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Jim Fuller edited Mode Visibility.tex
almost 9 years ago
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\section{Mode Visibility}
Solar-like oscillations are created by standing waves with frequencies near $\nu_{\rm max}$ that are driven by stochastic energy input from turbulent near-surface convection. The value of $\nu_{\rm max}$ is determined by the evolutionary state of the star, and on the
red giant branch (RGB) RGB more evolved stars
generally have smaller $\nu_{\rm max}$. Waves excited near the stellar surface propagate downward as acoustic waves until their angular frequency $\omega$ is less than the local Lamb frequency for waves of angular degree $\ell$, i.e., until $\omega = L_l = \sqrt{l(l+1)} c_s/r$, where $c_s$ is the local sound speed and $r$ is the radial coordinate. At this boundary, part of the wave flux is reflected, and part of it tunnels into the core.
The wave resumes propagating inward as a gravity wave in the radiative core where $\omega < N$, where $N$ the buoyancy frequency. In normal red giants, wave energy that tunnels into the core eventually tunnels back out to produce the observed oscillation modes. We show here that the visibility of suppressed modes can be explained if wave energy leaking into the core never returns to the stellar envelope.