A new view on exoplanet transits: Transit of Venus described using three-dimensional solar atmosphere Stagger-grid simulations

1.1 MB·English

by  A. Chiavassa

Astronomy&Astrophysicsmanuscriptno.venus_v4 (cid:13)cESO2015
January27,2015
A new view on exoplanet transits:
Transit of Venus described using three-dimensional solar atmosphere
Stagger-grid simulations
A.Chiavassa1,C.Pere1,M.Faurobert1 G.Ricort1,P.Tanga1,Z.Magic2,3,R.Collet4,M.Asplund4
1 LaboratoireLagrange,UMR7293,CNRS,ObservatoiredelaCôted’Azur,UniversitédeNiceSophia-Antipolis,Nice,France
e-mail:[email protected]
5 2 NielsBohrInstitute,UniversityofCopenhagen,JulianeMariesVej30,DK–2100Copenhagen,Denmark
1 3 CentreforStarandPlanetFormation,NaturalHistoryMuseumofDenmark,UniversityofCopenhagen,ØsterVoldgade5-7,DK–
0 1350Copenhagen,Denmark
2 4 ResearchSchoolofAstronomy&Astrophysics,AustralianNationalUniversity,CotterRoad,WestonACT2611,Australia

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5 ABSTRACT
2
Context.An important benchmark for current observational techniques and theoretical modeling of exoplanet’s atmosphere isthe

] transitofVenus(ToV).Stellaractivityand,inparticular,convection-relatedsurfacestructures,potentiallycausefluctuationsthatcan
P affectthetransitlightcurves. SurfaceconvectionsimulationscanhelptheinterpretationofToVandalsoothertransitsoutsideour
E SolarSystem.
. Aims.Weusedrealisticthree-dimensional (3D)radiativehydrodynamical (RHD)simulationoftheSunfromtheStagger-gridand
h syntheticimagescomputed withtheradiativetransfercodeOptim3D toprovidepredictionsforthetransitofVenus(ToV)in2004
p observedbythesatelliteACRIMSAT.
- Methods.Wecomputed intensity maps from RHD simulation of theSun and produced synthetic stellar disk image as aobserver
o
wouldsee,accountingforthecentre-to-limbvariations.ThecontributionofthesolargranulationhasbeenconsideredduringtheToV.
r
t WecomputedthelightcurveandcomparedittotheACRIMSATobservationsandalsotothelightcurvesobtainedwithsolarsurface
s
representationscarriedoutusingradialprofileswithdifferentlimb-darkeninglaws.Wealsoappliedthesamesphericaltileimaging
a
[ methodusedforRHDsimulationtotheobservationsofcenter-to-limbSungranulationwithHINODE.
Results.WemanagedtoexplainACRIMSAT observationsof2004ToVandshowedthatthegranulationpatterncausesfluctuations

1 in the transit light curve. Wecompared different limb-darkening models to the RHD simulation and evaluated the contribution of
v thegranulationtotheToV.Weshowedthatthegranulationpatterncanpartiallyexplaintheobserveddiscrepanciesbetweenmodels
7 anddata.Moreover,wefoundthattheoverallagreementbetweenrealandRHDsolargranulationisgood,eitherintermofdepthor
0 Ingress/Egressslopesofthetransitcurve.Thisconfirmsthatthelimb-darkeningandthegranulationpatternsimulatedin3DRHD
2 Sunrepresent wellwhat isimagedbyHINODE.Intheend, wefound thattheVenus’saureolecontributionduringToV is∼ 10−6
6 timeslessintensethanthesolarphotosphere,andthus,accuratemeasurementsofthisphenomenaareextremelychallenging.
0 Conclusions.The prospects for planet detection and characterization with transiting methods are excellent with access to large a
. amountofdataforstars.Beingabletoexplainconsistentlythedataof2004ToVisanewstepforwardfor3DRHDsimulationsthat
1
arebecomingessentialforthedetectionandcharacterizationofexoplanets.Theyshowthatthegranulationhavetobeconsideredas
0
anintrinsicincertitude,duetothestellarvariability,onprecisemeasurementsofexoplanettransitsof,mostlikely,planetswithsmall
5
diameters.Inthiscontext,theimportanceofacomprehensiveknowledgeofthehoststar,includingthedetailedstudyofthestellar
1
surfaceconvectionisdeterminant.
:
v
Keywords. Planet-starinteractions–Sun:granulation–Techniques:photometric–stars:atmospheres–hydrodynamics–radiative
i
X transfer
r
a
1. Introduction ternalstructures,andformationconditions(Madhusudhanetal.
2014).
Thedetectionofexoplanetorbitingaroundstarsisnowaroutine A transit event occurs when an (or more) exoplanet move
with more that 1500 confirmed planets and about 3400 candi- across the face of host star, hiding a small part of it, as seen
dates (as in fall 2014 from http://exoplanets.org, Wrightetal. byan observeratsome particularvantagepoint.Theexoplanet
2011). The study of exoplanet atmospheres can generally be blockssomeofthestarlightduringthetransitandcreatesaperi-
classifiedintotwomaincategories:(i)themeasurementoftime- odicdipinthebrightnessofthestar.Theamountoflightreduc-
varyingsignals,whichincludetransits, secondaryeclipses,and tionistypically∼ 1%,0.1%,and,0.01%forJupiter-,Neptune-
phase curves, and (ii) the spatially resolved imaging and spec- andEarth-likeplanets,respectively(Borucki&Summers1984).
troscopy.Thesetechniquesallowto explorethepropertyofex- This depends on the star-planet size ratio and on the duration
oplanet’s atmospheres and understand the diversity of chemi- of the transit, which, in turn, depends on the planet’s distance
calcompositionsofexoplanets,theiratmosphericprocesses,in- fromthehoststarandonthestellarmass.Thismethodismostly
Articlenumber,page1of11
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sensitive to large, short-period exoplanets, which display the largely used in the planetary community,as well as to the real
largest atmospheric signatures and make them popular targets observationsof the granulation pattern on the Sun. The aim of
for time-varying characterization studies (Madhusudhanetal. thisworkistotest,whetherthe3Dsurfaceconvectionapproach
2014). During both the primary and secondary transits, the tothe transittechniquegivesreliableresultsforthe benchmark
planet-star radius ratio can be deduced, and, for sufficiently caseoftheToV,whichalsoisimportantfortheinterpretationof
bright stars, also the exoplanet’s mass can be determined othertransitsoutsideourSolarSystem.
fromthehoststar’sradialvelocitysemi-amplitude(Mislisetal.
