Jim Fuller edited Mode Visibility.tex  almost 9 years ago

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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 $\nu_{\rm max}$.  We conclude that the cores of stars with suppressed dipole modes efficiently trap waves {\bf deplete dipole wave energy}  tunneling through the evanescent region. This is further supported by the normal $\ell=0$ mode visibility in suppressed pulsators (because radial modes do not propagate within the inner core) and the lack (or perhaps smaller degree) of suppression observed in $\ell=2$ modes by \cite{Mosser_2011}, because quadrupole modes have a smaller transmission coefficient $T$. {\bf When the depression mechanism operates, it must deplete nearly all of the dipole wave energy entering the core. A smaller degree of wave energy depletion would produce less mode visibility depression, which is inconsistent with the observed dipole mode visibilities of depressed pulsators.}  An additional consequence is that the larger effective damping rate for suppressed modes will lead to larger line widths in the oscillation power spectrum. The linewidth of a suppressed mode is $\tau^{-1} + \Delta \nu T^2_{\ell}$ and is generally much larger than that of a non--suppressed mode. The suppressed dipole modes in KIC 8561221 \cite{Garcia_2014} indeed have much larger linewidths than non-suppressed dipole modes in similar stars.