deletions | additions       diff --git a/Beyond_a_stellar_evolution_model__.tex b/Beyond_a_stellar_evolution_model__.tex  index ff827d4..b9a168b 100644  --- a/Beyond_a_stellar_evolution_model__.tex  +++ b/Beyond_a_stellar_evolution_model__.tex 
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where $M_{\rm{env}}$ is the mass of the convective envelope of the primary star. It is important to note that \citet{ver95} assumed circularization would proceed by a small secondary star (main sequence or white dwarf) imposing an equilibrium tide on a large giant, while the situation with KIC 9246715 is more complicated. For a thorough review of tidal forces in stars, see \citet{ogi14}.  For the MESA model described above with $M = 2.16 \ M_{\odot}$, we compute $\Delta \ln e = -4.52$ -3.04 \times 10^{-5}$  up until $t = 7.28 \times 10^8$ years (which corresponds (the age corresponding  to $R \simeq 8 \ R_{\odot}$. R_{\odot}$). Rewriting this as $\log [-\Delta \ln e] = -4.52$, a value clearly less than zero, indicates that the binary has \emph{not} had sufficient time to circularize its orbit. The two coeval 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. In contrast, given just another $0.4 \times 10^8$ years to evolve past the red giant branch toward the red clump, $\log [-\Delta \ln e]$ becomes greater than zero and the expectation is a circular orbit. Therefore, the observed $e = 0.35$ is consistent only with a younger red giant branch star, and not with a more evolved red clump star.  indicating that the eccentricity should have changed by more than 1 over the star's lifetime. The two coeval 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. In either case, this means that regardless of KIC 9246715's original eccentricity, it should have evolved to zero by the present day, when both stars are in the red clump phase. The observed $e = 0.35$ is inconsistent.  DISCUSS THE RESULT FURTHER. 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 (Section \ref{discuss}), a star spot present during one primary eclipse event only (Section \ref{segment}), a constraint on $v \sin i$ from spectra (Section \ref{parameters}), and asteroseismic period spacing consistent with red clump stars yet not clear enough to measure a robust core rotation rate (Section (see Section  \ref{discuss}).WRITE MORE ABOUT SYNCHRONIZATION OR LACK THEREOF HERE, AND CLEAN THE FOLLOWING PARAGRAPHS UP.  \textit{Centrifugal forces dissipate energy that would cause circularization. Causes individual rotations to synchronize (usually synchronization happens first, and circularization happens second). Neither of those things have happened here, but it seems like the rotation knows about the orbit (based on quasiperiodic spot modulations, not necessarily vsini, and certainly not a robust core rotation measure), so SOMETHING has happened... just not synchronization. This ``should have'' happened even faster since it's two RGs, not a RG + MS (or WD). The fact that both of them have convection zones that could be causing this centrifugal force situation means that this should have happened a long time ago in a hand-wavey sort of way.  The fact that only one star is oscillating points to how tidal activity may affect oscillations.  Important for other people because over half of cool stars should be in binaries! Using RGs to probe the galaxy has to be done carefully because of external influences of binarity on oscillations.}