2012).Ifthemassand/orradiusoftheexoplanetisgoodenough,
alsotheatmosphericdensitycanbepredictedgivinghintstothe 2. FromthehydrodynamicalsimulationoftheSun
current understanding of exoplanet formation processes. Even tosphericaltileimaging
moreinformationcanberetrievedbymeasuringthedepthofthe
transit: the radiation coming from the host star passes through The Sun is a natural reference for studying other stars and so-
the exoplanet’s atmosphere and it is absorbed to different de- lar models are essential for many studies in stellar and plan-
greesatdifferentwavelengths.Thiswavelength-dependentdepth etary astrophysics. Many of the observable phenomena occur-
of the transmission spectrum is directly linked to the absorp- ring on the surface of the Sun are intimately linked to convec-
tion features imprinted on starlight transmitted through the ex- tion.Moreover,theatmospherictemperaturestratificationinthe
oplanet’satmosphere(Seager&Sasselov2000;Brown2001). optical thin region, where the emerging flux form, is also af-
However,thetransitmethodhasseveraldrawbacks:(i)tobeob- fected by the interaction between radiative and convective en-
served,the exoplanetmust crossdirectly the line-of-sightfrom ergy transport. To account for all these aspects, it is impor-
the Earth (i.e., the star-planet system must be edge-on with re- tant to use realistic 3D radiative hydrodynamical (RHD) sim-
spect to the observer) and this is the case only for a small mi- ulations of convection (Stein&Nordlund 1998; Freytagetal.
nority of exoplanets. (ii) Another problem concerns the inter- 2012; Carlssonetal. 2004; Vögleretal. 2004). RHD simula-
transit duration that can last months to years, reducing drasti- tions of the Sun are widely used and compared in detail with
cally the number of detectable exoplanets. (iii) There is also observationsbytheastrophysicalcommunityusingdifferentnu-
a chance to observe the alignment with a background eclips- mericalcodes(e.g., Nordlundetal. 2009; Asplundetal. 2009;
ingbinarythatcauseblendsdifficulttodisentangle(Torresetal. Caffauetal.2011;Pereiraetal.2013).
2011). (iv) A last potential complication is the host star sur-
faceinhomogeneitiescausedbythepresenceofstellargranula-
2.1.Stellarmodelatmospheres
tion(e.g.,Chiavassaetal.2014)orthemagneticstarspots(e.g.,
Strassmeier2009). We used the solar simulation from the Stagger-grid of real-
Averyimportantbenchmarkforcurrentobservationaltech- istic 3D RHD simulations of stellar convection for cool stars
niquesandtheoreticalmodelingofexoplanet’satmosphereisthe (Magicetal. 2013). This grid is computed using Stagger-code
transitofVenus(ToV).VenusisinmanywaysanEarthanalogue (originallydevelopedbyNordlund&Galsgaard19952,andcon-
andit’stheclosestplanettransitwecanseeinourSolarSystem. tinuously improved over the years by its user community). In
ToVeventsarerare,astheyoccurinpairs8yearsapart,eachpair a cartesian box located at the optical surface (i.e., τ ∼ 1), the
separatedby121.5or105.5years,alternatingbetweendescend- code solves the time-dependent equations for conservation of
ing node(June pairs:1761/1769,2004/2012,...),and ascending mass,momentum,andenergycoupledtoanrealistictreatmentof
node (December pairs: 1631/1639,1874/1882, 2117/ 2125,...). the radiative transfer. The simulation domainsare chosen large
The 2004 and 2012 transits of Venus represent thus a crucial enoughtocoveratleasttenpressurescaleheightsverticallyand
leaponhuman-lifetimescale,asthemodernimagingtechnolo- toallowforabouttengranulestodevelopatthesurface,more-
gies available allow for the first time a quantitative analysis of over there are periodic boundary conditions horizontally and
theatmosphericphenomenaoftheplanetassociatedtoitstransit openboundariesvertically.Atthebottomofthesimulation,the
(Tangaetal. 2012). Spatial- and ground-based data have been inflows have a constant entropy and pressure. The simulations
collected and studied by different authors. Tangaetal. (2012) employrealisticinputphysics:(i)theequationofstateisanup-
performed the first photometric analysis of the "aureole"1 us- datedversionoftheonebyMihalasetal.(1988);(ii)theradia-
ingvariousground-basedsystemsandextractedfundamentalpa- tive transfer is calculated for a large number over wavelength
rametersof Venus’satmosphere.GarcíaMuñoz&Mills (2012) points merged into 12 opacity bins (Nordlund 1982; Skartlien
compared images of Venus during Ingress/Egress to 2004 data 2000) with opacitiesincludingcontinuousabsorptionand scat-
and provided guidelines for the investigation of the planet’s teringcoefficientsfromHayeketal.(2010)andlineopacitiesas
upper haze from vertically-unresolved photometric measure- described from Gustafssonetal. (2008), in turn based on the
ments.Ehrenreichetal.(2012)provideda theoreticaltransmis- VALD-2 database (Stempelsetal. 2001) of atomic lines. The
sion spectrum of the atmosphere of Venus dominated by car- abundancesemployedinthecomputationoftheSunsimulation
bondioxideabsorptionanddropletsofsulfuricacidcomposing arethelatestchemicalcompositionbyAsplundetal.(2009).
an upper haze layer (features not expected for a Earth-like ex-
oplanet)thatcouldbetestedwithspectroscopicobservationsof
2.2.Three-dimensionalradiativetransfer
2012transit.
