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\subsection{Full Orbital Solutions}\label{orbit}  To combine radial velocities, parameters from atmosphere modeling, and light curves into a single physical solution, we will use the Eclipsing Light Curve (ELC) code \citep{oro00}. This code uses a genetic algorithm or Monte Carlo Markov Chain (MCMC) optimizers to simultaneously solve for a suite of stellar parameters. ELC is particularly well-suited to this analysis because it considers any set of input observables simultaneously and minimizes a global $\chi^2$ function. ELC is based on the Wilson-Devinney code \citep{wil71}. In the limiting case where the two stars are sufficiently separated as to be spherical in shape, ELC has a ``fast analytic mode'' that uses the equations in \citet{gim06}. We will use this option for most of the RG/EBs because they are well-detached binaries. In cases where we expect tidal forces to be significant, ELC can incorporate effects such as ellipsoidal variations via a full treatment of Roche geometry \citep{avn75}. A preliminary fit for the light curve and radial velocity curves of KIC 9246715 is shown in Figure \ref{elcfig}.  \begin{figure}[h!]   \centering  \includegraphics[width=4.8in]{markovfit_fixT1.png}  \caption{Model %\begin{figure}[h!]   %\centering  %\includegraphics[width=4.8in]{markovfit_fixT1.png}  %\caption{Model  fit for KIC 9246715 using ELC with residuals. The top panels show the light curve, the middle panels show the radial velocities, and the bottom panels show a zoomed view of each eclipse. The red lines show the best-fit ELC model, black points show the observed \emph{Kepler} light curve, and blue points show observed radial velocities.} \label{elcfig}  \end{figure} %\label{elcfig}  %\end{figure}  In addition, ELC can be used to model star spots. It allows for up to two spots per star, and the user can specify spot latitude, longitude, size, and temperature scaling (constant, or radially dependent with a linear or Gaussian profile). Moving spots can be simulated by invoking non-synchronous rotation. We will split each RG/EB light curve into ``chunks'' when modeling spots, as we do not necessarily think a single spot would persist for several years. Each ``chunk'' will initially consist of one primary and one secondary eclipse, following the approach of, e.g., \citet{oro14}. This will help constrain the prevalence of spots on red giants during different epochs and distinguish between situations with small verses large spot covering fractions.  We recognize that star spots are not the only signature of stellar activity. We will also search spectra for any Ca II H \& K line emission, which could indicate the presence of faculae \citep{noy84}. These magnetically driven features are observed on the Sun even during solar minimum when sunspots are rare.  \subsection{Stellar Evolution Models}  To infer a binary system's past, we will assume the two stars evolved together and consider the evolution of radii with time. As discussed in \citet{mac14}, this is preferred for spectroscopic binaries over, e.g., the star's position in the H-R diagram, because radii are directly measured from the orbital solution while computing temperature and luminosity would rely on color transformations and bolometric corrections.   For a sample of oscillating RG/EBs and their otherwise similar non-oscillating counterparts, we will use the stellar evolution module of the Modules for Experiments in Stellar Astrophysics (MESA) code, called MESAstar \citep{pax11,pax13}, to model each red giant's evolution with appropriate microphysics. We will use our results from Sections \ref{specanal2} and \ref{orbit} as inputs, and select models such that both stars have at the same age their measured present-day masses and radii and the correct temperature ratio. Figure \ref{mesastar} shows example evolutionary tracks for several near-solar-mass stars, as calculated with MESAstar. This is just a small subset of what the program is capable of modeling.  \begin{figure}[h!]   \centering  \includegraphics[width=4.5in]{mesastar.png}  \caption{Evolution models from MESAstar for 0.9, 1.2, 1.5, and 2 $M_{\s}$ stars. The top panel shows the evolution tracks on a traditional Hertzsprung-Russell diagram while the bottom panel shows the same tracks in the central temperature/central density ($T_c - \rho_c$) plane. The solid red point is the location of each star on the zero-age main sequence, and the metallicity of all stars is set at $Z = 0.02$. In the bottom panel, the He core flash and subsequent evolution of the C/O core is shown. The dashed blue and heavy gray lines show two different constant electron degeneracies, and the dashed red line is a line of constant pressure relevant to the He core flash. Figure from \citet{pax11}.}  \label{mesastar}  \end{figure}