deletions | additions       diff --git a/Magnetic Constraints.tex b/Magnetic Constraints.tex  index 51a3114..7cd2c63 100644  --- a/Magnetic Constraints.tex  +++ b/Magnetic Constraints.tex 
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Above, we showed that incoming magneto-gravity waves will become trapped in the core if the magnetic field strength exceeds $B_c$ (equation \ref{eqn:Bc}) at some point within the core. Stars with suppressed dipole oscillation modes therefore 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 relations proposed by \citet{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 on during  the sub-giant branch 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. %As low-mass stars evolve up the RGB, their cores contract. If magnetic flux is conserved, the strength of their internal magnetic fields will increase.