Jim Fuller edited subsection_Stellar_Models_We_have__1.tex  almost 9 years ago

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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 $\mso$. Models have been evolved from the pre-main-sequence to the tip of the red giant branch \citep{Paxton_2010,Paxton_2013}. We chose a metallicity of $Z=0.02$ with a mixture taken from \citet{2005ASPC..336...25A}; the plasma opacity is determined using the OPAL opacity tables from \citet{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 exponentially decaying overshooting with $f_{\rm ov}= 0.018$ extends the mixing region beyond the convective boundaries \cite{2000A&A...360..952H}. We include in Section \ref{inlist} the inlist used for running the calculations.  We calculate the internal magnetic field of our stellar model shown in Figures \ref{fig:Prop} and \ref{Fig:Struc} as follows.We do this in two ways.  First, we extrapolate inward from a main sequence surface field of $B \sim 3\, {\rm kG}$, as appropriate for magnetic Ap stars \citep{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 in excess of $B \gtrsim 10^{5} \, {\rm G}$ are attainable near the core. To extrapolate to field strengths plausibly obtained within the radiative cores of red giants, we assume that the magnetic flux (calculated via the methods above) within the core is conserved as it contracts. This is a good approximation as for stable magnetic equilibria in the mass range discussed here, the timescale for the field to diffuse through the star (Ohmic timescale) is longer than the main sequence timescale. At each mass shell within a red giant, the field strength is then approximated by \begin{equation}  \label{eqn:BRG}  B_{\rm RG} = \bigg(\frac{r_{\rm MS}}{r_{\rm RG}}\bigg)^2 B_{\rm MS} \, ,