovery of Rp (regardless of whether or toasignificantunderestimationoftheerrors.Hence,wealsofit
notweincludeingressandegressdata),butonlyifthelightcurve Gaussianstodatacomposedofeveryoneinfourpointsfromthe
normalisationisdonewiththecorrectRpforeachpassband(us- originalCCFs (to compensate for the originalsampling rate of
ing the broadband Rp for all passbands meant only the broad- 0.25kms−1forameanpixelwidthof0.82kms−1);theseresults
bandRp wasrecovered).Hence,regardlessofthenormalisation areshowninblackinFig.2.
(i.e.B16orC16)orthebrightnessformulation(i.e.βorournu-
TotestthesignificanceofatrendinR withwavelength,we
merical approximation),we could only retrieve the parameters p
fitted the data with both a flat line and a linear regression, and
injectedintothesystemviathetransitlightcurvenormalisation, calculatedthereducedchi-squared,χ2, andtheBayesian Infor-
asexpectedfromSect.2. r
mation Criterion (BIC); the results are shown in Table 1. We
notethatevenifawavelength-dependentR isfound,itdoesnot
3.4.ReanalysisoftheHARPSdata p
confirm the B16 technique is valid, as we have already shown
OurapplicationoftheB16procedureonthesimulateddatacan- it is not mathematically possible to retrieve radius variations.
not explain the wavelength-dependent planet radii reported in Rather, it would serve as a red flag that we do not fully char-
B16. To further investigate this aspect, and to ensure we have acterise the interplayof the variouscomplexitiespresentin the
appliedtheB16methodcorrectly,wehavereanalysedthesame observations.Inparticular,stellaractivitycanaltertheobserved
threetransitsofHD189733bfollowingtheirtechnique,butus- stellar line shapes and their equivalent widths – which in turn
ing the Levenberg-Marquardt least-squares minimisation from couldleadtospuriousradiusvariationsfollowingSect.2.Since
MPFIT (Markwardt 2009, and references therein) rather than HD189733isaknownactivestarthisislikelyscenario;andin
IDL’s GAUSSFIT1. The results are plotted in Fig. 2, alongside agreementwithFig.5fromB16,whereinthesinglenightanal-
thosefromB162.Wedemonstratewecanreproduce(redpoints ysis with the most apparent slope, July 2007, is also the most
inFig.2)resultsin1-2σagreementwithB16(ingreen);hence, magneticallyactive(Ceglaetal.2016a).Moreover(andasnoted
we are confident we have applied their technique properly (in byB16),McCulloughetal.(2014)havearguedthattheapparent
boththe simulatedandobserveddata).However,we arguethat wavelengthdependencyintheirindependentobservationsofthis
with the correct treatment of the uncertainties the recovered system are best explained by un-occulted starspots rather than
theplanetatmosphere.
1 MPFIT did not produce significantly different results compared to When using the oversampled CCFs, both our analysis and
IDL’sGAUSSFIT,butitdidallowustopropagateourerrorsmorethor-
B16’sindicate a slight improvementin fit for the modelwith a
oughly(seeC16fordetails).
wavelength-dependent slope. However, we find a much worse
2 WenotethatweusedthesametransitparametersasB16,butthere
fit to the data than that found with the B16 results. The high
is a slight difference in the template mask used to obtain the CCFs.
χ2 from our reanalysis indicates an underestimation of the un-
B16 used the archival data available from the ESO website, where 2 r
nights used theG2 mask and 1night used the K5mask, whereasour certaintyinthedata,asonewouldexpectwhenusingtheover-
dataalwaysusedtheK5mask.However,thisdifferenceisunlikelyto sampledCCFs. We cannotexplainthe verylow χ2r forthe B16
impacttheanalysissinceeachnighthaditsownmasterCCF . wavelength-dependentfit, which indicatesthe modelis overfit-
out
Articlenumber,page4of5
Ceglaetal.:Limitationsofabrightness-basedapproachtochromaticexoplanetradii
ting the data. We note these tests were only performed on our Charbonneau, D.,Brown,T.M.,Noyes,R.W.,&Gilliland, R.L.2002,ApJ,
reanalysisoftheoversampleddataforcomparisonwithB16;for 568,377
ourconclusionsonthebest-fit,wereferthereadertotheanalysis Collier Cameron, A.,Bruce, V. A., Miller, G. R. M., Triaud, A.H. M. J., &
Queloz,D.2010,MNRAS,403,151
ontheCCFssampledeveryoneinfourpoints.
