|
arXiv:1001.0032v1 [astro-ph.SR] 30 Dec 2009Draft version November 15, 2018 |
|
Preprint typeset using L ATEX style emulateapj v. 08/22/09 |
|
ASTEROSEISMIC INVESTIGATION OF KNOWN PLANET HOSTS IN THE KEPLER FIELD |
|
J. Christensen-Dalsgaard1,2, H. Kjeldsen1,2, T. M. Brown3, R. L. Gilliland4, T. Arentoft1,2, S. Frandsen1,2, |
|
P.-O. Quirion1,2,5, W. J. Borucki6, D. Koch6, and J. M. Jenkins7 |
|
Draft version November 15, 2018 |
|
ABSTRACT |
|
In addition to its great potential for characterizing extra-solar p lanetary systems the Kepler mis- |
|
sionis providing unique data on stellar oscillations. A key aspect of Keplerasteroseismology is the |
|
application to solar-like oscillations of main-sequence stars. As an ex ample we here consider an ini- |
|
tial analysis of data for three stars in the Keplerfield for which planetary transits were known from |
|
ground-based observations. For one of these, HAT-P-7, we obt ain a detailed frequency spectrum and |
|
hence strong constraints on the stellar properties. The remaining two stars show definite evidence for |
|
solar-like oscillations, yielding a preliminary estimate of their mean dens ities. |
|
Subject headings: stars: fundamental parameters — stars: oscillations — planetary systems |
|
1.INTRODUCTION |
|
The main goal of the Kepler mission is to character- |
|
ize extra-solar planetary systems, particularly Earth-like |
|
planets in the habitable zone (e.g., Borucki et al. 2009). |
|
The mission detects the presence of planets through the |
|
minute reduction of the light from a star as a planet |
|
crosses the line of sight. Several observations of such |
|
reductions at fixed time intervals for a given star, and |
|
extensive follow-up observations, are used to verify that |
|
the effect results from planet transits and to characterize |
|
the planet. To ensure a reasonable chance of detection |
|
Keplerobserves more than 100,000 stars simultaneously, |
|
in a fixed field in the Cygnus-Lyra region. Most stars |
|
are observed at a cadence of 29.4 min, but a subset of |
|
up to 512 stars can be observed at a short cadence (SC) |
|
of 58.85s. Keplerwas launched on 6 March 2009 and |
|
data from the commissioning period and the first month |
|
of regular observations are now available. |
|
The very high photometric accuracy required to detect |
|
planet transits (Borucki et al. 2010; Koch et al. 2010) |
|
also makes the Keplerobservations of great interest for |
|
asteroseismic studies of stellar interiors. In particular, |
|
the SC data allow investigations of solar-like oscillations |
|
in main-sequence stars. Apart from the great astrophys- |
|
ical interest of such investigations they also provide pow- |
|
erful tools to characterize stars that host planetary sys- |
|
tems (Kjeldsen et al. 2009). |
|
In stars with effective temperature Teff<∼7000K we |
|
expect to see oscillations similar to those observed in the |
|
Sun (e.g., Christensen-Dalsgaard 2002), excited stochas- |
|
ticallybythe near-surfaceconvection. Theseareacoustic |
|
modes of high radial order; in main-sequence stars such |
|
1Department of Physics and Astronomy, Aarhus University, |
|
DK-8000 Aarhus C, Denmark: e-mail [email protected] |
|
2Danish AsteroSeismology Centre |
|
3Las Cumbres Observatory Global Telescope, Goleta, CA 93117 |
|
4Space Telescope Science Institute, 3700 San Martin Drive, B al- |
|
timore, MD 21218 |
|
5Canadian Space Agency, 6767 Route de l’A´ eroport, Saint- |
|
Hubert, QC, J3Y 8Y9 Canada (present address) |
|
6NASA Ames Research Center, MS 244-30, Moffett Field, CA |
|
94035, USA |
|
7SETI Institute/NASA Ames Research Center, MS244-30, Mof- |
|
