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Jim Fuller edited Mode Visibility.tex
almost 9 years ago
Commit id: 851e731943042b3c4f57a7955d89a1aeb34bfb51
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\label{eqn:vis}
\frac{V_{\rm sup}^2}{V_{\rm norm}^2} = \bigg[1 + \Delta \nu \, \tau \, T^2 \bigg]^{-1} \, ,
\end{equation}
where $\Delta \nu \simeq (2 t_{\rm cross})^{-1}$ \cite{Chaplin_2013} is the large frequency separation between overtone modes, and $\tau$ is the damping time of a radial mode with similar frequency. The value of $T^2$ can be easily calculated from a stellar model, whereas the envelope life-time is
{\bf $\tau \approx
10 5-10 \, {\rm
days}$ days}$} {\bf \cite{Dupret_2009,Corsaro_2012,Grosjean_2014,Corsaro_2015} } for stars ascending the RGB.
Most observed modes are near the frequency $\nu_{\rm max}$, which is determined by the evolutionary state of the star. On the RGB, more evolved stars generally have smaller $\nu_{\rm max}$.
Figure 1 compares our estimate for suppressed dipole mode visibility (equation \ref{eqn:vis}) with {\it Kepler} observations \cite{Mosser_2011,Garcia_2014}. The stars classified by \cite{Mosser_2011} as suppressed pulsators lie very close to our estimate. The striking agreement holds over a large baseline in $\nu_{\rm max}$ extending from the very early red giants KIC 8561221 \cite{Garcia_2014} and KIC 9073950 at high $\nu_{\rm max}$ to near the luminosity bump at low $\nu_{\rm max}$.
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