In this work, we present the transit light curve predictions The computation of the monochromatic emerging intensity is
obtainedfrom3DsurfaceconvectionsimulationoftheSunand performedusingthe3Dpurelocalthermalequilibriumradiative
compare them to the ToV occurred in 2004. Furthermore, we transfercodeOptim3D(Chiavassaetal.2009)andthesnapshots
compare 3D predictions to limb-darkening models of the Sun, of the RHD simulation of the Sun (see Table 1). The radiative
transfer equation is solved monochromatically using pretabu-
1 At the Ingress and Egress of ToV, the portion of the planet’s disk latedextinctioncoefficientsasafunctionoftemperature,density,
outsidetheSolarphotospherehasbeenrepeatedlyperceivedasoutlined
byathinandbrightarc,called"aureole" 2 http://www.astro.ku.dk/∼kg/Papers/MHD_code.ps.gz
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A.Chiavassaetal.:Anewviewonexoplanettransits:TransitofVenusdescribedusingthree-dimensionalsolaratmosphere
Table1.3DsimulationoftheSunfromStagger-gridusedinthiswork.
<T >a [Fe/H] logg x,y,z-dimensions x,y,z-resolution M R Numberoftilesb
eff ⋆ ⋆
[K] [cgs] [Mm] [gridpoints] [M ] [R ] overthediameter
⊙ ⊙
5768.51(Sun) 0.0 4.4 7.7×7.7×5.2 240×240×240 1.0 1.0 286
a HorizontallyandtemporalaverageoftheemergenteffectivetemperaturesfromMagicetal.(2013)
b N = π·R⊙
tile x,y−dimension
andwavelengthbasedonthesameextensiveatomicandmolec-
ularcontinuumandlineopacitydataasthelatest generationof
MARCS models (Gustafssonetal. 2008). We assume zero mi-
croturbulence and model the non-thermal Doppler broadening
of spectral lines using only the self-consistent velocity fields
presentinthe3Dsimulations.Weemployedthesamechemical
compositionof the 3D RHD simulations(Asplundetal. 2009).
The wavelength interval computed is 6684.0± 0.1 Å. The de-
tailedmethodsusedinthecodeareexplainedinChiavassaetal.
(2009).
2.3.Sphericaltileimaging
The computational domain of each simulation represents only
a small portion of the stellar surface (see, e.g., the central
panel of Fig. 10 and Fig 1 in Chiavassaetal. 2012). To ob-
tain an image of the whole solar disk accounting for limb-
darkenedeffects,weemploythesametilingmethodexplainedin
Chiavassaetal. (2010) and used also in Chiavassaetal. (2012,
2014).Optim3Dhasbeenusedtocomputeintensitymapsfrom
the solar simulation for different inclinations with respect to
thevertical,µ≡cos(θ)=[1.0000,0.9890,0.9780,0.9460,0.9130,
0.8610,0.8090,0.7390,0.6690,0.5840,0.5000,0.4040,0.3090,
0.2060,0.1040],withθbeingtheanglewithrespecttotheline- Fig. 1. Synthetic solar disk image computed at 6684.0 ± 0.1 Å of
of-sight (vertical axis), and for 30 representative snapshots of the RHD simulation of Table 1. The intensity range is [0.0–3.79 ×
the simulation adequatelyspaced apartso as to capture several 106ergcm−2s−1Å−1].Wegenerated50differentsyntheticsolardiskim-
convectiveturnovers. agestoaccountforgranulationchangeswithrespecttotime.
Wethenusedthesyntheticimages,chosenrandomlyamong
thesnapshotsin thetime-series,to mapontosphericalsurfaces 3. ModelingthetransitofVenusof2004
accounting for distortions especially at high latitudes and lon-
gitudescroppingthe square-shapedintensity mapswhendefin- June 8th 2004 was a very importantand rare date for monitor-
ing the sphericaltiles. The computedvalue of the θ-angle used ing the first of two close by (2004and 2012) transits of Venus
to generate each map depended on the position (longitude and visible from Earth, before 2117. Schneideretal. (2006), here-
latitude) of the tile on the sphere and was linearly interpolated afterSPW2006,tookthechanceandobtainedspace-basedsolar
among the inclination angles. The random choice of snapshots irradiancemeasurementswithACRIMSAT spacecraft.
avoid the assumption of periodic boundary conditions and the
resulting tiled spherical surface displays an artifactual periodic
3.1.ObservationswithACRIMSAT
granulation pattern (Fig. 1). The total number of tiles (N )
tile
needed to cover half a circumference from side to side on the The satellite mission ACRIMSAT3, launched in 1999 and
sphere is Ntile = x,y−dπi·mRe⊙nsion = 286, where R⊙ (transformedin founded by NASA through the Earth Science Programs Office
Mm)andthe x,y−dimensioncomefromTable1.Wegenerated at Goddard Space Flight Center, measured 0.0961% reduction
50 different synthetic solar disk images. Since the number of inthesolarintensitycausedbytheshadowoftheVenusduring
tilesnecessarytocoverthesphereislargerthanthetotalnumber histransitin2004(SPW2006).Thesemeasurementsweretaken
ofrepresentativesnapshotsofRHD simulation,sometilesmay withtheActiveCavityRadiometerIrradianceMonitor(ACRIM
randomlyappearsseveraltimesonthesolardiskatdifferentin- 3) instrument (Willson&Mordvinov2003). ACRIM 3 was de-
clinations.Therefore,the50syntheticimagesarenotcompletely signedtoprovideaccurate,highlyprecise,andtraceableradiom-
independent, but we assume that they are a good enough sta- etryoverdecadaltimescales,todetectchangesinthetotalenergy
tistical representation to estimate the granulation changes with receivedfromtheSunbytheEarth.ACRIM3provides32second
respect to time during the ToV. Fig. 2 displays the fluctuation exposureshuttermeasurementscharacterizedbyopen(observa-
ofthegranulationstructuresforaparticularcutinthesynthetic tions)andclosed(calibration)measurements.Themeasurement
disk images. The solar disk intensity fluctuates at the scale of precisionis0.01%(SPW2006).
the tile and the maximum intensity varies between [3.74–3.87]
×106ergcm−2s−1Å−1. 3 http://acrim.jpl.nasa.gov
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A&Aproofs:manuscriptno.venus_v4
Fig.2.Cutatx=0,y>0for50differentsyntheticsolardiskimages(one
exampleinreportedFig.1).Theintensityprofilesarenormalizedtothe
intensityatthediskcenter(R=0.0).ThegreenlineistheRHD<3D>
averageprofile.
