Meredith L. Rawls edited Discussion.tex  over 8 years ago

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\subsubsection{Global asteroseismic parameters of the main oscillator}  \label{subsubsec_main_osc}  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 $\Delta \nu = 8.31 \pm 0.01 \ \mu \rm{Hz}$. Because the ELC results yield $T_2/T_1=0.989$ (Table \ref{table1}) and the stellar atmosphere analysis gives $T_1 = 4990 \pm 90 \ \rm{K}$ and $T_2 = 5030 \pm 80 \ \rm{K}$ (Section \ref{parameters}), we assume an effective temperature $T_{\rm{eff}} = 5000 \pm 100 \ \rm{K}$ 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}\footnote{Other scaling relation corrections, such asthose in  \citet{cha11} or \citet{kal10}, lead to slightly larger corrected $\Delta \nu$ values, but \citet{mos13} specifically aims to account for the fact that oscillating red giants are not in the asymptotic regime.}. 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 via $\Delta \nu_{\rm{as}} = \Delta \nu_{\rm{obs}} (1 + \zeta)$, where $\zeta = 0.038$. With this correction of the large spacing, we obtain $M = 2.17 \pm 0.12 \ M_{\odot}$ and $R = 8.26 \pm 0.16 \ R_{\odot}$. In terms of mean density and surface gravity, which independently test the $\Delta \nu$ and $\nu_{\rm{max}}$ relations, respectively, we find $\bar{\rho}/\bar{\rho}_{\odot} = (3.862 \pm 0.009) \times 10 ^{-3}$ and $\log g = 2.942 \pm 0.007$. A comparison of key parameters determined from all our different modeling techniques is in Table \ref{table2}. Based on the distribution of mixed modes, \citet{gau14} reported that the oscillation pattern period spacing was typical of that of a star from the secondary red clump, i.e., a core-He-burning star that has not experienced a helium flash. However, this conclusion was based on a period spacing of $\Delta \Pi \simeq 150 \ \rm{sec}$ (Mosser, private communication) which is difficult to measure robustly from a noisy oscillation spectrum. Red giant branch stars have smaller period spacings than red clump stars, and ($\Delta \Pi = 150 \ \rm{sec}$, $\Delta \nu = 8.31 \ \mu \rm{Hz}$) puts the oscillating star on the very edge of the asteroseismic parameter space that defines the secondary red clump \citep{mos14}. Therefore, while asteroseismology does indicate the oscillator in KIC 9246715 is a red clump star, there is a large uncertainty attached to the classification. This result is supported statistically by \citet{mig14}, who report it is more likely to find red clump stars than red giant branch stars in asteroseismic binaries in \emph{Kepler} data. This is largely due to the fact that evolved stars spend more time on the horizontal branch than the red giant branch. We note that due to the large noise level of the mixed modes, we are unable to measure a core rotation rate in the manner of \citet{bec12} and \citet{mos12}. 

\subsubsection{Surface gravity disagreement}  The asteroseismic $\log g$ measurement nearly agrees with those from ELC, yet all three are some 0.3 dex lower than the spectroscopic $\log g$ values, as can be seen in Table \ref{table2}. This discrepancy is similar to the difference found for giant stars by \citet{hol15}. They investigate a large sample of stars from the ASPCAP (APOGEE Stellar Parameters and Chemical Abundances Pipeline) which have $\log g$ measured via spectroscopy and asteroseismology. They find that spectroscopic surface gravity measurements are roughly 0.2--0.3 dex too high for core-He-burning (red clump) stars and roughly 0.1--0.2 dex too high for shell-H-burning (red giant branch) stars. \citet{hol15} speculate the difference may be partially due to a lack of treatment of stellar rotation, and derive an empirical calibration relation for a ``correct'' $\log g$ for red giant branch stars only. However, the stars in KIC 9246715 do not rotate particularly fast ($v_{\rm{rot}} \sin i \lesssim 8 \ \rm{km \ s}^{-1}$, which includes a contribution from macroturbulence as discussed in Section \ref{parameters}), so we cannot dismiss this discrepancy so readily.