deletions | additions       diff --git a/subsection_Stellar_evolution_and_tidal__.tex b/subsection_Stellar_evolution_and_tidal__.tex  index 8424790..84a9e68 100644  --- a/subsection_Stellar_evolution_and_tidal__.tex  +++ b/subsection_Stellar_evolution_and_tidal__.tex 
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\subsection{Stellar evolution and tidal forces}\label{tides}  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 and assume no mass loss. Recall that the masses and radii of each star are $M_1 = 2.16 \pm 0.04\ M_{\odot}$, $M_2 = 2.14 \pm 0.03\ M_{\odot}$, $R_1 = 7.90 \pm 0.04 \ R_{\odot}$, and $R_2 = 8.33 \pm 0.04 \ R_{\odot}$. The stage of each model star's life as it ages in Figure \ref{fig:mesa} is color-coded. Two vertical lines of constant mass (corresponding to $M_1$ and $M_2$) and two lines of constant radii (corresponding to $R_1$ and $R_2$) are shown. From this, we conclude As expected, the fact  that we find very similar masses for  both stars are coeval, because they can exist in is not surprising. In general, coeval stars on  the same evolutionary state at red giant branch must have masses within $1\%$ of each other, whereas there is slightly more freedom on  the same time. horizontal branch due to its longer evolutionary lifetime.  Stellar evolution modeling using standard input parametrization  places both stars on the red giant branch. They Specifically, the derived radii  are too small by at least $0.5 \ R_\odot$ compared to the models,  to have evolved past this stage onto the red clump. We consider several possibilities that could explain why these stars' nearly identical evolutionary histories appear to place them on the red giant branch while the asteroseismic period spacing suggests they are on the red clump:  \begin{itemize} 
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%If these physical differences are significant enough, stellar evolution may proceed differently than we expect, and it may be possible to create red clump stars with smaller radii.  \item The noisy period spacing estimate ($\Delta \Pi \simeq 150 \ \rm{sec}$) may not be measuring what we expect due to rotational splitting of mixed oscillation modes. If the true period spacing is closer to $\Delta \Pi \simeq 80 \ \rm{sec}$, this would explain the disagreement. A detailed discussion of rotational splitting behavior in slowly rotating red giants is explored in \citet{gou13}.  \end{itemize}