The centre-to-limb variations of solar Fraunhofer lines imprinted upon lunar eclipse spectra - Implications for exoplanet transit observations

1.5 MB·English

by  Fei Yan

Astronomy&Astrophysicsmanuscriptno.CLV-paper (cid:13)cESO2015
January13,2015
The centre-to-limb variations of solar Fraunhofer lines imprinted
upon lunar eclipse spectra
Implications for exoplanet transit observations
F.Yan1,2,3,R.A.E.Fosbury3,M.G.Petr-Gotzens3,G.Zhao1,andE.Pallé4,5
1 KeyLaboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, 20A DatunRoad,
ChaoyangDistrict,100012Beijing,China
5
e-mail:[email protected], [email protected]
1
2 UniversityofChineseAcademyofSciences,19AYuquanRoad,ShijingshanDistrict,100049Beijing,China
0
3 EuropeanSouthernObservatory,Karl-Schwarzschild-Str.2,85748GarchingbeiMünchen,Germany
2
4 InstitutodeAstrofísicadeCanarias,C/víaLáctea,s/n,38205LaLaguna,Tenerife,Spain

n 5 Dpto.deAstrofísica,UniversidaddeLaLaguna,38206LaLaguna,Tenerife,Spain
a
J
Received—–;accepted—–
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1

ABSTRACT
]
P
Theatmospheresofexoplanetsarecommonlystudiedbyobservingthetransitoftheplanetpassinginfrontofitsparentstar. The
E
obscurationofpartofthestellardiskduringatransitwillrevealaspectsofitssurfacestructureresultingfromgeneralcentre-to-limb
. variations(CLVs). Thesebecomeapparentwhenformingtheratiobetweenthestellarlightinandoutoftransit. Thesephenomena
h
canbeseenparticularlyclearlyduringtheprogressofapenumbrallunareclipse,wheretheEarthtransitsthesolardiskandmasks
p
differentregionsofthesolardiskastheeclipseprogresses. Wheninferringthepropertiesoftheplanetaryatmosphere,itisessential
-
o thatthiseffectoriginatingatthestarisproperlyaccountedfor. Usingthedataobservedfromthe2014-April-15lunareclipsewith
r theESPaDOnSspectrograph mountedontheCanadaFranceHawaiiTelescope(CFHT),wehaveobtainedforthefirsttimeatime
t
s sequence of the penumbral spectra. These penumbral spectra enable us tostudy thecentre-to-limb variations of solar Fraunhofer
a lineswhentheEarthistransitingSun. TheNaiandCaiiabsorptionfeaturesreportedfrompreviouslunareclipseobservationsare
[ demonstrated to be CLV features, which dominate the corresponding line profiles and mask possible planetary signal. Detecting

atmosphericspeciesinexoplanetsviatransitspectroscopymustaccountfortheCLVeffect.
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v Keywords. planetsandsatellites:atmospheres–eclipse–Earth
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0
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1. Introduction isingtheatmospheresoftheseterrestrialexoplanetsisnotwithin
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thereachofcurrentinstrumentation,thedetectionofsometheir
0
.With the discovery of almost 2000 exoplanets in the last atomicandmolecularcomponentsisverylikelytobecomepos-
1two decades, the characterisation of their atmospheres has be- siblewiththenextgenerationoflargeground-andspace-based
0come a new and rapidly-evolving field. Different atomic, telescopes(Hedeltetal.2013). TheEarthitselfcanbeusedasa
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ionic, and molecular species have already been detected in benchmarkforthefuturedetectionofEarth-likeexoplanets,for
1
exoplanet atmospheres. Using Hubble Space Telescope data, example,usinglunareclipsestoobtainthetangentiallong-path
:
vCharbonneauetal. (2002) detected sodium in the atmosphere transmissionspectrumoftheEarth’satmosphere.
iof HD 209458b for the first time by comparing the Nai dou-
X Severallunareclipseobservationshavebeenmadewiththe
blet absorptionlines in and out of transit. Snellenetal. (2008)
aimofobtainingthetransmissionspectrumoftheEarth’satmo-
rthenconfirmedtheNaiabsorptioninHD209458busingground-
a sphere.Someofthesehavereportedtheanomalousbehaviourof
based telescope data. Sodium has also been detected in sev-
certain atomic absorption features. Palléetal. (2009, hereafter
eralothergiantexoplanetssuchasHD189733b(Redfieldetal.