ACRIMSAT cannot observe the Sun continuously because
theline-of-sightisoccultedbytheEarthduringitsorbitaround
the Sun. In SPW2006, these periodic interruptionswere deter-
mined for time intervals spanning the ToV using a definitive
a posterioriorbitalephemerisderivedfroma contemporaneous
epochal satellite element set provided by the North American
Aerospace Defense Command. SPW2006 reports (Figure 2 in
SPW2006)theapparentpathofthecenterofVenusasseenfrom
ACRIMSAT withrespecttotheheliocenterastheplanetcrossed
the face of the Sun. ACRIMSAT’s observations are interrupted
for ∼30 minutes by Earth occultation during each of its ∼100
minuteorbits.Thedurationof2004ToVis∼5.5hours.
Inthiswork,weusethetrajectorycoordinatesofVenusextracted
fromSPW2006tosimulatethepassageoftheplanetonthesyn-
theticsolardiskofFig.1.
3.2.EvaluationofVenus’saureolewithHINODE
Telescopeimages,withinstrumenttypicallyupto 15to20cm,
report cusp extension tending to transform the thin crescent of
Venusintoaringoflightsincethemid18thcentury(fordetailed
historicalreviewsseeLink1969;Edson1963).Whilethesephe-
nomena can be ascribed to light diffusion, during transits the
contribution of refraction (3-4 orders of magnitude stronger)
showsup.Traditionally,itsdiscoveryisattributedtoLomonosov
(wholivedbetween1711and1765; Marov2005).AstheToV
are rare, also the data concerningthe aureole are sparse. How-
ever, thanks to the coordinatedgiant leap in the observationof
2004ToV, as well as the moderntechnologiesallowed a quan- E
titativeanalysisoftheatmosphericphenomenaassociatedtothe N
ToV(Tangaetal.2012).Theauthorsperformedforthefirstpho-
tometricanalysisandobtainedspatiallyresolveddataproviding Fig.3. Toppanel: Image(1024×1024 pixels)of Venus(darkcircu-
measurementsof the aureoleflux as a functionof Venus’slati- larsubaperture)transitingtheSun(brighterareas)inJune5th2012as
tudealongthelimb. seenbyHINODESOT/SPspectropolarimeter(totalintensityStokepa-
The aureole is a distorted (strongly flattened) image of a rameterI)intheredfiltercenteredat6684.0±0.1Å(Redfilter).The
portionofthesolarphotosphere.Assuchthesurfacebrightness intensityrangeis0.–2.7×103DNpixel−1s−1 (whereDNisdatanum-
bers, Litesetal.2013).Theintensityplottedisthesquarerootofthe
of the photosphere is the same in the aureole. For this reason,
intensitytobetterdisplaythe"aureole".Centralpanel: Samefigureas
although the aureole is very thin (< 40 km above the cloud
abovewiththecontrasthighlyincreasedtofittheradiusoftheplanet,
deck)itiscleartheoverallcontributiontothetransitphotometry
yellow circle, with the procedure described in the text (R = 274.91
deservesaspecificevaluation.Todothis,weneededhighspatial fit
pixels).Thecenter of theSunislocatedinSouth-East direction. Bot-
resolutionimagesofVenusduringatransit,and,onlyHINODE tompanel: Threedimensional viewof theimagesabove. Theaureole
contributionisvisibleintheregionjustoutsidethesolardisk.
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A.Chiavassaetal.:Anewviewonexoplanettransits:TransitofVenusdescribedusingthree-dimensionalsolaratmosphere
spacecraft could provide that. Unfortunately, the satellite was
launched after 2004 and thus we used observationscarried out center of Venus
during ToV of 2012, assuming that there were no changes in
Venus’satmospherebetween2004and2012.
HINODE (Kosugietal. 2007) is a joint mission between the -1s
sKpiancgedoamgenlacuienschoefdJainpan2,00U6n,itaenddSstiantcees,tEheunro,pteh,easnpdecUtrnoipteod- -1xel x
larimeterSOT/SP(Litesetal.2001;Tsunetaetal.2008)allows N pix
thesolarcommunitytoperformspectropolarimetryofthesolar D
photosphere under extremely stable conditions. SOT/SP pro-
vides0.32arcsecangularresolutionmeasurementsofthevector
magnetic fields on the Sun through precise spectropolarimetry
of solar spectral lines with a spatial resolution of 0.32 arcsec
andphotometricaccuracyof10−3(Ichimotoetal.2008).
pixel
We obtained HINODE observations of June 5th 2012 ToV
Fig. 4. Representative radial intensity profiles within the ring region
from through the HINODE data on-line archive. We used
(R ±20mpixels)intheimageofFig.3,whichincludestheaureolecon-
SOT/SP Stokes I images (i.e., the total intensity measured) fit
tribution.Thebluedottedcurvecorrespondstotheobservations,while
in the red filter (6684.0 ± 0.1 Å). The data are reduced and thegreensolidlinetothebestfit(seetextfordetails).Theverticalred
calibratedforalltheslitpositions(i.e.,correspondingto"level1" dashedlineisthelocationofVenus’sradius.
data). The solar diameter in that period was 31.7′(∼951.1′′for
the radius), the geometrical distance at the Sun surface, seen
under one arcsecond was R /951.1× 0.109 = 732.1 km Fig.1correspondingtothesamesizeandshapeofHINODEob-
⊙SOHO
(with R = 696342 km measured by SOHO spacecraft, servationofFig3.Thentherelativeintensityduetotheaureole
⊙SOHO
Emilioetal. 2012). The spatial resolution of the image is isIratio = Iaureole×(cid:16)Isynthcut/Isynthglobal(cid:17)×(1/IHinode),knowingthat
1im02ag4ex1i0s2t4hepnix1e1ls1(.6F1ig×.31)1a1n.d611′′poixre8l1=.701.1×098′1′,.7th1eMsizme,owfietahch1 (cid:16)Isynthcut/Isynthglobal(cid:17)=0.0118.Table2reportsvaluesoftheorder
of10−6,fartooweaktobedetected,alsoconsideringthepreci-
pixelequalto79.80km.
sion level of ACRIMSAT (∼ 10−5) and the heightof the transit
(10−4, Fig. 6). We therefore do not consider the aureole in our
Thecontributionfromtheaureolewascomputedasfollows:
modeling.
