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

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\subsubsection{Global asteroseismic parameters of the oscillating star}  \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). \revise{The frequency at maximum amplitude of solar-like oscillations $\nu_{\rm{max}}$ is measured by fitting the mode envelope with a Gaussian function and the background stellar activity with a sum of two semi-Lorentzians. The large frequency separation $\Delta\nu$ is obtained from the filtered autocorrelation of the time series \citep{mos09}.} Differences with respect to previous estimates are negligible, as we find $\nu_{\rm{max}} = 106.4 \pm 0.8$ and $\Delta \nu = 8.31 \pm 0.01 0.04  \ \mu \rm{Hz}$. 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 \revise{applications, such as \citet{cha11} or \citet{kal10}, assume the observed $\Delta \nu$ is equal to the asymptotic value, which is not correct.} \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}.