deletions | additions       diff --git a/Beyond_a_stellar_evolution_model__.tex b/Beyond_a_stellar_evolution_model__.tex  index 42b0093..949807a 100644  --- a/Beyond_a_stellar_evolution_model__.tex  +++ b/Beyond_a_stellar_evolution_model__.tex 
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For the MESA model described above with $M = 2.15 \ M_{\odot}$, \revise{we compute $\Delta \ln e = -x.x \times 10^{-5}$ up until $t = 8.3 \times 10^8$ and $\Delta \ln e = -x.x \times 10^{-5}$ up until $t = 9.3 \times 10^8$ years (the ages corresponding to $R \simeq 8.3 \ R_{\odot}$). Rewriting these as $\log [-\Delta \ln e] = -x.x$ and $\log [-\Delta \ln e] = -x.x$, which are both less than zero}, indicates that the binary has \emph{not} had sufficient time to circularize its orbit, though it is possible the system's initial eccentricity was higher than the $e = 0.35$ we observe today.  The two stars in KIC 9246715 have very similar masses, radii, and temperatures, so this rough calculation is valid both for Star 1 acting on Star 2 and vice versa. Given more time to evolve past the tip of the red giant branch and well onto the red clump (with $R \simeq 25 \ R_\odot$ for the second time), $\log [-\Delta \ln e]$ becomes greater than zero and the expectation is a circular orbit. Therefore, the observed eccentricity is consistent with \revise{both a red giant branch star aged approximately $8.3 \times 10^8$ years and with a secondary red clump star just past the tip of the red giant branchwith  aged approximately $9.3 \times 10^9$ years.} Tidal forces also tend to synchronize a binary star's orbit with the stellar rotation period, generally on shorter timescales than required for circularization \citep{ogi14}. Hints of KIC 9246715's stellar rotation behavior are present throughout this study: quasi-periodic light curve variability on the order of half the orbital period, \revise{residual scatter between light curve observations and the best-fit model during both eclipses}, a constraint on $v_{\rm{rot}} \sin i$ from spectra, and an asteroseismic period spacing consistent with a red clump star yet not clear enough to measure a robust core rotation rate.