Meredith L. Rawls edited section_Physical_parameters_of_the__.tex  almost 8 years ago

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In this work, we adopt the masses and radii from \citet{fra13,gau16,raw16} from binary modeling for the 14 double-lined systems. We further adopt the masses and radii from \citet{gau16} for the four single-lined systems which were derived by combining the asteroseismic scaling relations with the mass function and inclination from eclipse modeling. The single-lined binaries' masses and radii have larger systematic uncertainties than their double-lined counterparts because the asteroseismic scaling relations are known to overestimate mass by about 15\% on average for evolved stars \citep{gau16}.  To ensure consistent results between JKTEBOP and ELC, we model a representative subset of RG/EBs using ELC with differential evolution Monte Carlo Markov Chain optimizers \citep[DE-MCMC,][]{ter06}. We find a full dynamic solution for seven systems with 16 free parameters: $P_\textrm{orb}$, $T_\textrm{conj}$, $i$, $e \cos \omega$, $e \sin \omega$, the temperature of one star ($T_{\textrm{eff}, 1}$ or $T_{\textrm{eff}, 2}$), the mass of one star $M_1$, the amplitude of one star's radial velocity curve $K_1$, the fractional radii of each star, $R_1/a$ and $R_2/a$, the temperature ratio $T_2/T_1$, the \emph{Kepler} contamination factor, and stellar limb darkening parameters for the triangularly parameterized quadratic law \citep{kip13}. One of the seven RG/EBs modeled with ELC is a single-lined binary, and we fit the same 16 free parameters but note that the mass ratio, component masses, scale of the system, and component radii are unconstrained. Each ELC optimization run is continued long enough to compute more than 400,000 models and achieve a robust global solution. In all cases, the stellar masses and radii agree within \textbf{ONE OR TWO??} sigma with those from \citet{gau16}. We present all the masses and radii in Table \ref{table:mrcompare} \ref{tab:mrcompare}  and show the consistency of the two binary modeling techniques in Figure \ref{fig:mrcompare}. % put table and figure here