1. The dark circular subaperture corresponding to Venus in
Table2.Integratedintensitycontributions(I )ofmaximum,min-
Fig. 3 (central panel) was fitted using Newton-based fit aureole
imumand average values fromtheaureole (Fig. 4),together withthe
method(Pratt 1987). We selected the points where approx-
related ratio (I ) to the total emerging intensity from the synthetic
imatively resides Venus’s radius (yellow numbered crosses ratio
SunofFig.1.
in the figure).The fitting methodreturned the center of the
planet as well as its radius (or impact parameter), a in the I ×105 I ×10−6
figure,withaVenusradiusR =274.91pixels. aureole ratio
fit [DNpixel−1s−1]
2. Thepositionofthecenterandtheradiusknown,weextracted
Average 1.2 1.0
a ring of 40 pixelsin the outer regionsof Venuswithin the
Max 6.0 5.4
regionR ±20pixels.
fit Min 0.4 0.3
3. Weextracted215radialintensityprofileswithintheringre-
gion(arepresentativeexampleisreportedinFig.4).
4. We fitted the aureole contribution using a gaussian law (3
free parameters) for the peak and a straight line equation
3.3.Modelingthetransitwith3DRHDsimulationoftheSun
(2freeparameters)forthebackground.Thenwe integrated
over the radius the intensity subtended by the gaussian fit- Theobservationsgivethetransitparameterssuchas:thegeomet-
ting curve for each of the 215 radial profiles. We obtained ricallyderivedtransitdepthandcontacttimes,theratiobetween
theradialcontributionoftheaureole. Venus’sandSun’sradii,andthepositionsofVenuswithrespect
5. We repeated this procedure for 50 other images during the totheheliocenterasafunctionsoftimegiventhespacecraftand
IngressandEgressofToVwithsimilarresults. planetaryorbits. In the following,we explainhowwe modeled
theToVusingRHDsimulationoftheSunasabackground.The
Fig. 4 shows the typical signal of the aureole in the ring stepsare:
region selected close to Venus’s radius. The peak is signifi-
cantandmuchlargerthanthebackgroundsignal(alwayslower 1. weusethesyntheticsolarimage(Fig.1)asthebackground
than ∼20 DNpixel−1s−1). The contribution of the aureole cor- emittingsource;
responding to the 215 radial intensity profiles is in the range 2. Venusis modeledby a disk of radiusRVenus = 0.0307R⊙ ∼
I = [0.4−6.0]×105 DNpixel−1s−1 withanaveragevalue 8.5pixels(Fig.5)withtotalintensity0.0961%of I
aureole synthglobal
of< I >=1.2×105DNpixel−1s−1 (Table2). (percentagefluxdecrementduring2004transit,SPW2006);
aureole
TorelatetheaureoleintensitytothefullSun,weusethe3Dsyn- 3. theplanetdiskcrossesthesolardiskfollowingtheapparent
thetic solar disk image of Fig. 1. First, we define I as the trajectoryofVenusasseenfromACRIMSAT (seeSPW2006
Hinode
totalemergingintensityfromFig3(toppanel),I asthe formoredetailsandFig.5):
synthglobal
total emerging intensity from the synthetic Sun of Fig. 1, and 4. the intensity of the system is collected for every transiting
I asintensityemergingfromacutinthesyntheticdiskof step.
synthcut
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Fig.5.Toppanel: SyntheticsolardiskimageinthevisibleoftheRHD
simulationwiththedifferentpositionsofToVasseenfromACRIMSAT.
ThecomputedwavelengthisthesameasinFig.1.Theunusualapparent
trajectoryofVenusisinducedbythespacecraftorbit(seetext).Bottom
panel: enlargementfromtoppanel.
Theintensity mapof Fig. 5 is a statistical representationof
theSunataparticularmomentduringthetransit.Theapparent
trajectoryofVenusontheSunischaracterizedby(seeSPW2006
formoredetails):(i)aperiodicspatialandtemporalmodulations
in the locationof Venusasit traversesthe solardisk causedby Fig.6.Toppanel:ToV2004lightcurve(blackdashedline)forthe3D
the projectionon theSun oftheshiftingof theline-of-sightin- RHDsimulationof the Sun(Fig.5) compared tothephotometric ob-
ducedbythespacecraftorbit;(ii)avertical(north-south)ampli- servations (red dotswith error bars, Schneideretal. 2006) taken with
ACRIM3mountedonACRIMSAT.Theobservationshavebeennormal-
tudevariationsresultingfromthenear-polarorbitof thespace-
izedto1,dividingtheoriginaldata(Figure3of Schneideretal.2006)
craft; (iii) an horizontal (east-west) component manifesting in
by1365.88 W/m2. Thelightcurve hasbeen averaged(withthegreen
nonlinearspacings in the planetaryposition along its projected
shadedenotingmaximumandminimumvalues)over50differentsyn-
path in equaltime intervalsdue to orbitplanenotbeing on the
theticsolardiskimagestoaccountforgranulationchangeswithrespect
line-of-sightdirectiontotheSun. totime.Bottompanel: sameasabovebutforoneparticularrealization
Thetemporalfluctuationsistakenintoaccountusingthe50 amongthe50syntheticsolardiskimages.
different synthetic solar disk images computed. The resulting
light curve from the ToV is reported in Fig. 6. The light curve
hasbeenaveragedover50possiblerealizationsofsolardisk.The aresultofthereflectivespacecraftparallacticmotionofVenus,
decreaseoftheSun’slightisduetotheplanetoccultationandde- the planet’s apparent path crosses regions of the Sun with sur-
pendsontheratiobetweentherespectivesizeofVenusandthe face brightnessesveryclose to the stellar limb.This affectsthe
Sunaswellasonthebrightnesscontrast.Themagnitudeofthis slopeofthelightcurvethatismoreshallowduringEgresswith
intensity variationdependsonthe ratioof the size of Venuson respecttotheIngress.Thisaspectisveryconstrainingfortransit
thebrightnesscontrastbetweenthesolardiskandtheplanet.As modelingandcrucialtovalidatetheRHDsimulationused.
