Jim Fuller edited Mode Visibility.tex  almost 9 years ago

Commit id: 7844d46abffada409b0f33c4ef23fbb978e73172

deletions | additions      

       

\label{eqn:vis}  \frac{V_{\rm sup}^2}{V_{\rm norm}^2} = \bigg[1 + \Delta \nu \, \tau \, T^2 \bigg]^{-1} \, ,  \end{equation}  where $\Delta \nu \simeq (2 t_{\rm cross})^{-1}$ \citep[e.g.,][]{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  $\tau \approx 10 \, {\rm days}$ \citep{Dupret_2009,Corsaro_2012,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 \citep{Mosser_2011,Garcia_2014}. The stars classified by \citet{Mosser_2011} as suppressed pulsators fall within the range of our estimate. The striking agreement holds over a large baseline in $\nu_{\rm max}$ extending from near the luminosity bump at low $\nu_{\rm max}$ to the very early red giants KIC 8561221 \citep{Garcia_2014} and KIC 9073950 at high $\nu_{\rm max}$.