fett Field, CA 94035, USAmodes approximately satisfy the asymptotic relation |
|
νnl≃∆ν0(n+l/2+ǫ)−l(l+1)D0 (1) |
|
(Vandakurov 1967; Tassoul 1980). Here νnlis the cyclic |
|
frequency, nis the radial order of the mode and lis |
|
the degree, l= 0 corresponding to radial (i.e., spher- |
|
ically symmetric) oscillations. Also, ∆ ν0is essentially |
|
the inverse sound travel time across the stellar diameter; |
|
this is closely related to the mean stellar density ∝angbracketleftρ∗∝angbracketright: |
|
∆ν0∝ ∝angbracketleftρ∗∝angbracketright1/2.D0depends sensitively on conditions |
|
near the center of the star; for stars during the central |
|
hydrogenburningphasethisprovidesameasureofstellar |
|
age. Finally, ǫis determined by conditions near the stel- |
|
lar surface. This regular form of the frequency spectrum |
|
simplifies the analysis of the observations, and the close |
|
relation between the stellar properties and the param- |
|
eters characterizing the frequencies make them efficient |
|
diagnostics of the properties of the star. This has been |
|
demonstrated in the last few years through observations |
|
of solar-like oscillations from the ground and from space |
|
(for reviews, see Bedding & Kjeldsen 2008; Aerts et al. |
|
2009; Gilliland et al. 2010a). |
|
Even observations allowing a determination of ∆ ν0 |
|
provide useful constraints on ∝angbracketleftρ∗∝angbracketright. With a reliable de- |
|
termination of individual frequencies ∝angbracketleftρ∗∝angbracketrightis tightly con- |
|
strained and an estimate of the stellar age can be ob- |
|
tained. This can greatly aid the interpretation of obser- |
|
vations of planetary transits (e.g., Gilliland et al. 2010b; |
|
Nutzman et al. 2010). We note that photometric obser- |
|
vations such as those carried out by Keplerare predom- |
|
inantly sensitive to modes of degree l= 0−2. As indi- |
|
catedbyEq.(1)thesearesufficienttoobtaininformation |
|
about the core properties of the star. |
|
Ground-based transit observations have identified |
|
three planetary systems in the Keplerfield: TrES-2 |
|
(O’Donovan et al. 2006; Sozzetti et al. 2007), HAT-P-7 |
|
(P´ al et al. 2008), and HAT-P-11 (Dittmann et al. 2009; |
|
Bakos et al. 2010). These systems have been observed |
|
byKeplerin SC mode. Their properties (cf. Table 1) |
|
indicate that they should display solar-like oscillations |
|
at observable amplitudes, and hence they are obvious |
|
targets for Keplerasteroseismology. Here we report the |
|
results of a preliminary asteroseismic characterization of2 Christensen-Dalsgaard et al. |
|
TABLE 1 |
|
Properties of transiting systems. |
|
Name KIC No Teff(K) [Fe/H] L/L⊙log(g) (cgs) vsiniSource |
|
(kms−1) |
|
HAT-P-7 10666592 6350 ±80 0.26±0.08 4 .9±1.1 4.07±0.06 3.8±0.5 (a) |
|
6525±61 0.31±0.07 4 .09±0.08 (b) |
|
HAT-P-11 10748390 4780 ±50 0.31±0.05 0.26±0.02 4.59±0.03 1.5±1.5 (c) |
|
TrES-2 11446443 5850 ±50−0.15±0.10 1.17±0.10 4.4±0.1 2 ±1 (d) |
|
5795±73 0.06±0.08 4 .30±0.13 (b) |
|
Note. — Sources: (a): P´ al et al. (2008); (b): Ammler-von Eif et al . (2009); (c): Bakos et al. (2010); (d): Sozzetti et al. (2007 ). In some |
|
cases asymmetric error bars have been symmetrized. |
|
the central stars in the systems, based on the early Ke- |
|
plerdata. |
|
2.OBSERVATIONS AND DATA ANALYSIS |
|
We have analyzed data from Kepler for three |
|
planet-hosting stars using a pipeline developed for |
|
fast and robust analysis of all Keplerp-mode data |
|
(Christensen-Dalsgaard et al. 2008; Huber et al. 2009). |
|
Each time series contains 63324 data points. SC data |
|
characteristics and minor post-pipeline processing are |
|
discussed in Gilliland et al. (2010c). In addition a limb- |
|
