Properties of extrasolar planets and their host stars - a case study of HAT-P-7

0.94 MB·English

by  Vincent Van Eylen

Astron. Nachr./AN333,No.10,1088–1091(2012)/DOI10.1002/asna.201211832
Properties of extrasolar planets and their host stars –
a case study of HAT-P-7
V.VanEylen1,2,(cid:63),H.Kjeldsen1,J.Christensen-Dalsgaard1,andC.Aerts2
1 StellarAstrophysicsCentre,DepartmentofPhysicsandAstronomy,AarhusUniversity,NyMunkegade120,
DK-8000AarhusC,Denmark
2 InstituutvoorSterrenkunde,KatholiekeUniversiteitLeuven,Celestijnenlaan200B,B-3001Heverlee,Belgium
Received15August2012,accepted15August2012
3 Publishedonline3December2012
1
0
2 Keywords stars:individual(HAT-P-7)–stars:oscillations–planetarysystems–stars:fundamentalparameters

n DatafromtheKeplersatellite(Q0-Q11)areusedtostudyHAT-P-7.Thesatellite’sdataareextremelyvaluableforastero-
a seismicstudiesofstarsandforobservingplanetarytransits;inthisworkwedoboth.Anasteroseismicstudyofthehoststar
J improvestheaccuracyofthestellarparametersderivedbyChristensen-Dalsgaardetal.(2010),whofollowedlargelythe
8 sameprocedurebutbasedtheanalysisononlyonemonthofKeplerdata.Thestellarinformationiscombinedwithtransit
observations,phasevariationsandoccultationstoderiveplanetaryparameters.Inparticular,weconfirmthepresenceof
] ellipsoidalvariationsasdiscoveredbyWelshetal.(2010),butrevisetheirmagnitude,andwerevisetheoccultationdepth
R (Boruckietal.2009),whichleadstodifferentplanetarytemperatureestimates.Allotherstellarandplanetaryparameters
S arenowmoreaccuratelydetermined.
.
h (cid:13)c 2012WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
p
-
o
1 Introduction et al. (2010), based on early Kepler data (Q0-Q1). After
r
t the initial discovery of its exoplanet HAT-P-7b (Pa´l et al.
s
a TheKeplermissionwaslaunchedonMarch6,2009.Itwas 2008),phasevariationsandplanetaryoccultationsweredis-
[ designed explicitly to be able to detect earth-size planets, coveredinKepler’sQ0data(Boruckietal.2009),andcon-

1 includingthoseinthehabitablezone.Thedetectionmethod sequently the planetary temperature and atmosphere were
v forKeplertoachievethisgoalismeasuringplanetarytran- studied(Christiansenetal.2010;Spiegel&Burrows2010).
2 sits to a high level of photometric precision. To improve Additionalellipsoidalvariationswerelaterdiscoveredinthe
7
the chances of detection, a large number of stars have to light curve (Welsh et al. 2010) and the system is currently
4
bemonitoredforalongperiodoftime,preferablycontinu- the only planetary case where this effect has been found.
1
. ously.ItwasquicklyrealisedthatKeplerwouldalsoprovide HAT-P-7 has a surprising inclination angle: a study of the
1
extremelyvaluabledatatostudystellarpulsations.Datafor Rossiter-McLaughlineffectinradialvelocitydatahasfound
0
this purpose are obtained from a subset of the about 500 ittoberetrogradeorpolar(Winnetal.2009).Theseauthors
3
1 stars that are sampled every 58.8 seconds (short cadence), also suggest the presence of a third body. A study of tran-
: outofamuchlargersetofabout150000starsobservedat sit timings based on EPOXI data found no evidence of an
v
i arateof29.4minutes(Boruckietal.2008). additionalplanet(Ballardetal.2011).
X
Thesatelliteorbitsinanearth-trailingheliocentricorbit Here, we make a preliminary anaysis of the system
r (ETHO),witha55◦Sunavoidanceangle,andcontinuously basedonalmostthreeyearsofKeplerdata.Wederivestellar
a
observesapatchoftheskycentredontheCygnus-Lyrare- pulsation frequencies and perform an asteroseismic mod-
gion.Thedataareorganisedintoquarters;aftereachquarter elling to derive the properties of the host star. The plane-
thephotometerisrolled90◦tokeepthesolararrayspointed tary system is then studied making use of these newly de-
attheSun.Thiscausesa42hourdatagap(Haasetal.2010). terminedstellarproperties.
