deletions | additions       diff --git a/section_Magnetic_Greenhouse_Effect_Magnetic__.tex b/section_Magnetic_Greenhouse_Effect_Magnetic__.tex  index 0bbbf97..b81f7cc 100644  --- a/section_Magnetic_Greenhouse_Effect_Magnetic__.tex  +++ b/section_Magnetic_Greenhouse_Effect_Magnetic__.tex 
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\end{equation}  and $v_{A,r}$ is the radial component of the Alfven velocity.  %Figure \ref{fig:cartoon} illustrates the basic properties of waves in red giants with strongly %magnetized magnetized  cores, while Figure \ref{fig:Prop} shows a propagation diagram for a red giant model %with a magnetic 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 depressed 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.