deletions | additions       diff --git a/Magnetic Constraints.tex b/Magnetic Constraints.tex  index 027cf4e..2bcfa01 100644  --- a/Magnetic Constraints.tex  +++ b/Magnetic Constraints.tex 
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{\bf Dipole oscillation modes can be depressed if the} magnetic field strength exceeds $B_c$ (equation \ref{eqn:Bc}) at some point within the core. {\bf We therefore posit that stars with depressed dipole oscillation modes have minimum core field strengths of $B_{c,{\rm min}}$.} Stars with normal dipole oscillation modes cannot have radial field strengths in excess of $B_{c,{\rm min}}$ within their H-burning shells. However, they may contain larger fields away from the H-burning shell, or they may contain fields that are primarily horizontal (e.g., strong toroidal fields).  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. sharply, {\bf primarily because $\nu_{\rm max}$ decreases.}  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 sub-giant 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 an {\bf inference} of $B$ at the H-burning shell via equation \ref{eqn:Bc}, evaluated at the transition frequency $\omega = 2 \pi \nu_c$. 
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