This work uses Q0-Q11 data of HAT-P-7, which has been
continuouslyobservedinKepler’sshortcadencemode.
2 Stellarproperties
HAT-P-7(KIC10666592,visualmagnitude10.46,spec-
traltypeF8)hasbeenidentifiedasaplanethostbyground-
Stellar pulsations cause temperature variations, which lead
based observations prior to the start of the Kepler mission
to flux variations. The frequencies are observed from the
(Pa´l et al. 2008). It is one of the most extensively studied
power spectrum. Different models are then compared with
star-planet systems known to date. A study of the stellar
the observed frequencies and the best fit leads to the stel-
pulsations has been carried out by Christensen-Dalsgaard
lar properties. The procedure followed here resembles the
(cid:63) Correspondingauthor:e-mail:[email protected] asteroseismic analysis of HAT-P-7 based on only the first
monthofKeplerdata(Christensen-Dalsgaardetal.2010).
(cid:13)c 2012WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
Astron.Nachr./AN(2012) 1089
Fig.2 Ane´chellediagramshowingtheobservedfrequen-
cies(red)andthebestmodel(blue).
µHz (compared to a previous accuracy of 1.4 µHz). They
areillustratedinFigure2.
Fig.1 Topfigure:oversampled(red)andsmoothedpower
spectrum(black),showingregularspacingsgovernedbythe 2.2 Modelling
asymptotic equation (eq. 1). Bottom figure (zoom): mode
identificationforthreeobservedfrequencies.Analgorithm Tocalculateevolutionmodelsandadiabaticoscillationfre-
determinesthemaximainthesmoothedspectrum,therele- quencies,weusetheAarhuscodes(Christensen-Dalsgaard
vant maxima (vertical lines) are selected manually making 2008a,b). Evolution tracks were calculated for a grid of
use of the asymptotic equation. Sometimes, an average of models with mass range 1.33-1.70 M(cid:12) and metallicity
twomaximaisused(e.g.l=2modeinthisfigure). 0.015-0.035.Theconvectivecorewasmodelledwithover-
shootinunitsofthepressurescaleheightofαov = 0,0.1
and0.2.Basedontheobservedlargeseparationanestimate
2.1 Observationsanddataanalysis ofthedensityisobtained(Whiteetal.2011),whichisused
to select relevant time steps in the stellar evolution tracks,
The raw Kepler data are detrended and normalised, and
forwhichfrequenciesarethencalculated.
transit-like features are removed using a specifically de-
Thecalculatedfrequenciesarecomparedwiththeobser-
signed median filter. The filtered photometry is then used
vations,aftercorrectingfornear-surfaceeffectsthatarenot
tocalculateapowerspectrum.Aspectrumwithasampling
modelledproperly.Theempiricalcorrectionlawisgivenby
rateof0.005µHzisused,whichmeansanoversamplingof
(Kjeldsenetal.2008):
about three times. A median filter with a period of 1 µHz
is used to smooth the power spectrum, to remove the fine (cid:20)ν (n)(cid:21)b
ν (n)−ν (n)=a obs , (2)
structure of the spectrum, caused by the finite lifetime of obs best ν
0
themodes.
whereν isareferencefrequencyandaandbareparameters
The location of individual frequencies is governed by 0
to be determined. In addition, we set ν (n) = rν (n),
theasymptoticequation(Tassoul1980): best ref
where r should be close to one as the reference model
(cid:18) 1 (cid:19) should be close to the initial best model. In practice, we
ν ≈∆ν n+ l+(cid:15) −δν . (1)
n,l 2 0l setb = 4.90(thesolarvalue)andwefindthebestfitforr
anda(foreachmodelindividually).Wecanthencalculate
In this equation, νn,l is the frequency with radial order n thereferencemodel,forcomparisonwiththeobservedfre-
andangulardegreel(neglectingrotationalsplittingsothere quencies. The best model is then picked by comparing the
is no dependence on m), and ∆ν and δν0l the large and observedfrequencieswiththecorrectedmodelfrequencies.
