deletions | additions       diff --git a/Beyond_a_stellar_evolution_model__.tex b/Beyond_a_stellar_evolution_model__.tex  index d0bb6ad..f60e1d7 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} \simeq -1.7 f {\left(  \frac{T_{\rm{eff}}}{4500 \rm{K}} \right)^{4/3} \right)}^{4/3}  \left( \frac{M_{\rm{env}}}{M_{\odot}} \right) \frac{M_{\odot}}{M} \frac{M_2}{M} \frac{M+M_2}{M} \left( \frac{R}{a} \right)^8 \ \rm{yr}^{-1}, \end{equation}  where $f$ is a dimensionless factor of order 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 its convective envelope, $M_2$ is the mass of the companion star, and $a$ is the semi-major axis of the binary orbit. 
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