Jim Fuller edited subsection_Stellar_Models_We_have__1.tex  about 9 years ago

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\end{equation}  where $B_{\rm RG}$ is the field strength while on the RGB, $r_{\rm RG}$ and $r_{\rm MS}$ are the radial coordinates of the shell on the RGB and MS, respectively, and $B_{\rm MS}$ is the MS field strength. Mass shells enclosing $M \sim 0.2 M_\odot$ (which are located just outside the MS core and near the H-burning shell on the lower RGB) typically contract by a factor of $\sim \! 10$ from the MS to the lower RGB, i.e., $r_{\rm MS}/r_{\rm RG} \sim 10$ for stars of $\sim 1.6 \, M_\odot$. The magnetic field may therefore be amplified by a factor of $\sim \! 100$, and field strengths in excess of $10^6 \, {\rm G}$ are quite plausible within the H-burning shells of RGB stars.   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 $10^{3} \, {\rm G}$ (as described above), with an artificial cap at a field strength of $3 \times 10^{4} \, {\rm G}$. 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). 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 internal stellar structure.