deletions | additions       diff --git a/Magnetic Constraints.tex b/Magnetic Constraints.tex  index 8c2617a..67e2261 100644  --- a/Magnetic Constraints.tex  +++ b/Magnetic Constraints.tex 
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In red giant cores, the right hand side of equation \ref{eqn:Bc} is typically minimized at the peak in $N$ corresponding to the sharp density gradient within the H-burning shell. Therefore, gravity waves are most susceptible to magnetic alteration in the H-burning shell. The observation of a star with suppressed dipole modes therefore provides a lower limit to the field strength at the location of the H-burning shell,   \begin{equation}  \label{eqn:BHburn}  B(r_H) B_c(r_H)  \geq \sqrt{\frac{\pi}{2}} \frac{\sqrt{\rho_H} r_H \omega^2}{N_H} \, . ,  \end{equation}  with the $H$ subscript indicating the right hand side of equation \ref{eqn:BHburn} should be evaluated near the H-burning shell where $B_c$ is minimized.   Figure \ref{fig:DipoleBEvol} shows the value of $B_c(r_H)$ for dipole modes as a function of stellar radius for an evolving star with $M=1.5M_\odot$. At the lower subgiant branch, where the stellar radius is $R\sim 3 R_\odot$, field strengths near $B_c \sim 10^7 \, {\rm G}$ are required for magnetic suppression. As the star evolves up the red giant branch, the value of $B_c$ decreases sharply as the value of $r_H$ decreases and $N_H$ increases. By the bump, field strengths of under $10^4 \, {\rm G}$ are sufficient for magnetic suppression. At the clump, field strengths of a few times $10^{4} \, {\rm G}$ are sufficient. As discussed above, these field strengths are easily attainable for the descendants of magnetic Ap stars. Magnetic suppression on the early sub-giant branch is likely to be less common due to the higher field strengths required.