deletions | additions       diff --git a/subsection_Stellar_Models_We_have__1.tex b/subsection_Stellar_Models_We_have__1.tex  index e3304ac..cd55310 100644  --- a/subsection_Stellar_Models_We_have__1.tex  +++ b/subsection_Stellar_Models_We_have__1.tex 
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\subsection{Stellar Models}  We have used the Modules for Experiments in Stellar Evolution (MESA, release 7385) code to evolve low-mass stars with initial mass in the range 1-3.0$\,M_\odot$. Models have been evolved from the pre-main-sequence to the tip of the red giant branch \cite{Paxton_2010,Paxton_2013}. We chose a metallicity of $Z=0.02$ with a mixture taken from \cite{2005ASPC..336...25A}; the plasma opacity is determined using the OPAL opacity tables from \cite{Iglesias_1996}. Convective regions are calculated using the mixing-length theory (MLT) with $\alpha_{\rm MLT} = 2.0$. The boundaries of convective regions are determined using the Ledoux criterion. An {\bf Overshooting is parameterized by an  exponentially decaying overshooting with diffusivity that decays over a distance  $f_{\rm ov}= 0.018$ extends the mixing region beyond ov} H$ above  the convective boundaries \cite{2000A&A...360..952H}. boundary \cite{2000A&A...360..952H}, with $f_{\rm ov}= 0.018$.}  We include in Section \ref{inlist} the inlist used for running the calculations. To estimate plausible magnetic field strengths within the cores of red giants, we use two methods. First, we extrapolate inward from a main sequence surface field of $B \sim 3\, {\rm kG}$, as appropriate for magnetic Ap stars \cite{Auri_re_2007}, assuming the field is a pure dipole such that the field strength scales as $B \propto r^{-3}$. Since the radius of the convective core is typically $r_c \sim R/10$ for low mass main sequence stars, field strengths of $B > 10^{5} \, {\rm G}$ are attainable near the core.  
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Figure \ref{Fig:Struc} shows the density, mass, and magnetic field profiles of the $1.6 \, M_\odot$ stellar model used to generate Figure \ref{fig:Prop}. To make this model, we extrapolate a dipole field inward from a surface value of $3 \times 10^{3} \, {\rm G}$ (as described above), with an artificial cap at a field strength of $5 \times 10^{4} \, {\rm G}$. We then calculate the corresponding RGB field profile using the flux conservation described above (for simplicity we set the field equal to zero in convective regions of the RGB model). This relatively conservative approach yields a field strength of $\sim \! \! 10^6 \, {\rm G}$ at the H-burning shell, sufficient for magnetic suppression of dipole oscillation modes. We note that field strengths of this magnitude are orders of magnitude below equipartition with the gas pressure, and therefore have a negligible influence on the stellar structure.