deletions | additions       diff --git a/subsection_Stellar_evolution_and_tidal__.tex b/subsection_Stellar_evolution_and_tidal__.tex  index 2b76cad..b2cbd61 100644  --- a/subsection_Stellar_evolution_and_tidal__.tex  +++ b/subsection_Stellar_evolution_and_tidal__.tex 
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In general, coeval stars on the red giant branch must have masses within $1\%$ of each other, \revise{whereas masses can differ more on the horizontal branch due to its longer evolutionary lifetime. Both model stars in Figure \ref{fig:mesa} can be the same age on the horizontal branch, but not on the red giant branch. Without $\alpha > 2$, the MESA model stars on the horizontal branch are always larger than those in KIC 9246715. We consider several ideas as to why the MESA models and the evolutionary stage determined from asteroseismic mixed-mode period spacing in Section \ref{subsubsec_mixed} may differ:}  \begin{itemize}  \item Mass loss: Adding a prescription formoderate  red-giant-branch mass loss ($\eta = 0.4$, \revise{a commonly adopted value of the parameter describing mass-loss efficiency},  see \citealt{mig12}) \citealt{mig12,ren88})  to the MESA model does not appreciably change stellar radius as a function of evolutionary stage. Even a more extreme mass-loss rate ($\eta = 0.7$) does not significantly affect the radii, essentially because the star is too low-mass to lose much mass. \item He abundance: Increasing the initial He fraction in the MESA model does not allow for smaller stars in the red clump phase, because shell-H burning is very efficient with additional He present. As a result, the star maintains a high luminosity and therefore a larger radius as it evolves from the tip of the red giant branch to the red clump.  \item Convective overshoot: The MESA models in this work assume a reasonable overshoot efficiency as described above ($f = 0.016$). We tried varying this from 0--0.03, and can barely make a red clump star as small as $8.3 \ R_\odot$ when $f = 0.01$. With less overshoot, the RGB phase as shown in Figure \ref{fig:mesa} increases in duration, which allows a higher probability for stars of $M_1$ and $M_2$ to both be on the RGB.  \item Period spacing: The period spacing $\Delta \Pi_1 = 150 \ \rm{s}$ may not be measuring what we expect due to rotational splitting of mixed oscillation modes. If the true period spacing is closer to $\Delta \Pi_1 \simeq 80 \ \rm{s}$, \revise{this would put the oscillating star on the red giant branch. However, as demonstrated in Section \ref{subsubsec_mixed}, the mixed modes do agree best with a secondary red clump star.} A detailed discussion of rotational splitting behavior in slowly rotating red giants is explored in \citet{gou13}.