darkened transit light curve model fit has been removed |
|
and 5-σclipping applied to remove outlying data points |
|
from each of the time series. The frequency analysis con- |
|
tains four main steps: |
|
1. We calculate an oversampled (factor of four) ver- |
|
sion ofthe power spectrum by using a least-squares |
|
fitting. We smoothed the spectrum to 3 µHz reso- |
|
lution to remove the fine structure caused by the |
|
finite mode lifetime. |
|
2. We correlated the smoothed power spectrum with |
|
an equally spaced comb of delta functions, sepa- |
|
ratedby∆ ν0/2,andconfinedtoaGaussian-shaped |
|
band with a full width at half maximum of 5∆ ν0. |
|
We adopted the maximum of this convolution over |
|
lags between 0 and 0.5 ∆ ν0as the filter output for |
|
each ∆ν0. |
|
3. After identifying the peak correlation for the best |
|
matched model filter and extracting the large sep- |
|
aration corresponding to this peak we calculate the |
|
folded spectrum (see Fig. 1b), i.e., the sum of the |
|
power as a function of frequency modulo the opti- |
|
mumlargeseparation(theonecorrespondingtothe |
|
peak correlation). The summed power is used to |
|
locate the p-mode structure and identify the ridges |
|
corresponding to the different mode degrees (based |
|
on the asymptotic relation). |
|
4. From the asymptoticrelationandthe identification |
|
of mode degrees we finally identify the position of |
|
the individual p-mode frequencies in the smoothed |
|
version of the power spectrum; when more than |
|
one mode is seen near the expected frequency we |
|
use the power-weighted average of the two peaks. |
|
Those extracted frequencies and the mode identifi- |
|
cations are used in the modeling. |
|
For observations with low signal-to-noise ratio it may |
|
not be possible to identify the individual frequencies. In 0 1 2 |
|
Fig. 1.— (a)PowerspectrumofHAT-P-7forfrequencies between |
|
300 and 3000 µHz. The spectrum is smoothed with a gaussian filter |
|
with a FWHM of 3 µHz. The noise level at high frequencies corre- |
|
sponds to 1.1 ppm in amplitude. The white curve is a smoothed |
|
power spectrum with a gaussian filter (150 µHz FWHM). A fit to |
|
the background (dashed white curve) is also shown. The exces s |
|
power and the individual p-modes are evident. (b) Folded pow er |
|
spectrum, between 750 and 1500 µHz, for HAT-P-7 for a large sep- |
|
aration of 59 .22µHz. Indicated are the positions corresponding to |
|
radial modes ( l= 0) and non-radial modes with l= 1 and 2. The |
|
measured positions are used to identify the individual osci llation |
|
modes in panel (a). (c) ´Echelle diagram (see text) for frequencies |
|
of degree l= 0, 1, and 2 in HAT-P-7; a frequency separation of |
|
59.36µHz and a starting frequency of 10 .8µHz were used. The |
|
filled symbols, coded for degree as indicated, show the obser ved |
|
frequencies, while the open symbols are for Model 3 in Table 2 , |
|
minimizing χ2 |
|
ν.3 |
|
such cases the analysis is carried through step 2, to de- |
|
termine the maximum response and hence an estimate of |
|
the large separation. |
|
Results on the three individual cases are presented in |
|
§4. |
|
3.MODEL FITTING |
|
Stellar evolution models and adiabatic oscillation |
|
frequencies were computed using the Aarhus codes |
|
(Christensen-Dalsgaard 2008a,b), with the OPAL |
|
equation of state (Rogers et al. 1996) and opacity |
|
(Iglesias & Rogers 1996) and the NACRE nuclear reac- |
|
tion parameters (Angulo et al. 1999). In some cases (see |
|
below) diffusion and settling of helium were included, |
|
using the simplified formulation of Michaud & Proffitt |
|
(1993). Convection was treated with the B¨ ohm-Vitense |
|
