deletions | additions       diff --git a/Beyond_a_stellar_evolution_model__.tex b/Beyond_a_stellar_evolution_model__.tex  index 59651db..3881e8a 100644  --- a/Beyond_a_stellar_evolution_model__.tex  +++ b/Beyond_a_stellar_evolution_model__.tex 
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From \citet{ver95}, the timescale $\tau_c$ on which orbital circularization occurs is given by  \begin{equation}  \frac{1}{\tau_c} \equiv \frac{\rm{d} \ln e}{\rm{d}t} = f \left( \frac{L}{M_{\rm{env}}R^2} \right)^{1/3} \frac{M_{\rm{env}}}{M} \frac{M_2}{M} \frac{M+M_2}{M} \left( \frac{R}{a} \right)^8. \right)^8,  \end{equation}  Here, where  $f$ is a dimensionless factor of order unity unity, $M$, $L$,  and $R$ are the mass, luminosity, and radius of a giant star with dissipative tides,  $M_{\rm{env}}$ is the mass of the its  convective envelope envelope, $M_2$ is the mass of the companion star, and $a$ is the semi-major axis  of the primary star. binary orbit.  We integrate this expression over the lifetime of the star KIC 9246715  to estimate the total expected change in orbital eccentricity, $\Delta \ln e$. We assume $a$ is constant, $f = 1$, and further assume that there is  no mass loss. Because KIC 9246715 is a well-separated binary, we can separate the integral into a part that is independent of the orbit and a part that must be integrated over time: %To estimate the change in eccentricity over the lifetime of KIC 9246715, we integrate over the orbit circularization timescale: 
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