small separations while (cid:15) is an offset coming from second We use a χ2 minimisation to determine which model fits
order and near-surface effects. This theoretical relation is best:
used to identify the individual modes, from the smoothed
power spectrum. The entire procedure is illustrated in Fig- χ2 = 1 (cid:88)(cid:16)ν(obs)−ν(mod)(cid:17)2. (3)
(N −1)σ2 nl nl
ure1. ν nl
Wehavedetermined14(l = 0),13(l = 1)and16(l = The frequencies of the best model are shown together
2)frequencies,whichconstituteatotaloftenmorefrequen- with the observational frequencies in the e´chelle diagram
cies than the initial asteroseismic analysis (Christensen- inFigure2.Withtheexceptionofanumberoffrequencies
Dalsgaard et al. 2010). The frequencies were determined (between1200and1400µHz)forl=1,thefrequenciesare
with an average standard error estimated to be σ = 0.75 modelledverywell,resultinginχ2 =3.65.Gaussiannoise
ν
www.an-journal.org (cid:13)c 2012WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
1090 V.VanEylenetal.:Propertiesofextrasolarplanetsandtheirhoststars
Table 1 Parameters obtained for star (HAT-P-7) and its the bottom of the transit depends on the limb darkening,
planet(HAT-P-7b). modelledbyaquadraticintensityprofile(Winn2010):
HAT-P-7 I(X,Y)∝1−u (1−µ)−u (1−µ)2, (4)
1 2
Mass(M(cid:12)) 1.361±0.021 √
Z 0.01904±0.0015 with µ = 1−X2−Y2 and (X,Y) the coordinates on
0
[Fe/H] 0.13 aunitcircle.Thecoefficientsuk areconstantsdefiningthe
Age(Gyr) 2.19±0.12 precise shape of the limb-darkening law. We have simply
Radius(R(cid:12)) 1.904±0.010 used them as fitting parameters. The modelled transit is
Temperature(K) 6259±32 shown in Figure 3. We have also made a new estimate of
Density(g/cm−3) 0.2781±0.0017
theplanetarymass,usingtheradialvelocityvaluesderived
Luminosity(L ) 4.996±0.098
(cid:12) byPa´letal.(2008).
logg(cgs) 4.98±0.13
Ellips.var.d(ppm) 59±1
3.3 Phasevariations
HAT-P-7b
Orbitalperiod(d) 2.20473506(11)
Theplanetarysystemistidallylocked,whichcausesthestar
Orbitalinclinationi(◦) 86.68±0.14
toalways‘see’thesamesideoftheplanet,whileadistant
M (M ) 1.741±0.028
p J
observerseestheplanetarydaysideandnightsideatdiffer-
R (R ) 1.431±0.011
p J
T (K) 2470±10 ent times. However, for HAT-P-7 the situation is slightly
day
T (K) 1772±10 complicated. The close orbit of the planet has induced a
night
A 0.193±0.002 tidal distortion on the star: rather than being oblate due to
g
rotation, it has its longest axis towards the planet and the
shortestaxisperpendiculartotheorbitalplane.Thiscauses
ellipsoidal variations (which peak at phases near 0.25 and
was added to the observational frequencies to create 1000
0.75),whichshouldbeaddedtothephasevariations(Pfahl
differentfrequencysets.Foreach,thebestmodeliscalcu-
et al. 2008; Welsh et al. 2010). HAT-P-7 is the only cur-
latedandthestellarparametersarecalculated.Theaverage
rentlyknownsystemwithellipsoidalvariationscausedbya
andstandarddeviationoftheseparametersarepresentedin
planet.Wemodelthefluxthroughoutoneorbitalphaseas
Table1.
(cid:18)R (cid:19)2 sin(α)+(π−α)cos(α)
3 Planetaryproperties f(Φ,i) = A p (5)
g a π
cos(2α)
3.1 Period −d
π
Thetimeofeachindividualtransitismeasuredandusedto with the orbital phase Φ ∈ [0,1] taken as 0 at maximum
determine the planetary period. Assuming a perfectly Ke- radial velocity of the star, so that the phase angle α is de-
plerian orbit, we fit a straight line through all transit times fined as cosα = −sinisin2πΦ. The first part of f(Φ,i)
(taking gaps into account; whenever a transit is measured istheLambertlawforasphere(Charbonneauetal.1999),
incompletelyitisignored).Duetothelargeamountofmea- where A is the planetary albedo and a is the semi-major
g
sured transits (286), the period is determined very accu- axis. A non-zero value for d corresponds to the ellipsoidal
rately. An O-C plot has been calculated, which compares variations.WerefertoTable1forvaluesandtoFigure3for
the observed and the calculated transit times to look for a thebestfit.