(1958) mixing-length formulation, with a mixing length |
|
αML= 2.00 in units of the pressure scale height roughly |
|
corresponding to a solar calibration. In some models |
|
with convective cores, overshoot was included over a dis- |
|
tance of αovpressure scale heights. Evolution started |
|
from chemically homogeneous zero-age models. The ini- |
|
tial abundances by mass X0andZ0of hydrogen and |
|
heavy elements were characterized by the assumed value |
|
of [Fe/H], using as reference a present solar surface com- |
|
position with Zs/Xs= 0.0245 (Grevesse & Noels 1993) |
|
and assuming, from galactic chemical evolution, that |
|
X0= 0.7679−3Z0. |
|
From the observed ∆ ν0, effective temperature and |
|
composition an initial estimate of the stellar parame- |
|
ters was obtained using the grid-based SEEK pipeline |
|
(Quirion et al., in preparation). Smaller grids were then |
|
computed in the vicinity of these initial parameters, to |
|
obtaintighterconstraintsonstellarproperties. ForHAT- |
|
P-7 the analysis of the observations yielded frequencies |
|
of individually identified modes; here the analysis was |
|
based on |
|
χ2 |
|
ν=1 |
|
N−1/summationdisplay |
|
nl/parenleftBigg |
|
ν(obs) |
|
nl−ν(mod) |
|
nl |
|
σν/parenrightBigg2 |
|
,(2) |
|
whereν(obs) |
|
nlandν(mod) |
|
nlare the observed and model fre- |
|
quencies, σνis the standard error in the observed fre- |
|
quencies (assumed to be constant) and Nis the num- |
|
ber of observed frequencies. In addition, we considered |
|
χ2=χ2 |
|
ν+χ2 |
|
T, whereχ2 |
|
Tis the corresponding normalized |
|
square difference between the observed and model effec- |
|
tive temperature. When χ2 |
|
νwas available we minimized |
|
it along each evolution track and considered the result- |
|
ing minimum values, and the corresponding value of χ2, |
|
as a function of the parameters characterizing the mod- |
|
els (see Gilliland et al. 2010b, for details). When only |
|
the large separation ∆ ν0could be determined from the |
|
observations, we identified the model along each track |
|
which matched ∆ ν0and considered the resulting χ2 |
|
Tas |
|
a function of the model parameters. |
|
4.RESULTS |
|
4.1.HAT-P-7 |
|
The observed power spectrum for HAT-P-7 is shown |
|
in Fig. 1a. The presence of solar-like p-mode peaks, with |
|
a maximum power around 1.1mHz, is evident. At high |
|
frequency the noise level in the amplitude spectrum is1.1 parts per million (ppm), with some increase at lower |
|
frequency, likely due to the effects of stellar granulation. |
|
Carrying out the correlation analysis described in §2 |
|
we determined the large separation as ∆ ν0= 59.22µHz. |
|
Figure 1b shows the resulting folded spectrum. This |
|
clearly shows two closely spaced peaks, identified as cor- |
|
responding to modes of degree l= 0 and 2, and single |
|
peak separated from these two by approximately ∆ ν0/2, |
|
corresponding to l= 1. On this basis we finally deter- |
|
mined the individual frequencies, identifying the modes |
|
from the asymptotic relation; the final set includes 33 |
|
p-mode frequencies, determined with a standard error |
|
σν= 1.4µHz. These frequencies, corresponding to ra- |
|
dial orders between 11 and 24, are illustrated in Fig. 1c |
|
in an ´ echelle diagram (see below). |
|
A grid of models was computed for masses between |
|
1.41 and 1 .61M⊙, [Fe/H] between 0.17 and 0.38, and |
|
αov= 0,0.1 and 0.2, extending well beyond the end of |
|
central hydrogen burning. The modeling did not include |
|
diffusion and settling. At the mass of this star the outer |
|
convection zone is quite thin, and as a result the set- |
|
tling timescale is much shorter than the age of the star. |
