Jim Fuller edited figures/DipoleEvolProp/caption.tex  almost 9 years ago

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\label{fig:Prop2}  {\bf Top:} Sound speed, $v_s$, gravity wave radial group velocity, $v_{g,r}$ (for $\omega=\omega_{\rm max}$), and Alfven speed, $v_A$, for the stellar model shown in Figures \ref{fig:Prop} and \ref{fig:Prop2}. Waves travel at a group velocity of $v_s$, $v_{g,r}$, and $v_A$ for acoustic, gravity, and Alfven waves, respectively. Because $v_A \ll v_s$, the magnetic field has a negligible effect on the stellar structure. {\bf Bottom:} Radial wave number, $k_r$, for a wave with $\omega=\omega_{\rm max}$, as a function of radius. We have plotted the wavenumbers of acoustic waves (p-waves), fast magneto-gravity waves (mg-waves), (fast-waves),  slow magneto-gravity waves (slow-waves), Alfven waves (a-waves), and the evanescent part of the wave (ev-wave). The dashed blue line shows the wavenumber for gravity waves (g-waves) in the absence of a magnetic field. The solid black line shows the minimum of $r^{-1}$ or $H^{-1}$ (where $H$ is a pressure scale height). Because ${\rm min} \big(r^{-1},H^{-1}\big) \ll k_r$ for each type of wave deep in the radiative zone, a WKB analysis of wave propagation is appropriate.