gravitational influence from additional bodies in the sys-
tem.Nosinuisoidalpatternwasdetected,andvariationsare
3.4 Occultation
at the level of the observational error level for individual
transit times (≈ 0.00015 days). After the period has been When the planet moves behind the star, an occultation oc-
calculated,thetimeseriesisfolded(calculatedmodulothe curs. The depth δ (λ) gives information about the plan-
flux
period). etary dayside temperature. By combining the information
with the phase variations, we can also obtain the night-
side temperature. We approximate both star and planet as
3.2 Transitshape
ablackbodyanduse
From the folded time series, the transit is modelled. The (cid:18)R (cid:19)2 B (T )
transit duration determines the impact parameter, which is δflux(λ)= Rp Bλ(Tp), (6)
directly related to the orbital inclination. The transit depth ∗ λ (cid:63)
determinestherelativeplanetaryradius,whichcanbecom- where B (T) is the Planck function (Winn 2010), which
λ
bined with the stellar radius (derived in the previous sec- we integrate over the Kepler bandpass. The exact occulta-
tion),toobtaintheabsoluteplanetaryradius.Theshapeof tion depth is calculated by simply comparing the averages
(cid:13)c 2012WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.an-journal.org
Astron.Nachr./AN(2012) 1091
We have not been able to model a few frequencies prop-
erly (see Figure 2), a problem that did not present itself in
the earlier analysis by Christensen-Dalsgaard et al. (2010)
becauseofthefewerfrequenciesobserved,andalowerob-
servational accuracy. Ellipsoidal variations were found by
Welsh et al. (2010), and we confirm that the phase curve
cannot be fit without including this effect. Welsh et al.
(2010) find a variation of 37 ppm (no errors quoted, based
on Kepler Q0-Q1 data), which is considerably lower than
our value of 59 ± 1ppm. All planetary values have im-
provedaccuracy.Mostareingeneralagreementwithearlier
work. Our planetary temperatures are significantly lower
than all earlier temperature determinations (Borucki et al.
2009;Christiansenetal.2010;Pa´letal.2008;Welshetal.
2010).Theyallusedanoccultationdepthof130±11ppm
(Boruckietal.2009),which isalmosttwiceashighasthe
valuederivedinthiswork;theanalysiswasdonebasedonly
onKeplerQ0data,andthemodellingdidnotincludeellip-
soidal variations as they were not yet discovered in HAT-
P-7 at the time. On the other hand, the temperature in this
work assumes a blackbody, which is an oversimplification
andalsocausesthetemperatureerrortobeunderestimated.
Welshetal.(2010)andChristiansenetal.(2010)usedmore
realisticatmospheremodels,anditshouldbeinterestingto
seehowtheyareaffectedbytherevisedoccultationdepth.
This work shows the excellent quality Kepler can now
deliver, both for studying stellar pulsations and planetary
Fig.3 Aftertheplanetaryperiodisdetermined,theobser-
transits. Asteroseismology is likely to take up an increas-
vations(blue)arefolded.Thisallowsforadetailedstudyof
inglyimportantroleinstudyinghoststarsofexoplanets.
the planetary transit (top figure), phase variations (caused
by planetary day-nightside and ellipsoidal variations, mid- Acknowledgements. Theresearchleadingtotheseresultshasre-
dle figure), and planetary occultation (bottom). The black ceivedfundingfromtheEuropeanResearchCouncilundertheEu-
lineshowsadatafit,thecoloreddatapointsareusedincal- ropeanCommunity’sSeventhFrameworkProgramme(FP7/2007–
culatingtheoccultationdepth. 2013)/ERC grant agreements n◦227224 (PROSPERITY) and
n◦267864 (ASTERISK). Funding for the Stellar Astrophysics
CentreisprovidedbyTheDanishNationalResearchFoundation.
of data points inside and just outside the occultation, as WearegratefultotheentireKeplerteamfortheeffortsleadingto
shown in Figure 3. We find an occultation depth of 71.85 thishighlysuccessfulmission.
±0.23partspermillion.Weassumethatallplanetaryflux
comes from radiation (albedo zero), so the quoted temper- References
aturevalueisanupperlimit.Theindicatedaccuracyofthe
quotedtemperaturesshouldbeseenastheinternalerrorof Ballard,S.,Christiansen,J.L.,Charbonneau,D.,etal.2011,ApJ,
usingablack-bodyspectrumtodescribethespectrumofthe 732,41
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