|
Including settling, without compensating effects such as |
|
partial mixing in the radiative region or mass loss, leads |
|
to a rapid change in the surface composition which is |
|
inconsistent with the observed [Fe/H]; for simplicity we |
|
therefore neglected these effects for HAT-P-7.8 |
|
The computed frequencies were corrected according to |
|
the procedure of Kjeldsen et al. (2008) for errors in the |
|
modeling of the near-surface layers, by adding a(ν/ν0)b |
|
wherea= 0.1158µHz,ν0= 1000µHz andb= 4.9. As |
|
discussed in §3, for each evolution track, characterized |
|
by a set of model parameters, we minimized the depar- |
|
tureχ2 |
|
νof the model frequencies from the observations, |
|
defining the best model for this set. |
|
We first consider χ2 |
|
νas a function of the effective |
|
temperature of the models (Fig. 2a). It is evident |
|
that there is a clear minimum in χ2 |
|
ν; this is consistent |
|
with the determination of Teffby P´ al et al. (2008) but |
|
not with the somewhat higher temperature obtained by |
|
Ammler-von Eif et al. (2009) (see also Table 1). Thus |
|
in the following we use the observed quantities from |
|
P´ al et al. (2008). |
|
Since the frequencies to leading order are determined |
|
by the mean stellar density ∝angbracketleftρ∗∝angbracketright, Fig. 2b,c show χ2 |
|
νand |
|
χ2as functions of ∝angbracketleftρ∗∝angbracketright. It is evident that the best-fitting |
|
modelsoccupyanarrowrangeof ∝angbracketleftρ∗∝angbracketright, withawell-defined |
|
minimum. Fittingaparabolato χ2inpanel(c)weobtain |
|
the estimate ∝angbracketleftρ∗∝angbracketright= 0.2712±0.0032gcm−1. In Fig. 2d |
|
χ2is shown against model age. Here the variation with |
|
model parameters is substantially stronger, resulting in |
|
a greater spread in the inferred age; in particular, it is |
|
evident, not surprisingly, that the results depend on the |
|
extent of convective overshoot. From the figure we esti- |
|
matethattheageofHAT-P-7isbetween1.4and2.3Gyr. |
|
Examples of evolution tracks are shown in Fig. 3; pa- |
|
rameters for these models are provided in Table 2. They |
|
were chosen to give the smallest χ2 |
|
νfor each of the three |
|
values of αovconsidered. Also shown are the locations |
|
8Artificially suppressing settling in the outer layers, whil e in- |
|
cluding diffusion and settling in the core, leads to results t hat are |
|
very similar to those presented here.4 Christensen-Dalsgaard et al. |
|
TABLE 2 |
|
Stellar evolution models fitting the observed frequencies for HAT-P-7. |
|
No M ∗/M⊙Age Z0X0αovR∗/R⊙/angbracketleftρ∗/angbracketrightTeffL∗/L⊙χ2 |
|
νχ2 |
|
(Gyr) (gcm−3) (K) |
|
1 1.53 1.758 0.0270 0.6870 0.0 1.994 0.2718 6379 5.91 1.08 1.2 1 |
|
2 1.52 1.875 0.0290 0.6809 0.1 1.992 0.2708 6355 5.81 1.04 1.0 4 |
|
3 1.50 2.009 0.0270 0.6870 0.2 1.981 0.2718 6389 5.87 1.00 1.2 4 |
|
Note. — Models minimizing χ2 |
|
ν(cf. Eq. 2) along the evolution tracks, illustrated in Fig. 3 . The models have been selected as providing |
|
the smallest χ2 |
|
νfor each of the three values of the overshoot parameter αov. The smallest value of χ2 |
|
νis obtained for Model 3. |
|
Fig. 2.— Results of fitting the observed frequencies to a grid of |
|
stellar models (see text for details). Plusses, stars and di amonds |
|
correspond to modelswith αov= 0 (no overshoot), 0.1, and 0.2. (a) |
|
Minimum mean square deviation χ2 |
|
νof the frequencies (cf. Eq. 2) |
|
along each evolution track, against the effective temperatu reTeff |
|
of the corresponding models. The vertical dashed and dotted lines |
|
indicate the effective temperatures found by P´ al et al. (200 8) and |
|
Ammler-von Eif et al. (2009). (b) Minimum mean square devia- |
