this is for holding javascript data
Meredith L. Rawls edited Refined ELC Models.tex
over 8 years ago
Commit id: c890fedb0230a150878fd71ad9df03a8c4384d2e
deletions | additions
diff --git a/Refined ELC Models.tex b/Refined ELC Models.tex
index 9cc6142..a7f8dc5 100644
--- a/Refined ELC Models.tex
+++ b/Refined ELC Models.tex
...
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 with
poorly-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 a
notably 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.}