Meredith L. Rawls edited Physical parameters.tex  almost 9 years ago

Commit id: 9d99706632c4855c60d8c4abc937b7e46c186b69

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We use ELC to solve for 16 parameters: orbital period $P_{orb}$, zeropoint $T_{conj}$ (this sets the primary eclipse to orbital phase $\phi_{ELC} = 0.5$ instead of $\phi = 0$), orbital inclination $i$, $e \sin \omega$ and $e \cos \omega$ (where $e$ is eccentricity and $\omega$ is the longitude of periastron), the temperature of the primary star $T_1$, the mass of the primary star $M_1$, the amplitude of the primary 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 quadratic limb darkening law. The scale of the system (and hence the component masses and radii) is uniquely determined given the primary star mass, the amplitude of its radial velocity curve, and the orbital period.  Error bars for each fit parameter are estimated by scaling the measured error values so that $\chi^2 \sim N$, where $N$ is the number of data points in one of three data sets (light curve of the binary, radial velocity of Star 1, and radial velocity of Star 2). We then assign one-sigma errors for each parameter corresponding to the value that gives $\Delta \chi^2 = \chi^2_{\rm{min}} + 1$. The results for the all-eclipse ELC model are shown in Figure \ref{fig:ELCresult} and presented in the ``All-eclipse model'' column of Table \ref{table1}. These values are used to constrain the spectral disentangling process described in Section \ref{atm}.