patrick gaulme edited Discussion.tex  over 8 years ago

Commit id: b531001a3a893e043dc2c669d326282712042d20

deletions | additions      

       

\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). \textbf{In few words, the \textbf{The  frequency at maximum amplitude of solar-like oscillations $\nu\ind{max}$ $\nu_{\rm{max}}$  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{Mosser_Appourchaux_2009}.} 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 as \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}.