patrick gaulme edited Discussion.tex  almost 9 years ago

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When \citet{gau13} and \citet{gau14} analyzed the oscillation modes of KIC 9246715 to estimate global asteroseismic parameters, only one set of modes was found. Of the 15 oscillating red giants in eclipsing binaries in the \emph{Kepler} field, KIC 9246715 is the only one with a pair of giant stars (the rest are composed of a giant star and a main sequence star). The oscillation spectrum as well as its representation as an \'echelle diagram are shown in Figures \ref{fig:seismo} and \ref{fig:echelle}. Based on the distribution of mixed modes, \citealt{gau14} reported that the oscillation pattern was typical of that of a star from the secondary red clump, i.e., a star that burns He in the core, without having experienced an He flash. For a single oscillating star, the mode amplitudes are quite low ($A_{\rm{max}}(l=0) \simeq 14$ ppm, and not 6.6 as erroneously reported by \citealt{gau14}) with respect to the 20 ppm we expect based on mode amplitude scaling relations \citep{cor13}. In addition, the light curve displays photometric variability as large as 2\% peak-to-peak, which is typical of the signal created by spots on stellar surfaces. The pseudo-period of this variability was observed to be about half the orbital period, which suggests resonances in the system. \citet{gau14} speculated that star spots may be responsible for inhibiting oscillations on the smaller star, and a similar behavior was observed in five other RG/EB systems.  We now re-estimate $\nu_{\rm{max}}$ and $\Delta \nu$ for the oscillation spectrum in the same way as \citet{gau14}, but by using the whole \textit{Kepler} dataset (Q0--Q17). Differences with respect to previous estimates are negligible, as we find $\nu_{\rm{max}} = 106.4 \pm 0.8$ and $\Delta \nu = 8.31 \pm 0.01 \mu \rm{Hz}$. As regards effective temperatures, given that light-curve modeling leads to $T_2/T_1=0.98$ and that from our APO spectra $T1 = 4990\pm90$~K and $T_2=5030\pm80$~K, we assume an effective temperature $T_{\rm{eff}}=5000\pm100$~K in the asteroseismic scaling equations. To determine mass, radius, surface gravity, and mean density, we use the scaling relations after correcting $\Delta \nu$ for the red giant regime \citep{mos13}. In essence, instead of directly plugging the observed $\Delta \nu_{\rm{obs}}$ into Equations \ref{density} and \ref{gravity}, we estimate the asymptotic large spacing $\Delta \nu_{\rm{as}}$ as follows: $\Delta \nu_{\rm{as}} = \Delta \nu_{\rm{obs}} (1 + \zeta)$, where $\zeta = 0.038$. With this correction of the large spacing, we obtain $M = 2.21 2.17  \pm 0.12 \ M_{\odot}$ and $R = 8.30 8.26  \pm 0.16 \ R_{\odot}$. In terms of mean density and surface gravity, which independently test the $\Delta \nu$ and $\nu_{\rm{max}}$ relations, respectively, we find $\bar{\rho}/\bar{\rho}_{\odot} = (3.862 \pm 0.009)\ 10 ^{-3}$ and $\log g = 2.944 2.942  \pm 0.007$. %\begin{equation} \label{radeq}  %\left( \frac{R}{R_\odot} \right) \simeq \left( \frac{\nu_{\rm{max}}}{\nu_{\rm{max, \ \odot}}} \right) \left( \frac{\Delta \nu}{\Delta \nu_\odot} \right)^{-2} {\left( \frac{T_{\rm{eff}}}{T_{\rm{eff, \ \odot}}} \right)}^{0.5}