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

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\label{review}  \subsection{Binary modeling}  \citet{gau16} and \citet{raw16} used JKTEBOP \citep{sou09} and the Eclipsing Light Curve (ELC) program \citep{oro00} to simultaneously fit a combination of light curves and radial velocity observations for a total of 17 RG/EBs observed by \emph{Kepler}. \citet{fra13} did the same for KIC 8410637, which brings the total to 18. For the 14 systems with radial velocity curves for both stars, this gives a full dynamic solution: orbital period $P_{orb}$, zeropoint, $P_{\textrm{orb}}$, zeropoint $T_0$,  orbital inclination $i$, eccentricity and argument of periastron (parameterized as $e \sin \omega$ and $e \cos \omega$), component masses, component radii, and the effective temperature ratio.For the remaining four systems that have a radial velocity curve for one star only, we can determine relative radii and no component masses.  Of the 18 total systems, 14 have red giants that exhibit solar-like oscillations, which were analyzed in \citet{gau14,gau16} to derive global asteroseismic parameters. In this work, we adopt the masses and radii from reported in  \citet{fra13,gau16,raw16} from dynamic eclipsing  binary modeling models  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 We note that 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\% and radius by about 5\%,  on average average,  for evolved stars \citep{gau16}. To ensure consistent results between the binary modeling programs  JKTEBOP \citep[][, used in \citealt{gau16}]{sou13}  and ELC, ELC \citep[][, used in \citealt{raw16}]{oro00},  we model a representative subset of seven  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 The input datasets are identical to those described in \citet{gau16}: detrended \emph{Kepler} light curves and  radial velocity curve $K_1$, the fractional radii of each star, $R_1/a$ and $R_2/a$, the temperature ratio $T_2/T_1$, curves from  the \emph{Kepler} contamination factor, ARCES spectrograph  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, APOGEE. For KICs 9291629  and 9970396,  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 include eight  and achieve a robust global solution. The stellar masses all agree within one sigma with those 12 binned $BVRI$ photometry points, respectively,  from\citet{gau16} and the stellar radii generally agree within two sigma. There are a few exceptions: EXPLAIN THEM HERE. We present all  the masses and radii 1 m robotic telescope at APO. These observations were taken  inTable \ref{tab:mrcompare}  and show out of eclipse to better constrain  the consistency stellar flux ratios. Detailed descriptions  of these new observations and  the two binary ELC  modeling techniques technique are available  in Figure \ref{fig:mrcompare}. \citet[][Chapter 3]{rawPhD}.  % put table Using ELC, 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 figure here $R_2/a$, 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, KIC 8702921, 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. For each system, the ELC optimization run is continued long enough to compute more than 400,000 models and arrive at a robust global solution.  The stellar masses all agree within one sigma with those from \citet{gau16} and the stellar radii generally agree within two sigma. We present all the masses and radii in Table \ref{tab:mrcompare} and show the consistency of the two binary modeling techniques in Figure \ref{fig:mrcompare}. There are four stars which do not have radii that agree within two sigma: both stars in KIC 3955867 and the main sequence companion stars in KICs 7037405 and 9291629. They are shown as open circles in the right portion of Figure \ref{fig:mrcompare}, where it can be seen that two are slightly larger in ELC than JKTEBOP and two are slightly smaller. The offset is not systematic, and can be attributed to a difference in how stellar atmospheric parameters are modeled in the two techniques over the broad \emph{Kepler} bandpass. The JKTEBOP models in \citet{gau16} assume a fixed quadratic limb darkening law for the main sequence star and fit only the first order term for the quadratic law of the red giant. On the other hand, ELC fits the reparameterized quadratic limb darkening law \citep{kip13} for both stars together with a model stellar atmosphere integrated over the \emph{Kepler} bandpass to set the intensity at the stellar surface normals. The error bars for stellar radii from both methods are likely underestimated because neither limb darkening parameterization is an accurate representation of reality.