Meredith L. Rawls edited Refined ELC Models.tex  over 8 years ago

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We therefore calculate a second set of parameters based on the root-mean-square (RMS) of \revise{six ELC models, one for each light curve segment, excluding the seventh segment which has significantly higher contamination in both eclipses}. Each segment still includes the full set of radial velocity data. The values reported are the RMS of these seven models, $a_{\rm{RMS}} = \sqrt{\frac{1}{n} \sum_{i=1}^n (a_i^2)}$, plus or minus the RMS error, $\sqrt{\frac{1}{n} \sum_{i=1}^n (a_i - a_{\rm{RMS}})^2}$. These are reported in Table \ref{table1}. \revise{Temperature is excluded because the white-light \emph{Kepler} bandpass is not well-suited to constrain stellar temperatures, and the RMS errors among each light curve segment are artificially small.}  For all parameters, the all-eclipse model and the LC segment model agree \revise{within $2\sigma$. However, we We  note that $\omega$, the \emph{Kepler} contamination, and $R_1$ all have significantly larger error bars in the LC segment results than the all-eclipse results. This reflects the an  inherent degeneracy between viewing angle and stellar radius in a binary with grazing eclipses, which is exacerbated by uncertainties in limb darkening and temperature, as well as varying contamination between quarters. When we hold both stars'  limb darkening fixed withpoorly-constrained  theoretical values $q1 $q_1  = 0.49$ and $q2 $q_2  = 0.37$ \citep{claret}, \citep{cla13},  we find an ELC solution that gives $R_1 = 7.86 \pm 0.02 \simeq 7.9  \ R_\odot$, $R_2 = 8.22 \pm 0.02 \simeq 8.2  \ R_\odot$,and  $\omega = 17.37 \pm 0.01 \simeq 17.4  \ \rm{deg}$, however, and contamination as high as 5 \%. However,  this solution  has anotably  higher $\chi^2$ than the models which include allow triangularly sampled quadratic  limb darkening as coefficients \citep{kip13} to be  free parameters. parameters, and it is important to consider that theoretical limb darkening values are poorly constrained for both giant stars and wide bandpasses.  We therefore  adopt the all-eclipse ELC solution in this work because it has the lowest $\chi^2$ and uses all available data to constrain the system.}