deletions | additions       diff --git a/Magnetic Constraints.tex b/Magnetic Constraints.tex  index cf61c00..8b38547 100644  --- a/Magnetic Constraints.tex  +++ b/Magnetic Constraints.tex 
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\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 $M=1.5M_\odot$. We have evaluated $B_c$ for angular frequencies $\omega = \omega_{\rm max} = 2 \pi \nu_{\rm max}$, where $\nu_{\rm max}$ is the frequency of maximum power, evaluated via the scaling relation   \begin{equation}  \label{eqn:numax}  \nu_{\rm max} \ \nu_{{\rm max}, \odot} \bigg(\frac{M}{M_\odot}\bigg) \bigg(\frac{R}{R_\odot}\bigg)^{-2} \bigg(\frac{T}{T_\odot}\bigg)^{-1/2}   \end:equation}  from \cite{Huber_2011}, with $\nu_{{\rm max}, \odot} = 3090 \mu{\rm Hz}$.  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 $\sim \! 3 \times 10^{4} \, {\rm G}$ 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. Equation \ref{eqn:BHburn} can be rearranged to provide an upper limit to the frequencies of oscillation modes which can be magnetically suppressed:  \begin{equation}  \omega_c = \bigg[ \sqrt{\frac{2}{\pi}} \frac{B_H N_H}{\sqrt{\rho_H} r_H} \bigg]^{1/2},  \end{equation}  where $B_H$ is the field strength in the H-burning shell. The maximum suppression frequency is $\nu_c = \omega_c/(2 \pi)$. Modes with $\nu < \nu_c$ will be strongly suppressed, whereas modes with $\nu > \nu_c$ will not be.  Figure \ref{fig:DipoleBEvol} shows the value of $\nu_c$ given plausible field strengths $B_H$ of red giants with magnetic cores. The value of $\nu_c$ increases as stars evolve up the RGB, just as the minimum field strength