P09)observedthelunareclipseof16August2008,andobtained
2008) and WASP-17b (Woodetal. 2011). Potassium was de-
transmission spectra from the umbral lunar eclipse. In P09’s
tectedinHD80606b(Colónetal.2012)andXO-2b(Singetal. spectra,theCaiiabsorptionfeaturesaredetectedandweakNai
2011),whileFossatietal.(2010)reportedthedetectionofMgii
absorptions also appear. Vidal-Madjaretal. (2010, hereafter
in WASP-12b. All of these used transmssion spectroscopy
V10)observedthesamelunareclipseasP09,buttheyretrieved
during transits. Molecular features have also been detected
the transmission spectrum from the penumbral rather than the
in exoplanet atmospheres, such as H O (Grillmairetal. 2008),
2 umbral eclipse. In V10, the authors detected relatively strong
CO (Brogietal. 2012), CO2 (Swainetal. 2009), and CH4 Nai D lines absorption but no Caii absorption. Arnoldetal.
(Swainetal.2008).
(2014, hereafter A14) observed the penumbrallunar eclipse in
In recent years, nearly 100 Earth-sized or smaller exoplan- December2010andtheirresultsaresimilartothoseofV10,i.e.
ets have been discovered, one of them being in the habitable Nai absorption is detected while Caii is not. Yanetal. (2014)
zoneofitshoststar(Quintanaetal.2014). Althoughcharacter- observedthelunareclipseofDecember2011andneithertheNai
Articlenumber,page1of9
northeCaiiabsorptionfeaturesaredetectedinthetransmission
spectrumobtainedfromtheumbraleclipse.
The interpretation of these discrepancies is not straightfor-
wardsincetheEarth’stransmissionspectrafromtheseobserva-
tions are retrievedusing differentmethods. Althoughthere are
Nai,Cai,andCaiilayersintheEarth’sionosphere,accordingto
ourresearch,theNaiorCaiiabsorptionfeaturesintheobserved
Earth’s transmission spectra are probably due to the centre-to-
limb variation (CLV) of the solar lines rather than the absorp-
tionsintheEarth’satmosphere.
ThestrongsolarFraunhoferlineshaveprominentvariations
in both line intensity and profile from centre to limb cross the
solar disk. Athayetal. (1972) used the Fei line’s CLV spec-
trumto generallyinterprettheCLV effect. Formoststrongso- Fig.1. AschematicofapenumbraleclipseasseenfromtheMoon.
lar Fraunhoferlines, the normalisedspectralline fromthe cen- HerePenumbraAandPenumbraBrepresenttheviewsfromtwodiffer-
tre disk is deeper than that from the limb. The observed CLV entpenumbrallocations(indicatedinFig.2).
features are used to understand detailed solar physics and to
guide the modelling work. For example, AllendePrietoetal.
(2004)observedtheCLVofsolarlinesandusedthistotestnon- Moon),itistheintegrationoftheentiresolardisk. Theumbral
Local ThermodynamicEquilibrium line formation calculations spectrumresults from the integratedlight of the solar disk that
and Koesterkeetal. (2008) used the CLV data to test 3D solar is refracted by the Earth’s atmosphere into the umbral shadow
hydrodynamicsimulations. (GarcíaMuñozetal.2012). Thelineshapeintheumbralspec-
Since a lunar eclipse shares similarities with an exoplanet trumvaries,dependingonwhichpartofthesolardiskhasbeen
transit, this CLV effect can also be present in transit spectra. refracted. However, the line shape difference between the um-
The corresponding features will be considerably weaker since bralspectrumandthebrightMoonspectrumisrelativelysmall,
theplanetonlyblocksasmallfractionofthestellarsurfacedur- andthepenumbralspectrumexhibitssignificantdifferences(see
ingtransit. However,theCLVeffectcanstillhaveaninfluence Fig.3fordetails).
ontheinterpretationofatomiclinedetectionsinexoplanetatmo-
spheresandshouldbeproperlytreated.
2.1.TheApril2014lunareclipseobservations
For the detection of sodium in HD 209458b,
Charbonneauetal. (2002) considered the CLV in the Nai Weusedthefiber-fedESPaDOnSspectrographmountedonthe
D lines and concludedthat the contributionwas small for their CanadaFranceHawaiiTelescope(CFHT)forourobservations.
observation. Redfield et al. (2008) modelled the CLV effect The spectrograph covers a wavelength range of 370–1050 nm
on the Nai D lines in HD 189733b (the CLV is referred to in a single exposure. The ‘object only’ mode was used to
as differential limb darkening in their paper), and the model achievehighspectralresolvingpower(averageresolution:λ/∆λ
shows that this contributionis much smaller than the observed ∼ 81,000). The observation began when the Moon was in the
Nai absorption. However,for stellar lines that have significant Earth’s umbra and lasted until the Moon was fully out of the
CLV effects or if the observation is performed at high spectral Earth’sshadow.Weusednon-siderealtrackingtolocatethefiber
resolution,thiseffectcouldbecomeimportant. at the Eudoxus crater during the entire observation. The Eu-
We observedthelunareclipseinApril2014andobtaineda doxuscrater is chosen because it enables us to access different
set of spectra at differentstages of the eclipse. The changesin phases of the umbraleclipse as its trace is close to the umbral
thesolarlineprofilescausedbytheCLVcanclearlybeseenin center. Fig. 2 shows the trace of Eudoxus with respect to the
ourdata. InSection2,weuseourlunareclipsedatatodemon- Earth’s shadow. We obtained a sequence of spectra from the
stratethiseffectandcompareitwiththesolarspectralAtlas. In umbra,penumbra,andbrightMoon,andweperformedthestan-
Section 3, the Nai and Caii features observed in previous lu- dard data reductionprocedureusing the CFHT Upena pipeline
nareclipseobservationsarecomparedwiththespectralfeatures 1.