|
tionχ2 |
|
νagainst the mean density /angbracketleftρ∗/angbracketrightof the corresponding models. |
|
(c) As (b), but showing the combined χ2. (d)χ2against the age |
|
for the models that minimize χ2 |
|
ν; the different ridges correspond to |
|
the different masses in the grid, the more massive models resu lting |
|
in a lower estimate of the age.Fig. 3.— Theoretical HR diagram with selected evolutionary |
|
tracks, corresponding to the models defined in Table 2. The ’+ ’ in- |
|
dicate the models along the full set of evolutionary sequenc es mini- |
|
mizing the difference between the computed and observed freq uen- |
|
cies. The box is centered on the LandTeffas given by P´ al et al. |
|
(2008), with a size matching the errors on these quantities. |
|
of the models minimizing χ2 |
|
νalong each of the computed |
|
tracks; these evidently fall close to a line in the HR di- |
|
agram, corresponding to the small range in ∝angbracketleftρ∗∝angbracketright. The |
|
range of luminosities, from P´ al et al. (2008), is based on |
|
modeling and hence has not been used in our fit; even |
|
so, it is gratifying that the present models are essentially |
|
consistentwiththesevalues. Also,asindicatedbyFig.2a |
|
andTable 2, the best-fitting models areclose to the value |
|
ofTeffobtained by P´ al et al. (2008). |
|
The match of the best-fitting model (Model 3 of Ta- |
|
ble 2) to the observed frequencies is illustrated in a so- |
|
called´ echelle diagram (Grec et al. 1983) in Fig. 1c. In |
|
accordance with Eq. (1) the frequency spectrum is di- |
|
vided into slices of length ∆ ν, starting at a frequency of |
|
10.8µHz; the figure shows the location of the observed |
|
(filled symbols) and computed (open symbols) frequen- |
|
cies within each slice, against the starting frequency of |
|
the slice; the model results extend to the acoustical cut- |
|
off frequency, 1930 µHz, of the model. There is clearly a |
|
very good overall agreement between model and obser- |
|
vations, including the detailed variation with frequency |
|
which reflects the frequency dependence of the large sep- |
|
aration, as a possible diagnostics of the outer layers of |
|
the star (e.g., Houdek & Gough 2007). |
|
We have finally made a fit of the inferred ∝angbracketleftρ∗∝angbracketright, as |
|
well asTeffand [Fe/H] from P´ al et al. (2008), to com- |
|
puted evolutionary tracks from the Yonsei-Yale compi- |
|
lation (Yi et al. 2001). This was based on a Markov |
|
Chain Monte Carlo analysis to obtain the statistical |
|
properties of the inferred quantities (see Brown 2010, |
|
for details). This resulted in M= 1.520±0.036M⊙, |
|
R= 1.991±0.018R⊙and an age of 2 .14±0.26Gyr. |
|
We note that the age estimate reflects the specific as-5 |
|
sumptions in the Yonsei-Yale evolution calculations; as |
|
indicated by Fig. 2d the true uncertainty in the age de- |
|
termination is likely somewhat larger. |
|
4.2.HAT-P-11 |
|
For HAT-P-11 the oscillation amplitudes were much |
|
smaller than in HAT-P-7, as expected from the general |
|
scaling of amplitudes with stellar mass and luminosity |
|
(e.g., Kjeldsen & Bedding 1995). Thus with the present |
|
short run of data it has only been possible to determine |
|
thelargeseparation∆ ν0= 180.1µHzfromthemaximum |
|
in the correlation analysis. We have matched this to a |
|
grid of models, including diffusion and settling of helium, |
|
with masses between 0.7 and 0 .9M⊙and [Fe/H] between |
|
0.21 and 0.41. These models provide a good fit to the |
|
observed TeffandL/L⊙; note that in the presentcase the |
|
luminosity is based on a reasonably well-determined par- |
|
