deletions | additions       diff --git a/subsection_Magneto_Gravity_Waves_The__.tex b/subsection_Magneto_Gravity_Waves_The__.tex  index 60c8dca..73a3632 100644  --- a/subsection_Magneto_Gravity_Waves_The__.tex  +++ b/subsection_Magneto_Gravity_Waves_The__.tex 
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\label{eqn:magnetogravity2}  v_{A,r} \sim v_{g,r} \, .  \end{equation}  Here, we have used $\mu v_A \sim v_{A,r}$ because $k_r \gg k_\perp$ for gravity waves in the WKB limit. Therefore, the radial component of the field dominates the interaction between the magnetic field and gravity waves. Equation \ref{eqn:magnetogravity2} shows that gravity waves will be strongly modified when the radial component of the Alfven velocity is comparable to the radial component of the gravity wave group velocity. Another way of expressing this is that gravity waves will be altered when $\omega \lesssim \omega_{MG}$, \omega_{\rm MG}$,  where the magneto-gravity wave frequency is defined as \begin{equation}  \label{eqn:maggrav2}  \omega_{MG} \omega_{\rm MG}  = \sqrt{2 v_{A,r} N k_\perp}. \end{equation}  %In a magnetized red giant core, the value of both $N$ and $v_A$ will increase from the exterior of the radiative zone inward. Incoming gravity waves become increasingly Alfvenic magneto-gravity waves as they propagate toward the helium core. If the magnetic field strength becomes large enough to satisfy equation \ref{eqn:magnetogravity2}, the waves are very strongly altered by the magnetic field. They may either reflect (i.e., they become evanescent as in equation \ref{eqn:magnetodisp3}), or they may transform into purely Alfven waves. Both processes are likely to occur for an arbitrary field geometry.