causedbyCLV.InSection4,wefurtherdiscusstheCLVeffect Thepenumbralspectralsequenceconsistsofabout60spec-
on exoplanettransit spectroscopy. The telluric sodium absorp- trafromdifferentpenumbrallocations,enablingustostudythe
tion and the Raman scattering in lunar eclipse spectra are also line shape change. We labelthe locationclose to the umbraas
discussedinSection4. PenumbraAandthelocationclosetothebrightMoonasPenum-
braB(Fig.1 andFig.2).Fig.3showsthechangesoftheHαline
profile.Thespectrainthisfigurearetheratiosofthepenumbral
2. TheeffectofCLVonlunareclipseobservations
spectra to a bright Moon spectrum. The bottom of this figure
A penumbral lunar eclipse happens when the Moon enters the showstheratioofatypicalumbraltothebrightMoonspectrum
Earth’s penumbral shadow. An observer on the Moon in the forcomparison.
penumbra would see the Earth blocking different parts of the Atthebeginningofourpenumbraleclipseobservation(cor-
solar disk (as shown in Fig. 1). Thus the penumbral spectrum responding to Penumbra A), the line shape is generally shal-
comprises the integrated spectrum of the Sun, which is partly lower than that in the bright Moon spectrum, which results in
eclipsedbytheEarth.Whenobservingdifferentlocationsonthe the ‘emission’ feature in Fig. 3. As the eclipse proceeds, the
Moon in the Earth’s penumbra, the observed spectra are inte- Hα line becomes deeper. When the observed location is close
gratedfromdifferentpartsofthesolardisk.Sincethesolarlines to Penumbra B, the Hα line becomes the deepest, even deeper
vary in profile from the centre to limb, the line profiles in the thaninthebrightMoonspectrum.AsthischangeoftheHαline
penumbralspectravaryastheeclipseproceeds.Forthespectrum
observedfromtheun-eclipsedMoon(whichiscalledthebright 1 http://www.cfht.hawaii.edu/Instruments/Upena/
Articlenumber,page2of9
F.Yan etal.:Thecentre-to-limbvariationsofsolarFraunhoferlinesimprinteduponlunareclipsespectra
1.2
1.1
1.0 Penumbra A
o
ati
r
0.9
Penumbra B
0.8
Umbra
Fig. 2. The trajectory of the observed Eudoxus crater for the 15
April 2014 lunar eclipse. The arrow on the trajectory indicates the 0.7
moving direction of the crater. Here we choose two points on the 6500 6520 6540 6560 6580 6600 6620
trajectory (A and B) to indicate different eclipsing stages. Point A Wavelength(Å)
andBcorrespondtothePenumbraAandPenumbraBviewssketched
in Fig. 1. The figure is reproduced from the NASA eclipse website
Fig.3. ThechangeofHαlineshapeindifferentpenumbraspectra.The
(http://eclipse.gsfc.nasa.gov/lunar.html).
spectraaretheratiosofthenormalisedpenumbraltobrightMoonspec-
tra.Theratiosareshiftedsequentiallyby0.02forclarity.Eightpenum-
bralspectrawhichweretakeneverytenminutesarechosentorepresent
shapeiscorrelatedwiththeeclipsegeometry,weconcludethat
differentpenumbrallocations. Theupperspectrumcorrespondstothe
itresultsfromtheCLVeffect.
penumbral positionclosetotheumbra(PenumbraAinFig.2), while
Sincepreviousstudiesof lunareclipse observationsuse the
thelowerspectrumcorrespondstothepositionclosetothebrightMoon
penumbral spectrum obtained at a position close to the umbra
(PenumbraBinFig.2).Thenormalisedratiooftheumbraltothebright
(i.e. PenumbraA),wewillonlydiscussthistypeofpenumbral Moonspectrumisalsoshown atthebottomof thefigureforcompar-
spectrumbelow. ison. Thisumbral spectrum isthe sumof seven individual exposures
thatweretakenatpositionsclosetotheedgeoftheumbra(i.e.closeto
PenumbraA).Thetotalobservedtimeforthisumbralspectrumisabout
2.2.CLVfeaturesinthespectrum 20minutes. Theumbral spectrumhasarelativelylowsignal-to-noise
ratioandstrongtelluricabsorptionlines.Theradialvelocitydifferences
Fig. 4a displaysthe ratio of an observedpenumbralto a bright
betweenthesespectrahavebeencorrected.
