Meredith L. Rawls edited Discussion.tex  almost 9 years ago

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These relations should be valid only for oscillation modes of large radial orders $n$, where pressure modes can be mathematically described in the frame of the ``asymptotic development'' \citep{tas80}. Even though red giants do not perfectly match these conditions, because the observed oscillation modes have radial orders $n < 10$, the scaling relations do appear to work (CITATION MAYBE??). Quantifying how well they work and in what conditions is more challenging. This is why measuring oscillating stars' masses and radii independently from seismology is so important.  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}. \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. CAN YOU ELABORATE ON WHAT CHARACTERISTICS OF THE OSCILLATION PATTERN SHOW THIS??  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 $\Delta \nu = 8.31 \pm 0.01 \mu \rm{Hz}$. 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, and assuming $T_{\rm{eff}} = 5050 \pm 100 \ \rm{K}$, we obtain $M = 2.21 \pm 0.12 \ M_{\odot}$ and $R = 8.30 \pm 0.16 \ R_{\odot}$. In terms of mean density and surface gravity, which independently test the $\Delta \nu$ and $\nu_{\rm{max}}$ relations, respectively, we find $\bar{\rho}/\bar{\rho}_{\odot} = (3.862 \pm 0.009) \times 0.009)\  10 ^{-3}$ and $\log g = 2.944 \pm 0.007$. %\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}