Articlenumber,page6of11
A.Chiavassaetal.:Anewviewonexoplanettransits:TransitofVenusdescribedusingthree-dimensionalsolaratmosphere
causesthatcouldaffect theirdeficiencyin lightcurvefitting of
thetransitdata.Intheirwork,theyarguedthatinstrumentalmea-
surementerrorsandintrinsicsolarvariationscomparedtoimper-
fectionsinthelimb-darkeningmodelitselfmaybethecause.In
thiscontext,RHDsimulationoftheSunbringsanewinsighton
the impact of the granulation thanks to the excellent matching
showedinFig.6.ThenumericalboxofaRHDsimulationisro-
tatedwithadeterminedmu-angle(seeSection2.3)beforecom-
puting the emerging intensity. There is not a pre-adopted limb
darkeningfunctionandthefinalresultisthedirectoutputofthe
emergingintensityataparticularmu-angle.
Table 3. Limb-darkening coefficients used in this work with the law
Iµ/I1 =1−P4k=1ak(cid:16)1−µk/2(cid:17)(Claret2000)andastarwithsolarparam-
etersorforthe<3D>profileoftheRHDsimulation(Fig.2,greenline)
ortheintensityprofileofHINODEdata(Fig.7,greenline).
Fig.7.Cutat x=0,y>0indifferentsynthetic solardiskimageseither Reference a1 a2 a3 a4
built from Claret (2000) (light blue curve), Magicetal. (2014) (red Claretetal.2000 0.5169 -0.0211 0.6944 -0.3892
curve), RHD <3D> profile (black curve, from Fig. 2) and HINODE Magicetal.2014 0.5850 -0.1023 0.5371 -0.2580
dataforthequietsun(greencurve,usedinSection3.5).Theintensity FitRHD<3D> -3.8699 13.3547 -15.4237 6.1910
profilesarenormalizedtotheintensityatthediskcenter(R=0).
FitHINODEdata 18.32 -38.49 36.05 -12.20
The data obtained in 2004 for the ToV (see Section 3.1) We tested different limb-darkening laws represent the Sun.
has been provided to us by Glenn H. Schneider (University of Forthispurpose,webuiltsyntheticimagesrepresentingtheso-
Arizona,privatecommunication).Unfortunately,2012ToVdata larsurfaceusingradialprofilesobtainedwiththelimb-darkening
are not helpful in our work because they had too large error lawofClaret2000(basedon1DmodelatmospheresofKurucz
tboasrpsh.eVreen,uasndo,ccAuCltRedIM0.039p6r1o%vidoefdthcealtiobtraalteadreoabosfertvhaetiSounnspwhioth- 1979):Iµ/I1 = 1−P4k=1ak(cid:16)1−µk/2(cid:17),expressedasthevariation
in intensity with µ-angle that is normalized to the disk-center
gaps resulting from the Earth occultations during the satellite
(I /I ).Thelimb-darkeningcoefficientsfora starwiththe stel-
orbit.Fig.6 showsthattheagreementbetweenourRHD simu- µ 1
larparametersoftheSunandforthevisiblerangeareinTable3.
lationandthedataisverygood.Theroot-mean-squaredeviation
The reader should note that Magicetal. (2014) used the same
(RMSD = Pni=1(ynˆi−yi)2; where yˆi are the predicted values, yi the RHD simulation of Table 1 to extract their coefficients. More-
observedvalues,andnthenumberofmeasurements)variesbe- over, we used the law of Claret to fit the average RHD profile
tween[9.1-9.5]×10−5forallthe50possiblerealizationsofsolar < 3D >of Fig.2 (greencurve)andreportedthecoefficientsin
granulationandisequalto9.1×10−5fortheaverageprofileplot- Table3.
tedinFig.6.Atthebottomofthelightcurve(∼8.4hUT),there The normalized intensity profiles of the different laws are re-
aresomeaperiodicvariations.SPW2006reportedthatthismay portedinFig.7.
resultfromintrinsicchangesinthetotalsolarirradianceoverthe For the circular subaperture representing the disk of Venus
sametimeintervalormayariseasVenusoccultsisolatedregions we used a constant flux. Fig. 8 (top) shows the three different
of the photosphere differing in local surface brightness (e.g., limb-darkening models: Magicetal. (2014) (RMSD = 9.0 ×
sunspots or smaller spatial scale localized features). Indeed, it 10−5, red curve), Claret (2000) (RMSD = 9.3 × 10−5, light
ispossiblethatmagneticstarspotscontaminatethetransitsignal blue curve), and the Claret law for the RHD < 3D > profile
(e.g.,Silva 2003;Lanzaetal. 2009).In the end,accountingfor (RMSD = 9.3×10−5, purple curve). Fig. 8 (bottom) displays
the granulation fluctuations allows to reduce the scatter on the that the central depression of Venus’s transit obtained with the
observedpointsatabout7h,9h,11hUT(Fig.6,bottompanel). limb-darkeneddiskofClaret(2000)(lightbluecurve)issystem-
Ourapproachisstatisticalandaimsnottofullyexplaintheob- aticallyundersizedwithrespecttothetransitwiththe3DRHD
served data but to show thatour RHD simulationof the Sun is simulation(blackcurve),whilethereisabetteragreementwith
adapted (in terms of limb-darkening and emerging flux) to in- Magicetal.(2014)model(redcurve)andwiththeRHD<3D>
terpretsuchadataandthatthegranulationfluctuationshavean limb-darkening.Sincethemagnitudeoftheintensityvariationin
importanteffectofthelightcurvesduringthetransit.Theevalu- the light curve depends on the brightness contrast between the
ationofthegranulationcontributionisdoneinSection3.4. solar disk and Venus, it is noticeable that RHD synthetic disk
image differs from limb-darkening models with particular em-
phasisatthestellarlimb.Thecontributionofthegranulationto
3.4.3DRHDgranulationversuslimb-darkeningmodels
theToVcanberetrievedbytheabsolutedifferencebetweenthe
In the literature, in general, the contribution of the star to the limb-darkeningof the RHD < 3D > profile and the full RHD
transitisapproximatedbyaparametricrepresentationofthera- ToV(purplecurveinbottompanelofFig.8).Wecomputedthe
dial limb-darkened surface profile. This approach neglects the RMS = 1.7×10−5 of this difference and foundthat it is ∼5
3D
surface inhomogenietiescaused by the granulation pattern, the smaller than the RMSDs of the different models. Even if the
intensitybrightnessdecreaseistakenintoaccount,dependingon granulationcontributionisnotlargeenoughtoexplainthewhole
thelimb-darkeninglawused.Asaconsequence,theslopeofthe observeddiscrepancies,it is source of an intrinsic noise due to
lightcurveintheIngressandEgressmaybeaffecteddifferently. the stellar variability, that may affect precise measurements of
In SPW2006, the authors used this method and examined the exoplanettransitsof,mostlikely,planetswithsmalldiameters.