Moonspectrum. Herethepenumbralspectrumwastakenwhen
theobservedlocationwasclosetotheumbra,whichmeansthe
penumbral spectrum is mainly from the limb part of the solar
disk (correspondingto Penumbra A in Fig. 1). In contrast, the nounced than in the adjacent continuum (Athay 1972). The
brightMoonspectrumis from the wholesolar disk andso it is continuumlimbdarkeningismoreprominentatblue/UVwave-
themixoflimbandcentresolarspectra. Thisspectralratiocan lengthsbecauseoftheamplificationofthetemperatureinduced
therefore be qualitatively regarded as the limb to centre spec- intensityvariationintheWienside(shortwavelengthregion)of
trumplusaconstant. ItcanbeseeninFig.4athatthesolarline theblackbodycurve.ThisalsomakesthemeanCLVfeaturesbe-
featuresclearlyshowupespeciallytowardsthebluepartofthe comemoresignificantforthelineslocatedattheblue/UVwave-
spectrum.StrongabsorptionlinessuchastheCaiiT(Caiinear- lengths.
infraredtriplet),CaiiH&K,Hα,Hβ,andtheMgiblinesappear InadditiontothegeneralCLVfeaturesdescribedabove,the
prominentlywhiletheNaiDlinesfeaturesarerelativelyweak. detailedprofilehas a complicatedstructure, whichdiffersfrom
To better demonstrate the CLV effect in a lunar line to line. Forexample, the line core becomesbroaderin the
eclipse, the solar spectrum from the Kitt Peak Solar Atlas limbspectrumthaninthecentrespectrum,whichmakestheline
(Brault&Testerman 1972; Kurucz 2005) is used as a compar- coreCLVfeaturedifferfromthatofthelinewing. Thiscanbe
ison. TheAtlascomprisestwo setsof spectra: oneobservedat seenforexampleintheCaiiTandNaiDlinesshowninFig.5
thecentreofthesolardiskwithµ = 1.0(whereµ = cos(θ),θis and 6. The line core CLV is due to the Doppler broadening,
the angle between the normal to the solar surface and the line whichis strongerin the limbthanin the centrespectrum. This
of sight)andthe otherat a limbpositionwith µ = 0.2. All the differentialDopplerbroadeningmaybe interpretedeitherasan
spectra were taken when the Sun was quiet. The ratio of the increasedDopplervelocitywithheightorasananisotropyinthe
centre to limb Solar Atlas is shown in Fig. 4b and one can see Dopplervelocityfieldwherethehorizontalvelocityexceedsthe
thattheoverallfeaturesareverysimilartothoseinFig.4a. verticalvelocity(Athay1972). Othersolar phenomenasuchas
ThesegeneralfeaturesshowthatthestrongFraunhoferlines theconvectivemotionofthegranules(Dravins1982) alsocon-
aredeeperinthecentrethaninthelimbspectrum,whichmeans tribute to the detailed CLV features, but these are beyond the
the mean limb-darkening within the spectral line is less pro- scopeofthispaper.
Articlenumber,page3of9
Fig.4. (a)TheratioofapenumbralspectrumtoabrightMoonspectrumobservedonApril152014byCFHT.Thesolarlinesfeaturesremain
intheratiospectrum. ThedataisbinnedtoalowresolutionandtheRVdifferencebetweenthetwospectrahasbeencorrected. Thedashedline
regioniswherethetelluricH OandO linesareprominent.Theyarenotshownhereasweconcentrateonthesolarspectralfeature.(b)Theratio
2 2
ofthelimbsolarspectrumtothecentresolarspectrum.ThedataarefromtheKittPeakSolarAtlasandbinnedtoalowresolution.
3. CaiiandNaifeaturesinlunareclipse 3.1.CaiiandNaifeaturesinpreviouslowspectralresolution
observations observation
Palléetal. (2009) observed the 16 August 2008 lunar eclipse
Since ionised calcium and neutral sodium are present in the at a relatively low resolution (6.8 Å in the optical wavelength
Earth’s ionosphere and previousstudies of lunar eclipse obser- range). Theyregardedthepenumbralspectrumasthereference
vationsclaimedthe detectionof theirabsorptionlines, itis im- spectrumandobtainedtheEarth’stransmissionspectrumbyus-
portanttounderstandhowthesolarCLVaffectstheirdetections ingtheratiooftheumbraltothepenumbralspectrumtocancel
in the Earth’s transmission spectrum. For the CLV of the Caii out the solar spectral features. However, because of the CLV,
Fraunhoferlines(e.g.theCaiiTandCaiiH&K),wechoosethe thesolarabsorptionlineprofilesaredifferentintheumbraland
Caii 8662Å line as a demonstration. Fig. 5 shows the 8662Å penumbralspectra.Thesolarlineshapesintheumbralspectrum
line from both the Kitt Peak Solar Atlas and the CFHT lunar aresimilartothebrightMoonspectrumwhilethelineshapesin
eclipsedata.Theratioofthesolarlimbtocentrespectrum(mid- thepenumbralspectrumhaveasignificantCLVeffect. Thusthe
dle panel in Fig. 5) and the ratio of penumbra to bright Moon CaiiTandCaiiH&Klines,aswellastheweakNaiDlinesab-
spectrum(bottompanel)arequitesimilar. Fig.6showstheNai sorptionfeaturesinP09’stransmissionspectrum,aremostlikely
D lineat5889Å.TheCLVfeatureoftheNaiD lineissimilar tobetheresultoftheCLVeffect.
