deletions | additions       diff --git a/Magnetic Constraints.tex b/Magnetic Constraints.tex  index 805f0ff..5137b5f 100644  --- a/Magnetic Constraints.tex  +++ b/Magnetic Constraints.tex 
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Figure \ref{fig:Bc} shows the value of $B_{c,{\rm min}}$ as stars evolve up the RGB. We have calculated $B_{c,{\rm min}}$ for angular frequencies $\omega = 2 \pi \nu_{\rm max}$, and evaluated $\nu_{\rm max}$ using the scaling relation proposed by \cite{Brown_1991}. On the lower RGB, where $\nu_{\rm max} \gtrsim 250\,\mu$Hz, field strengths of order $B_{c,{\rm min}} \gtrsim 10^6 \, {\rm G}$ are required for magnetic suppression. As stars evolve up the red giant branch, the value of $B_{c,{\rm min}}$ decreases sharply as the value of $r$ at the H-burning shell decreases, and the value of $N$ increases. By the luminosity bump (near $\nu_{\rm max} \sim 40\,\mu$Hz), field strengths of only $B_{c,{\rm min}} \sim \!10^4 \, {\rm G}$ are sufficient for magnetic suppression. Stars therefore become more susceptible to magnetic suppression as they evolve up the RGB. Magnetic suppression during the subgiant phase (higher $\nu_{\rm max}$) and in higher mass stars ($M \gtrsim 2 M_\odot$) may be less common due to the larger field strengths required.  The critical field strength $B_c$ is dependent on wave frequency, and lower frequency waves are more susceptible to magnetic suppression. For a given field strength, there is a transition frequency $\nu_c$ below which modes will be strongly suppressed and above which modes will appear normal. Stars which show this transition are especially useful because they allow for a measurement an {\bf inference}  of $B$ at the H-burning shell via equation \ref{eqn:Bc}, evaluated at the transition frequency $\omega = 2 \pi \nu_c$. The lower RGB star KIC 8561221 analyzed by \cite{Garcia_2014} shows this transition. Using the approximate observed value of $\nu_c \approx 600 \, \mu{\rm Hz}$. We compute {\bf infer}  that the radial component of the magnetic field within the H-burning shell is $B \approx 1.5 \times 10^{7} \, {\rm G}$. G}$, {\bf although we cannot rule out the presence of larger fields away from the H-burning shell}.  This large field strength may indicate KIC 8561221 is the descendant of a magnetic Ap star whose internal field was much stronger than the typical surface fields of $B \sim 3 \, {\rm kG}$ of Ap stars \cite{Auri_re_2007}.