Articlenumber,page7of11
A&Aproofs:manuscriptno.venus_v4
Fig.8.Toppanel:ComparisonofdifferentToVlightcurves.Theblack
curve is the light curve combining the RHD simulation of the Sun
(Fig. 5 and Fig. 6). Thered and light blue curves represent the limb-
darkening Magicetal. (2014) and Claret (2000), respectively. In the
end, the purple curve represents the limb-darkening carried out using
Claret’slawfortheRHD<3D>profileofFig.2(greencurve).Inall
the cases, a constant value isused for Venus intensity. Bottom panel:
Differencebetweentheabovecurveswithrespecttothetransitcurveof
theRHDsimulationofFig.6.
3.5.3DRHDgranulationversusobservedsolargranulation
TheaimofthisSectionistocreateasolardiskimageusingthe
same procedure of RHD simulation (Section 2.3) but with, as
input,thegranulationpatternobservedontheSun.Forthispur-
pose, we recovered HINODE spectropolarimeter SOT/SP data
productcollectedbetweenDecember19andDecember202007
from High Altitude Observatory(HAO) website4. The data are
reducedandcalibratedforalltheslitpositions(i.e.,correspond-
ing to "level1" data). We used SOT/SP Stokes I images (i.e.,
thetotalintensitymeasured)integratedatthecontinuumwave-
lengthsveryclose theFe I linepairat6300Å butavoidingthe Fig.9.Suntotalintensityimage(370×370pixels)asseenbyHINODE
SOT/SP spectropolarimeter at different ∆µ and at continuum wave-
spectrallines: the emergingintensity is then compatible,in tex
lengths close to 6300 Å. Top panel is the center of the Sun and bot-
of wavelengths probed, to the intensity map of Fig. 1 and the
tom panel is the southern limb. The intensity range is, from the top,
4 http://www.csac.hao.ucar.edu/csac/archive.jsp#hinode 18–27×103-17–27×103-14–21×103-18–25×103DNpixel−1s−1.
Articlenumber,page8of11
A.Chiavassaetal.:Anewviewonexoplanettransits:TransitofVenusdescribedusingthree-dimensionalsolaratmosphere
HINODERedfilterusedinFig.3.Theoriginalimagesof1024
pixel-spectrographslit paralleltothe North-Southpolaraxisof
the Sun was successively located at 20 latitudes and scans of
370stepsof0.16′′inthedirectionperpendiculartotheslitwere
performed.Ateachpositionintheslit,theimageshavebeenin-
tegratedforabout5secondsandforatotaltimeofabout30min-
utes(ie.,370steps).Thisprovidesuswith20(1028×370pixels)
imagesallowingacompleterecordingofthecenter-to-limbvari-
ations of the solar disk. However, as the fields of view of the
imagesarepartlysuperimposedweextractedfromtheHINODE
images a set of 17 (370×370pixels) images forming a contin-
uous South-North stripe in the solar southern hemisphere. The
solar diameter in that period was 32.5′(∼975.3′′for the radius),
thegeometricaldistanceattheSunsurface,seenunderonearc-
secondwasR /975.3= 713.9km.Eachpixelis0.16′′,the
⊙SOHO
sizeofeachimage(Fig.9)isthen59.20×59.20′′or42.18×42.18
Mm,with1pixelequalto114km.
However, the images were too large compared to the syn-
theticmaps(Fig.10,centralpanel)weusedfortilingthespher-
ical surface of the Sun (Fig. 1) with RHD simulation. We then
dividedeachimagebyafactor10intheEast-Westaxisandbya
factor10intheNorth-Southpolaraxis.Weultimatelyobtained
several37×37imagesof∼4.2Mm(Fig.10,toppanel)in83µ
sub-steps.
Intheend,weappliedthetilingprocedureofSection2.3andob-
tainedtheToVforagranulationpatternbasedonHINODE ob-
servations(Fig.10,bottompanel).ThedeviationfromACRIM-
SAT observationsis RMSD = 8.7×10−5. Fig. 11 displays the
comparisonbetweenthelightcurveobtainedfromtheRHDsim-
ulation (Fig. 6, black dashed line) and the one calculated from
the ToV of Fig. 10 (bottompanel). The absolute differencebe-
tween the ToV curves (Fig. 11, bottom panel) shows a typi-
cal value of ∼ 5.0 × 10−5, which is close to what is reported
in Fig. 8 (bottom).However, the agreementis better, in partic-
ular for the Ingress/Egress slopes of the transit. This confirms
thatthelimb-darkeningandthegranulationpatternsimulatedin
the3DRHD solarsimulationrepresentwellwhatisimagedby
HINODE.ThiscomparisonwithHINODEdataisimportantbe-
cause allows another inspection of RHD simulation using data
withsmallernoisewithrespecttoToVdata.
Followingwhat we did in Section 3.4 for the RHD <3D> pro-
file, we used the limb-darkening law of Claret to fit the inten-
sity profile obtained from HINODE data (Fig. 7, green curve).
The coefficientsare reportedin Table 3. It is also noticeablein
Fig.7thegoodagreementbetweentheHinodeandtheRHDpro-
files. To obtain the contributionfrom the granulation,we com-
puted the limb-darkening ToV and subtracted it to the ToV of
the HINODE image. The resulting signature of the granulation
has an RMS = 3.0 × 10−5, which is comparable to the
Hinode
RMS =1.7×10−5duetothegranulationsignalinRHDToV.
3D
Both values are however lower than or of about the same or-
der of the smallest error bar of ACRIMSAT (2.7 × 10−5), and
thus the granulation signal cannot be unveiled with these data.
Nevertheless,Itshouldbenotethatthereisapossibilitythatthe
smallscalevariabilityproducedbytheRHDsimulationmaybe
slightlyunderestimatedduetothesnapshotchosen.
Fig. 10. Top panel: Cut of 37 × 37 pixels from Fig. 9 top panel.