2 2
to,butmuchweakerthan,theCaiiTlines. Inthemiddlepanel Figure 7 shows the detailed features at the positions of the
ofthisfigure,theone Åresolutionspectrum(shownasthegreen CaiiTlines. Heretheratioofthecentretolimbspectrumfrom
line)smearsthefeature,indicatinghowtheinstrumentalresolu- theKittPeakSolarAtlas(Fig.7a) isusedtomimictheumbral
tioncanaffecttheobservedstrengthoftheCLVfeature. topenumbralspectralratio. OurCFHTdataarealsoshownfor
Articlenumber,page4of9
F.Yan etal.:Thecentre-to-limbvariationsofsolarFraunhoferlinesimprinteduponlunareclipsespectra
Fig.5. Thedetailedlineshapeof Caii8662Åline. Toppanel: the
Fig.6. ThesameasFig.5butforNaiD lineat5890Å.
limbandcentrespectrafromtheKittPeakSolarAtlas. Middlepanel: 2
the ratio of the limb to centre Kitt Peak spectrum. The green line is
samedataconvolvedto1 Åresolution. Bottompanel: theratioofthe TheNaiD line featuresarerelativelyweakin P09. Thisis
penumbratobrightMoonspectrumfromCFHTlunareclipsedata(the
interpretedasCLVfeaturesoftheNaidoubletbeingweakerthan
samedatasetasshowninFig4a).
other strong Fraunhofer lines and consequentially not strongly
apparentatlowresolution.
comparison. Fig. 7b is the ratio of the bright Moon spectrum 3.2.Naifeaturesinprevioushighspectralresolution
to the penumbral spectrum from the CFHT observation and it
observations
showsabehaviourverysimilartothatconstructedfromtheSolar
Atlas. Fig.7dshowsthesamedataasinFig.7bbutconvolved Vidal-Madjaretal. (2010) observed the 16 August 2008 lunar
totheresolutionoftheP09data. ItisclearthattheCLVfeature eclipsewithhigh-resolutionspectroscopyandtheyobtainedthe
intheCFHTdataissimilartothespectruminP09(Fig.7c). transmissionspectrumbyusingtheratioofthepenumbraltothe
Articlenumber,page5of9
brightMoonspectrum.Intheirresultingtransmissionspectrum,
theNaiDfeaturesarenotwellcancelledoutandthezerolevel
shift (an offset of the spectral counts) is applied to correct the
broad features at Nai D positions (Fig. 10 in V10). This cor-
rectionresultsinadeeper‘absorption’featureatthelinecentre,
which the authorsinterpretto be the atomicsodium absorption
oftheEarth’satmosphere.However,weconcludethatthisisthe
CLV featureof the Nai D lines and the featureat the line core
originatesfromthedifferentialDopplerbroadeningbetweenthe
centreandlimbsolarspectraasdiscussedinSection2.2.
Arnoldetal. (2014) observed the 21 December 2010 lunar
eclipse with two high-resolution ESO spectrographs: HARPS
andUVES.TheyappliedasimilarmethodasV10andobtained
the high-resolution transmission spectrum from the penumbral
spectrum. IntheresultingtransmissionspectrumfromHARPS,
the Nai D features occur (Fig. 9 in A14) and the authors use
a Raman scattering modelto correctthe broadsignature of the
linewing(theRamanscatteringwillbediscussedinthenextsec-
tion). Thiscorrectionagainresultsinadeeper’absorption’fea-
tureatthelinecore,whichissimilartotheresultinV10. They
also applied a wavelength-dependentlimb darkeningto correct
thepenumbralspectrum.Thelimbdarkeningtheyusedisalow-
resolutionmodel(severalnanometres),thusitonlycorrectsthe
limb darkening of the continuum while the CLV of the Nai D
line remains in the ratio of the penumbral to the bright Moon
spectrum.