DiGloria,E.,Snellen,I.A.G.,&Albrecht,S.2015,A&A,580,A84
Fortheproperlysampleddataset,wefoundonlyamarginal Madhusudhan, N.,Knutson,H.,Fortney, J.J.,&Barman, T.2014,Protostars
improvement in the fit for the wavelength-dependent model, andPlanetsVI,739
anddonotdeemthisimprovementtobestatisticallysignificant Mandel,K.&Agol,E.2002,ApJL,580,L171
(see Table 1). Moreover,the best-fitflat model(R = 0.1569± Markwardt,C.B.2009,inAstronomicalSocietyofthePacificConferenceSe-
p ries,Vol.411,AstronomicalDataAnalysisSoftwareandSystemsXVIII,ed.
0.0003)lieswithin3σofthemeanR predictedbythesimula-
p D.A.Bohlender,D.Durand,&P.Dowler,251
tions.Theslightimprovementfortheslopedmodelisalsoheav- McCullough, P.R.,Crouzet, N.,Deming,D.,&Madhusudhan, N.2014,ApJ,
ilyinfluencedbyonlyacoupledatapointsfromasingletransit, 791,55
inAugust2007,asshowninthesubplotofFig.2.Ifthebest-fit Ohta,Y.,Taruya,A.,&Suto,Y.2005,ApJ,622,1118
Pont,F.,Sing,D.K.,Gibson,N.P.,etal.2013,MNRAS,432,2917
modelis robust, itshould withstandremovingthe Augusttran-
Sing,D.K.,Fortney,J.J.,Nikolov,N.,etal.2016,Nature,529,59
sit; however, doing so means the data is then best-fit by a flat Snellen,I.A.G.2004,MNRAS,353,L1
line(χ2 =1.6,BIC=11.1andχ2 =1.7,BIC=12.6forflatand
r r
sloped line, respectively).Consequently,we believe B16 likely
reportawavelength-dependenttrendinR duetoinsufficienter-
p
ror analysis, and that its agreement with the literature may be
purelycoincidental.
4. Conclusions
Weoutlineourconclusionsonapoint-by-pointbasisbelow.
– Thetechniquepresentedin B16 usingthe ratioof the areas
ofthelocal(starlightbehindtheplanet)totheout-of-transit
CCFcannotbeusedtodetermineR ,asR mustbeknown
p p
aprioriforthetransitlightcurvenormalisationrequiredfor
ground-based spectra. This is shown both analytically and
usingasimulatedstar-planetsystem.
– TheanalyticalβapproximationusedinB16alsointroduces
(slight) systematic trends with planet position due to inad-
equately accounting for limb darkening and fractional area
occultationeffects,andunderestimatesthevalueofR .
p
– WepostulatethattheR variationsreportedinB16arelikely
p
duetounderestimatederrors(largelyoriginatingfromuseof
oversampled CCFs), as our reanalysis of the HD189733b
transitsfurtherdemonstratesthattheonlyR recoverableis
p
thatinjectedintothetransitlightcurvenormalisation.
– Chromatic RM measurements from ground-based spec-
tra are not possible without taking the Doppler informa-
tion into account. Hence, for future measurements, we ad-
vise readers to either follow the works of Snellen (2004);
DiGloriaetal. (2015) or to apply the line-profile tomogra-
phyof CollierCameronetal. (2010) directly on each spec-
tralpassband.
Acknowledgements. We thank the referees, I. A. G. Snellen and S. Albrecht,
fortheircarefulreadingandconstructivecomments,whichimprovedtheclarity
ofthemanuscript.WealsothankF.Borsaforusefuldiscussions.Additionally,
HMCthanksE.deMooijforsuggestingweusesimulatedstarstotestthework
herein. HMCandCAWgratefully acknowledge supportfromtheLeverhulme
Trust(grantRPG-249).HMC,VB,CLandAWacknowledgethefinancialsup-
portoftheNationalCentreforCompetenceinResearch“PlanetS”supportedby
theSwissNationalScienceFoundation(SNSF).CAWalsoacknowledges sup-
portfromSTFCgrantST/L000709/1,andAWacknowledgesadditionalfinancial
supportdirectlyfromtheSNSF.ThisresearchhasmadeuseofNASA’sAstro-
physicsDataSystemBibliographicServices.
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