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Jim Fuller edited subsection_Stellar_Models_We_have__1.tex
about 9 years ago
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...
\label{eqn:BRG}
B_{\rm RG} = \bigg(\frac{r_{\rm MS}}{r_{\rm RG}}\bigg)^2 B_{\rm MS} \, ,
\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., $r_{\rm
RG}/r_{\rm MS} MS}/r_{\rm RG} \sim
1/10$ 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.