WereanalysedtheHARPSdatafromthe21December2010
lunar eclipse using the ratio of the bright Moon to penumbral
Moon spectrum to simulate the effective altitude calculation
method(Equation2inA14). Fig.8showstheresultofoursim-
ulation. The top panel is the original ratio of the bright Moon
tothepenumbralMoonspectrum. Thisissimilartothebottom
figure of Fig. 16 in A14. The middle panel is the ratio spec-
trum after the radial velocity (RV) correction. The RV differ-
encebetweenthebrightMoonandthe penumbralMoonisdue
tothemotionbetweentheEarth,Moon,andSun,aswellasthe
Rossiter-McLaughlineffect(Yanetal. inpreparation). Wecor-
rectthisRVdifferencetoperfectlyalignthesolarspectrallines. Fig. 8. The CLV features in the Nai D lines. Top panel: ratio of
AftertheRVcorrection,theCLVfeatureoftheNaiDlinesap- thebrightMoontopenumbralspectrumfromtheHARPSobservation
pearsclearly,andissimilartoFig.9inA14. Thebottompanel inDecember2010. Middlepanel: sameastop,exceptwiththeradial
inFig.8istheratioofthecentretolimbspectrumfromtheKitt velocitycorrectionsapplied.Bottompanel:thecentretolimbspectrum
fromtheKittPeakSolarAtlas.
Peak SolarAtlas andit correspondsclosely to the featurefrom
thelunareclipseobservation.
In fact, the Nai D feature in V10 is basically the same as
thatinA14exceptatalowerresolution.AsthespectrumofP09 of NaiDdoublet. BelowwequantitativelydiscusstheRingef-
isin a muchlowerresolution,theNaiD featurein P09isonly fectcontributioninboththeumbralandpenumbralspectra.
marginally observed. By comparing the Nai D feature in the GarcíaMuñoz&Pallé (2011) modelled the forward-
threepapers,wecanseethattheappearanceoftheCLVfeature scatteredsunlightspectrumduringa lunareclipse. Theirresult
isaffectedbythedataanalysismethod,spectralresolution,and shows that, at wavelength around Nai D doublet, the typical
theradialvelocitycorrection. amount of the forward-scattered sunlight received at the lunar
surface is 2×10−7 of the flux from the unobstructedSun (i. e.
the bright Moon). The amount here is for the atmospheric
4. Discussion model containing molecular and aerosol scattering and O
3
absorption, i. e. model dIII in GarcíaMuñoz&Pallé (2011).
4.1.Theforward-scatteredsunlightandtheRingeffect
In order to estimate the contribution of the scattered light, we
The forward-scattered sunlight from the Earth’s terminator at- use our CFHT observation to generate an eclipse light curve.
mosphere also contributes to the irradiance of the eclipsed Fig. 9 shows the observed fluxes, which are normalised to a
Moon(Link1972;Vollmer&Gedzelman2008).Intheforward- bright Moon spectrum taken at the meridian. The flux of the
scattered sunlight, there is a Raman scattering component that forward-scattered sunlight can be regarded as constant since it
transferscontinuumphotonsintoasolarabsorptionlinetomake is a diffuse component and the scattering angle changes little
the scattered line shallower. This filling-in of Fraunhoferlines duringthe eclipse. Itis clearthatthescattered lightproportion
iscalledtheRingeffect(Grainger&Ring1962)andcanchange is larger for an eclipse spectrum taken at a position close to
thesolarlineshapeinalunareclipsespectrum(Yanetal.2014). the umbral center where the irradiance of the lunar surface is
ThisRingeffectwasemployedbyA14tocorrectthelineshape small. For the umbral spectrum, the scattered light proportion
Articlenumber,page6of9
F.Yan etal.:Thecentre-to-limbvariationsofsolarFraunhoferlinesimprinteduponlunareclipsespectra
Fig.7. TheCLVfeaturesintheCaiiTlines.(a)Topleft:ratioofthecentretolimbspectrumfromtheKittPeakSolarAtlas.(b)Topright:ratio
ofthebrightMoonspectrumtothepenumbralspectrumfromourCFHTdata.(c)Bottomleft:theCaiiTfeatureinP09’stransmissionspectrum.
(d)Bottomright:thesameas(b)exceptconvolvedtotheresolutionofP09data.
can range from 0.01 to 10−4. For the penumbral spectrum, 4.2.TelluricSodiumabsorption
the proportion is determined mainly by the portion of the
unobstructedsolar disk and rangesfrom 10−4 to 2×10−7. For ThesodiumlayerexistingintheEarth’suppermesosphereorig-
example, the amount of scattered light is on the order of 10−5 inatesfrommeteoroids(Plane2003). SincethesodiumD2−D1
doubletareresonancelines, their absorptionfeaturesshouldbe
for Penumbra A (Fig. 1) where about 1/6 of the solar disk can
imprintedon the transmission spectrum if there is a significant
beseen.