4. Conclusionsandimplicationsfortransitstudies Central panel: intensity map of a small portion of the Sun surface
at µ=1 from the RHD of Table 1. The intensity range is [2.0–4.3 ×
ofextrasolarplanets
106ergcm−2s−1Å−1].Bottompanel:ToVonthesolardiskimagecon-
structedwiththetilingprocedureofSection2.3butwithrealgranula-
ModelingthetransitlightcurveofVenusasseenfromACRIM-
tionobservations (top panel and Fig. 9) of HINODE (see text for de-
SAT implies the importance to have a good representation of
tails).AconstantvalueisusedforVenusintensity.
the backgroundsolar disk and of the planetitself. For the Sun,
Articlenumber,page9of11
A&Aproofs:manuscriptno.venus_v4
thedifferentmodelsusedanditisdifficulttodisentanglethesig-
nalofthegranulationwiththedatausedinthiswork.Moreover,
we found that the Venus’s aureole contribution during ToV is
∼ 10−6 times less intense than the solar photosphere,and thus,
accurate measurements of this phenomena are extremely chal-
lenging.
Intheend,weappliedthesamesphericaltileimagingproce-
duretotheobservationsofcenter-to-limbSungranulationwith
HINODE and built a solar disk image. We then compared the
resultingtransitcurvesandfoundthattheoverallagreementbe-
tweenrealandRHDsolargranulationisverygood,eitherinterm
of depth or Ingress/Egress slopes of the transit. This confirms
thatthelimb-darkeningandthegranulationpatternsimulatedin
3DRHDSunrepresentwellwhatisimagedbyHINODE.
3DRHDsimulationsarenowestablishedasrealisticdescrip-
tionsfortheconvectivephotospheresofvariousclassesofstars.
Theyhavebeenrecentlyemployed:(i)inthepredictionofdiffer-
entialspectroscopyduringexoplanettransitstoreconstructspec-
traofsmallstellarsurfaceportionsthatsuccessivelybecomehid-
denbehindtheplanet(Dravinsetal. 2014);(ii)ortoassess the
transitlightcurveseffectofthelimb-darkeningissuedfrom3D
RHDsimulationswithrespectto1Dmodels.
TheToVisanimportantbenchmarkforcurrenttheoreticalmod-
elingofexoplanettransits.Beingabletoexplainconsistentlythe
dataof2004transitisthenanewstepforwardfor3DRHDsim-
ulations. This implies that our tiling procedure can be adapted
to exoplanet transits. Moreover, our statistical approach in this
workallowedtoshowthatthegranulationhavetobeconsidered
asanintrinsicincertitude,duetothestellarvariability,onprecise
measurementsofexoplanettransitsof,mostlikely,planetswith
small diameters. A possible solution to reduce this incertitude
istherepetitionofthetransitmeasurementsseveraltimesrather
thantakeasinglesnapshot.
Theprospectsforplanetdetectionandcharacterizationwith
transiting methods are excellent with access to a large amount
of data for different kind of stars either with ground-based
telescopes such as HATNet(Hungarian Automated Telescope
Network, Bakosetal. 2004), NGTS (Next Generation Transit
Survey,Wheatleyetal.2013),TRAPPIST (TRAnsitingPlanets
and PlanetesImals Small Telescope, Jehinetal. 2011), WASP
Fig.11. Toppanel: ToV light curves for RHD simulation (Fig.5and
(WideAngleSearchforPlanets, Pollaccoetal.2006)orspace-
Fig.6)andHINODESOT/SPspectropolarimeterdata(Fig.10,bottom
basedmissionslikeCHEOPS(CHaracterizingExOPlanetSatel-
panel).AconstantvalueisusedforVenusintensity.Bottompanel:Dif-
ferencebetweentheHINODEToVwithrespecttotheRHDsimulation. lite, Broegetal.2013;Kochetal.2010),COROT(Convection,
Rotation and planetary Transits, Baglinetal. 2006b,a), Kepler
(Boruckietal.2010),TESS(TransitExoplanetSurveySatellite,
weusedtherealistic,state-of-the-art,time-dependent,radiative- Rickeretal.2010),PLATO(PLAnetaryTransitsandOscillation
hydrodynamicstellar atmosphereof theSunfromtheStagger- ofstars,Raueretal.2014).
grid.ForVenus,weextractedandfittedradiallyaveragedprofiles Inthiscontext,3DRHDsimulationsareessentialforadetailed
fromhighspatialresolutionimagesofHINODE. quantitative analysis of the transits. Indeed, the interpretation
andthestudyoftheimpactofstellargranulationisnotlimitedto
We providedsynthetic solar disk image using the spherical
tile imaging method already applied in Chiavassaetal. (2014, theSun(Nordlundetal.2009)butRHDsimulationscoverasub-
stantialportionoftheHertzsprung-Russelldiagram(Magicetal.
2012, 2010). We applied a statistical approach to show that
2013; Trampedachetal. 2013; Ludwigetal. 2009), including
our RHD simulation of the Sun is adapted (in terms of limb-
darkening and emerging flux) to interpret such a data and that theevolutionaryphasesfromthemainsequenceovertheturnoff
thegranulationfluctuationshaveanimportanteffectofthelight uptothered-giantbranchforlow-massstars.
curves during the transit. Our procedure successfully explain
Acknowledgements. TheauthorsthankG.Schneider,J.M.Pasachoff,R.C.Will-
ACRIMSATobservationsof2004ToVandshowedthatthegran-
sonforproviding2004ToVdataandfortheenlighteningdiscussions.Theau-
ulationpatterncausesfluctuationsinthe transitlightcurve.We thorsacknowledgeAlphonseC.Sterling(NASA/MarshallSpaceFlightCenter)
compareddifferentlimb-darkeningmodelstoourRHDsimula- forthepreparationanddiffusionofthetransitimages.CPacknowledges fund-
tionandevaluatedthecontributionofthegranulationtotheToV. ingfromtheEuropeanUnionSeventhFrameworkProgram(FP7)undergrant
agreement number 606798 (EuroVenus). RC is the recipient of an Australian
Weshowedthatthegranulationpatterncanpartiallyexplainthe
Research Council Discovery Early Career Researcher Award (project number
observeddiscrepanciesbetweenmodelsanddata.However,the DE120102940).
amplitudeofthesignalisclosetothetypicaldifferencesbetween
Articlenumber,page10of11