deletions | additions       diff --git a/Magnetic_fields_can_provide_the__.tex b/Magnetic_fields_can_provide_the__.tex  index 47e9372..9afbc2d 100644  --- a/Magnetic_fields_can_provide_the__.tex  +++ b/Magnetic_fields_can_provide_the__.tex 
...
\label{eqn:maggrav}  \omega_{\rm MG} = \bigg[ \frac{2}{\pi} \frac{B_r^2 N^2}{\rho r^2} \bigg]^{1/4} \, .  \end{equation}  {\bf Figure\ref{fig:cartoon} illustrates the basic properties of waves propagating in a red giant with a strongly magnetized core, and Figure  \ref{fig:Prop} shows a wave propagation diagram in which a strong internal magnetic field prevents magneto-gravity wave propagation in the core.} In red giants, $B_c$ is typically smallest at the peak in $N$ corresponding to the sharp density gradient within the hydrogen burning (H-burning) shell (see Figure \ref{fig:Prop}). Therefore, gravity waves are most susceptible to magnetic alteration in the H-burning shell. The observation of a star with suppressed dipole modes thus provides a {\it lower limit} to the radial field strength (equation \ref{eqn:Bc}) evaluated in the H-burning shell. We refer to this field strength as $B_{c,{\rm min}}$. Magnetic suppression via horizontal fields can also occur, but in general requires much larger field strengths.  
...