sodiumlayerintheobservedatmosphere. UsinganaverageNa
concentration profile measured by Fussenetal. (2004) and the
Intheforward-scatteredsunlight,therotationalRamanscat- cross-sectiondatain Fussenetal. (2010), we areableto model
tering transfers a few percent of the continuum photons into theNa absorptionforthe integratedEarthatmosphere. TheNa
theFraunhoferlinesatUVtoopticalwavelengths(Noxonetal. transmissionspectrumforeachtangentialpathwithaminimum
1979;Langfordetal.2007). Foraneclipsespectrumtakenclose atmosphericaltitudeiscalculated,andthenthespectrawiththe
to the umbral center, this Raman scattering transfers roughly minimum altitudes from 0 km to 120 km are integrated to ob-
10−4 of the continuum into the lines after taking the forward- taintheintegratedabsorptionspectrum. Thismodelledabsorp-
scatteringsunlightproportioninthetotalirradianceintoaccount. tionspectrumisconvolvedtotheinstrumentalresolutionforES-
Thespectratakenatapositionawayfromtheumbralcenterwill PaDOnS/CFHTandtheequivalentwidthoftheD lineiscalcu-
1
have a lower filling-in effect. Here the estimation is for wave-
latedtobe0.007 Åwithamaximumabsorptiondepthof0.08.
lengthsaround600nm,however,thefilling-ineffectcanbesig-
As stated before, the penumbralspectrumis predominantly
nificantlystrongerattheblueorUVwavelengthswheretheto-
the directsunlightwith a small componentof light transmitted
talumbralirradianceislowerand consequentiallytheforward-
fromtheEarthatmosphere. Theactualratiobetweenthedirect
scattering proportion is larger. For a penumbral spectrum like
sunlightandtransmittedsunlightdependson the portionof the
Penumbra A, the Raman scattering transfers less than 10−6 of
solar disk that is not occulted by the Earth. Fig. 10 shows an
thecontinuumphotos,whichisanegligibleamount.
exampleofthetheoreticalNaabsorptionfeatureinapenumbral
spectrumwhen1/6ofthesolardiskcanbeseen(i.e. similarto
Fromtheaboveestimates, we concludethatthe Ring effect thePenumbraAinFig.1). TheCLVfeatureofthecorrespond-
can be important in the umbra especially for the spectra taken ingpenumbraltobrightMoonratiospectrumisalsoshownfor
closetotheumbralcenter,andthelineshapeofthestrongFraun- comparison.
hofer line is affected by both the Ring effect and CLV effect. WeemphasisethattheCLVfeaturesshownherearefromob-
However,thelineshapeinthepenumbralspectrumisdominated servations,notatheoreticalmodel. Itisdifficulttotheoretically
bytheCLVeffect,andtheRingeffectcanbesafelyignored. model the precise line profile for a given penumbral spectrum
Articlenumber,page7of9
4.3.TheCLVeffectinexoplanettransits
The standard way of detecting atomic or molecular species in
anexoplanetatmosphereisbyobservingthecorrespondingab-
sorption lines in and out of transit. Charbonneauet al. (2002)
detected Nai for the first time in an exoplanet atmosphere us-
ing the transit spectro-photometricmethod. They observedthe
spectra of the Nai D lines in HD 209458while the planetwas
transitingthestarandcomparedthiswithdataoutoftransit.The
absorptiondepthofNaiDlinesintransitwasseentobedeeper
thanthatoutoftransit, whichindicatestheexistenceofneutral
sodiumsomewhereintheplanetaryatmosphere.Sincetheplanet
blocks different parts of the stellar disk during the transit, the
CLVeffectofthestellarlinesneedstobeconsideredwhencom-
paringthe line depths. Charbonneauetal. (2002) modelledthe
effectoftheCLVoftheNaiDlinesandfoundthedifferenceof
theabsorptiondepthbetweenin-transitandout-of-transitcaused
bytheCLVeffecttobe1.5×10−5forabandwidthof12Å(5887–
5899Å). Thisvalueisatthelevelofphoton-noiseanditseffect
Fig.9. Fluxofthelunareclipsespectrumandtheforward-scattered ontheNaidetectionintheatmosphereofHD209458bisnegli-
sunlight.Thegreenlineisthetotalobservedcountspersecondbetween giblegiventhattheactualobserveddifferenceoftheNaiDlines
550–650 nm of the 292 lunar spectra that were observed with CFHT
depthis −23.2×10−5. Thusitis safe to ignorethe CLV effect
duringthe2014-Apr-15lunareclipse. Thenumbersarenormalisedto
a bright Moon spectrum taken at the meridian. The plot can be ap- fortheNaidetectionwithabroadbandwidthlike12Åusedin
proximatelyregardedasthelightcurveoftheeclipsedMoon,whichis Charbonneauetal.(2002). However,ascanbeseenfromFig.6,
normalised to the flux of the unobstructed Sun (i. e. the flux for the the Nai D line CLV feature is prominent in a high-resolution
bright Moon). Theblack solidlineistheestimatedforward-scattered spectrumanda12ÅbandwidthwillsmeartheCLVfeature. If
sunlightfromGarcíaMuñoz&Pallé(2011)andtheamountusedhere the observationis performedat a higher resolution that can re-
is2×10−7ofthefluxfromtheunobstructedSun.
solvethelineprofilewell,andanarrowerbandwidthisused,the
NaiDCLVfeaturewouldbecomemoreprominent.
