deletions | additions       diff --git a/Beyond_a_stellar_evolution_model__.tex b/Beyond_a_stellar_evolution_model__.tex  index e06e8c2..1451906 100644  --- a/Beyond_a_stellar_evolution_model__.tex  +++ b/Beyond_a_stellar_evolution_model__.tex 
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I(t) \equiv \int_0^t \left( \frac{T_{\rm{eff}}(t')}{4500 \rm{K}} \right)^{4/3} \left( \frac{M_{\rm{env}}(t')}{M_{\odot}} \right)^{2/3} \left( \frac{R(t')}{R_{\odot}} \right)^8 dt'. \nonumber  \end{equation}  For the MESA model described above with $M = 2.15 \ M_{\odot}$, \revise{we compute $\Delta \ln e = -2.27 -2.3  \times 10^{-5}$ up until $t = 8.3 \times 10^8$ and $\Delta \ln e = -0.17$ up until $t = 9.4 \times 10^8$ years (the ages corresponding to $R \simeq 8.3 \ R_{\odot}$). Rewriting these as $\log [-\Delta \ln e] = -4.6$ and $\log [-\Delta \ln e] = -0.77$}, which are both less than zero, indicates that the binary has \emph{not} had sufficient time to circularize its orbit, and 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 branch aged approximately $9.4 \times 10^8$ years.}