deletions | additions       diff --git a/subsection_Stellar_evolution_and_tidal__.tex b/subsection_Stellar_evolution_and_tidal__.tex  index 923020c..f14f491 100644  --- a/subsection_Stellar_evolution_and_tidal__.tex  +++ b/subsection_Stellar_evolution_and_tidal__.tex 
...
Over the course of KIC 9246715's life, both stars have evolved in tandem to reach the configuration we see today. We quantify this with simple stellar evolution models created using the Modules for Experiments in Stellar Astrophysics (MESA) code \citep{pax11,pax13,pax15}. Figure \ref{fig:mesa} presents a suite of models with various initial stellar masses. All the models include overshooting for all the convective zone boundaries with an efficiency of $f = 0.016$ \citep{her00}, assume no mass loss, \revise{and set the mixing-length parameter $\alpha = 2.5$. The standard solar value of $\alpha = 2$ does not allow for sufficiently small stars beyond the red giant branch}. The stage of each model star's life as it ages in Figure \ref{fig:mesa} is color-coded, and \revise{curved lines of constant radii corresponding to $R_1 \pm \sigma_{R_1}$ (gray) and $R_2 \pm \sigma_{R_2}$ (white), within the ranges of $M_1 \pm \sigma_{M_1}$ and $M_2 \pm \sigma_{M_2}$, respectively, are shown. There are two instances in each pair of model stars' lives when they have the same radii as the stars in KIC 9246715: once on the red giant branch, and again on the secondary red clump (horizontal branch).}  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.  \reviseagain{Stars \newrevise{Stars  1 and 2 in Figure \ref{fig:mesa} have horizontal branch ages of $8.13\substack{+0.08 \\ -0.06} \times 10^8 \ \rm{yr}$ and $8.36\substack{+0.08 \\ -0.06} \times 10^8 \ \rm{yr}$, respectively, and red giant branch ages of $9.17 \pm 0.17 \times 10^8 \ \rm{yr}$ and $9.42\substack{+0.20 \\ -0.13} \times 10^8 \ \rm{yr}$, respectively.} 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 for red-giant-branch mass loss ($\eta = 0.4$, \revise{a commonly adopted value of the parameter describing mass-loss efficiency}, see \citealt{mig12}) 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.