Ascanbeseenfromthesolarlimbtocentreratiospectrumin
Fig.4b,theNaiDCLVfeatureisrelativelyweakandbecomes
more significant for other strong Fraunhofer lines such as Hα
andCaiiH&K.ObservationsatblueandUVwavelengthsshould
dealmorecarefullywiththeCLVsincetheeffectbecomesmore
prominentatshorterwavelengths.
Late-type dwarf stars are thought to be promising targets
forexoplanetatmospheredetectionbecausetheplanetarytransit
depthislargerduetotherelativelylargeplanet-starradiusratio.
However, the CLV of the strong molecular absorption lines in
these stars could affect the correspondingmolecular detections
inexoplanetatmospheres. Fig.11showstheCObandCLVfea-
tureinanM-typedwarfcalculatedfromaKuruczgridmodel2.
Fromthemodel,wefindthattheCObandisdeeperinthelimb
spectrumthaninthecentrespectrum.Thisindicatesthatwhena
planettransitsthecentrepartofanM-typedwarf,theCOband
in the observedspectrumwill be deepercomparedto the spec-
trum out of transit, which could potentially be interpreted as a
planetaryCOabsorptionfeature.
We are currently performing a more detailed quantitative
Fig.10. TheoreticaltelluricNaabsorptionandtheCLVfeatureforthe
NaiD line(5896Å). ARVcorrectionhasbeenappliedtotheCFHT analysis of the CLV effect during exoplanet transits. Here we
1
spectra.TheCLVfeaturestilldominatesthelineprofileinapenumbral mentionthreegeneralaspectsthataffectthestrengthoftheCLV
spectrum,whichmakesthetelluricNaabsorptiondifficulttodetect. feature. The first concerns the star itself. The CLV effect de-
pendsonthe physicalparametersandthechemicalabundances
of the star so that different stellar types and different spectral
lines will exhibit different CLV signatures. The second aspect
is the geometry of the planet transit system, including both
becausethelineprofilechangesquicklywithtimeastheeclipse the planet-to-star radius ratio, which determines the obscured
proceeds(asdemonstratedinFig.3withHα).AlsotheRossiter- proportion of the stellar disk and the impact parameter of the
McLaughlineffectandtheconvectiveblueshiftcontributetothe planet’s transit trajectory on the stellar disk. The planet will
changeof the lineprofileandthe line position. Thus, although transit only the limb part of the stellar disk if b is close to 1
thetelluricsodiumdoubletshouldtheoreticallybepresentinthe (bistheimpactparameterintheunitofthestellarradius),while
penumbralspectrum,itsrelativelyweakabsorptionfeaturesare both the limb and the centre of the stellar disk will be blocked
maskedbythesignificantlineprofilechangeofthesolarsodium
doublet. 2 http://kurucz.harvard.edu/grids.html
Articlenumber,page8of9
F.Yan etal.:Thecentre-to-limbvariationsofsolarFraunhoferlinesimprinteduponlunareclipsespectra
Acknowledgements. ThisresearchusesdataobtainedthroughtheTelescopeAc-
cessProgram(TAP),whichisfundedbytheNationalAstronomicalObservato-
ries,ChineseAcademyofSciences,andtheSpecialFundforAstronomyfrom
1.04 M0V spectral type
theMinistryofFinance. Thestudyissupported bytheNational Natural Sci-
limb/centre
enceFoundationofChinaundergrantsNos.11390371and11233004.Wethank
theCFHTteamfortheobservations. Theauthorsthanktherefereeforuseful
1.02 suggestions.FeiYanacknowledgesthesupportfromESO-NAOCstudentship.
o
ati 1.00
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ThisCLVeffectisespeciallyimportantforstudyingtheatom
or ion absorptions in the transmission spectrum of the Earth’s
atmosphere. For previous lunar eclipse observations, the Caii
absorptionfeatureinPalléetal.(2009)andtheNaiDlinesfea-
ture in Vidal-Madjaretal. (2010) and Arnoldetal. (2014) are
shown to be most likely due predominately to the CLV of the
correspondingsolarlines insteadof the Naior Caii absorption
intheEarth’satmosphere. AlthoughtherearevariableCaiiand
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their relatively weak absorption features is difficult because of
theCLVfeatures.
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or ion absorptions in exoplanet atmospheres using the transit
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features, thus future molecular detections in planets transiting
M-typestarsshouldemployanaccuratestellarmodel.
Articlenumber,page9of9