allax. We havedetermined an estimateof ∝angbracketleftρ∗∝angbracketrightbyaverag- |
|
ing the results of those models which match the observed |
|
∆ν0and lie within 2 standard deviations ( ±100K) from |
|
the value of Teffprovided by Bakos et al. (2010); the re- |
|
sult is∝angbracketleftρ∗∝angbracketright= 2.5127±0.0009gcm−3. Although the for- |
|
mal error is extremely small, owing to a tight relation |
|
between the large separation and the mean density for |
|
stars in this region in the HR diagram, the true error is |
|
undoubtedly substantially larger. In particular, we ne- |
|
glected the error in the determination of ∆ ν0and these |
|
data have not allowed a correction for the systematic |
|
errors in the modeling of the near-surface layers of the |
|
star. |
|
4.3.TrES-2 |
|
Here also we were unable to determine individual fre- |
|
quencies from the present set of data. The expected am- |
|
plitudes are smaller than for HAT-P-7, and the noise |
|
level higher due to the fainter magnitude of TrES-2. |
|
The correlation analysis yielded two possible values of |
|
∆ν0: 97.7µHz and 130 .7µHz. For this star ∝angbracketleftρ∗∝angbracketrighthas |
|
been determined from the analysis of the transit light |
|
curve. Sozzetti et al. (2007) obtained ∝angbracketleftρ∗∝angbracketright= 1.375± |
|
0.065gcm−3, while Southworth (2009) found ∝angbracketleftρ∗∝angbracketright= |
|
1.42±0.13gcm−3. From the scaling with ∝angbracketleftρ∗∝angbracketright1/2thesmaller of the two possible values of ∆ ν0is clearly incon- |
|
sistent with these values of ∝angbracketleftρ∗∝angbracketright, while ∆ ν0= 130.7µHz |
|
yields models that are consistent with the observed Teff |
|
and log(g) of Sozzetti et al. (2007) as well as with these |
|
values of the mean density. Here we considered a grid |
|
of models with helium diffusion and settling, masses be- |
|
tween 0.85 and 1 .1M⊙and [Fe/H] between −0.25 and |
|
−0.05. Determining again the mean value of ∝angbracketleftρ∗∝angbracketrightfor |
|
those models that matched ∆ ν0and had Teffwithin two |
|
standard deviations of the value of Sozzetti et al. (2007) |
|
we obtained ∝angbracketleftρ∗∝angbracketright= 1.3233±0.0027gcm−3. As in the |
|
case of HAT-P-11 the true error is likely substantially |
|
higher. |
|
5.DISCUSSION AND CONCLUSION |
|
The present preliminary analysis provides a striking |
|
demonstration of the potential of Keplerasteroseismol- |
|
ogyanditssupportingroleintheanalysisofplanethosts. |
|
Thesestarswill undoubtedly be observedthroughout the |
|
mission and hence the quality of the data will increase |
|
substantially. For HAT-P-7 the detected frequencies are |
|
already close to what will be required for a detailed anal- |
|
ysis of the stellar interior, beyond the determination of |
|
the basic parameters of the star. Thus here we can look |
|
forward to a test of the assumptions of the stellar mod- |
|
eling; the resulting improvements will further constrain |
|
the overall properties of the star, in particular its age. |
|
Also, given the observed vsiniwe expect a rotational |
|
splitting comparable to that observed in the Sun, and |
|
hence likely detectable with a few months of observa- |
|
tions. For the other two stars there is strong evidence |
|
for the presence of solar-like oscillations; thus continued |
|
observations will very likely result in the determination |
|
of individual frequencies and hence further constraints |
|
on the properties of the stars. |
|
Funding for this Discovery mission is provided by |
|
NASA’s Science Mission Directorate. We are very grate- |
|
ful to the entire Keplerteam, whose efforts have led to |
|
this exceptional mission. The present work was sup- |
|
ported by the Danish Natural Science Research Council. |
|
Facilities: The Kepler Mission |
|
REFERENCES |
|
Aerts, C., Christensen-Dalsgaard, J., & Kurtz, D. W. 2009, |
|
Asteroseismology, Springer, Heidelberg, in the press |
|
Ammler-von Eif, M., Santos, N. C., Sousa, S. G., Fernandes, J ., |
|
Guillot, T., Israelian, G., Mayor, M., & Melo, C. 2009, A&A, |
|
507, 523 |
|
Angulo, C., et al. 1999, Nucl. Phys. A, 656, 3 |
|
Bakos, G. ´A., et al. 2010, ApJ, in the press (arXiv:0901.0282v2) |
|
Bedding, T. R., & Kjeldsen, H. 2008, in Proc. 14thCambridge |
|
Workshop on Cool Stars, Stellar Systems, and the Sun, ed. |
|
G. T. van Belle, ASP Conf. Ser., San Francisco, 384, 21 |
|
B¨ ohm-Vitense, E. 1958, ZAp, 46, 108 |
|
Borucki, W., et al. 2009, in Proc. IAU Symp. 253, Transiting |
|
Planets, eds F. Pont, D. Sasselov & M. Holman, IAU and |
|
Cambridge University Press, 289 |
|
Borucki, W., et al. 2010, Science, submitted |
|
Brown, T. M. 2010, ApJ, in the press (arXiv:0912:1639) |
|
Christensen-Dalsgaard, J. 2002, Rev. Mod. Phys., 74, 1073 |
|
Christensen-Dalsgaard, J. 2008a, Ap&SS, 316, 13 |
|
Christensen-Dalsgaard, J. 2008b, Ap&SS, 316, 113Christensen-Dalsgaard, J., Arentoft, T., Brown, T. M., Gil liland, |
|
R. L., Kjeldsen, H., Borucki, W. J., & Koch, D. 2008, in Proc. |
|
HELAS II International Conference: Helioseismology, |
|
Asteroseismology and the MHD Connections, eds L. Gizon & |
|
M. Roth, J. Phys.: Conf. Ser., 118, 012039 |
|
Dittmann, J. A., Close, L. M., Green, E. M., Scuderi, L. J., & |
|
Males, J. R. 2009, ApJ, 699, L48 |
|
Gilliland, R. L., et al. 2010a, PASP, in the press |
|
Gilliland, R. L., McCullough, P. R., Nelan, E. P., Brown, T. M ., |
|
Charbonneau, D., Nutzman, P., Christensen-Dalsgaard, J., & |
|
Kjeldsen, H. 2010b, ApJ, submitted |
|
Gilliland, R. L., et al. 2010c, ApJL, in the press |
|
Grec, G., Fossat, E., & Pomerantz, M. 1983, Sol. Phys., 82, 55 |
|
Grevesse, N., & Noels, A. 1993, in Origin and evolution of the |
|
Elements, eds N. Prantzos, E. Vangioni-Flam & M. Cass´ e |
|
(Cambridge: Cambridge Univ. Press), 15 |
|
Houdek, G., & Gough, D. O. 2007, MNRAS, 375, 861 |
|
Huber, D., Stello, D., Bedding, T. R., Chaplin, W. J., Arento ft, |
|
T., Quirion, P.-O., & Kjeldsen, H. 2009, Comm. in |
|
Asteroseismology, 160, 74 |
|
Iglesias, C. A., & Rogers, F. J. 1996, ApJ, 464, 943 |
|
Kjeldsen, H., & Bedding, T. R. 1995, A&A, 293, 876 Christensen-Dalsgaard et al. |
|
Kjeldsen, H., Bedding, T. R., & Christensen-Dalsgaard, J. 2 008, |
|
ApJ, 683, L175 |
|
Kjeldsen, H., Bedding, T. R., & Christensen-Dalsgaard, J. 2 009, |
|
in Proc. IAU Symp. 253, Transiting Planets, eds F. Pont, D. |
|
Sasselov & M. Holman, IAU and Cambridge University Press, |
|
309 |
|
Koch, D., et al. 2010, ApJL, submitted |
|
Michaud, G., & Proffitt, C. R. 1993, in Proc. IAU Colloq. 137: |
|
Inside the stars, eds A. Baglin, & W. W. Weiss, ASP Conf. |
|
Ser., San Francisco, 40, 246 |
|
Nutzman, P., Gilliland, R. L., McCullough, P. R., Charbonne au, |
|
D., Christensen-Dalsgaard, J.,Kjeldsen, H., Nelan, E. P., |
|
Brown, T. M., & Holman, M. J. 2010, ApJ, submitted |
|
O’Donovan, F. T., et al. 2006, ApJ, 651, L61P´ al, A., et al. 2008, ApJ, 680, 1450 |
|
Rogers, F. J., Swenson, F. J., & Iglesias, C. A. 1996, ApJ, 456 , |
|
902 |
|
Southworth, J. 2009, MNRAS, 394, 272 |
|
Sozzetti, A., Torris, G., Charbonneau, D., Latham, D. W., |
|
Holman, M. J., Winn, J. N., Laird, J. B., & O’Donovan, F. T. |
|
2007, ApJ, 664, 1190 |
|
Tassoul, M. 1980, ApJS, 43, 469 |
|
Yi, S., Demarque, P., Kim, Y.-C., Lee, Y.-W., Ree, C. H., |
|
Lejeune, T., & Barnes, S. 2001, ApJS, 136, 417 |
|
Vandakurov, Yu. V. 1967, AZh, 44, 786 (English translation: |
|
Soviet Ast., 11, 630) |