this is for holding javascript data
Meredith L. Rawls edited Physical parameters.tex
over 9 years ago
Commit id: a5aa80f1e1dbdef51eb762bfd772ba2bc1f51ff2
deletions | additions
diff --git a/Physical parameters.tex b/Physical parameters.tex
index 49bf07e..9ec0c00 100644
--- a/Physical parameters.tex
+++ b/Physical parameters.tex
...
\section{Physical parameters from light curve \& radial velocities}\label{model}
To derive physical and orbital parameters for KIC 9246715, we use the Eclipsing Light Curve (ELC) code \citep{oro00}. ELC employs photodynamical modeling with
either a genetic algorithm or Monte Carlo Markov Chain optimizers to simultaneously solve for a suite of stellar parameters. It is able to consider any set of input constraints simultaneously, i.e., a combination of light curves and radial velocities, and can use a full treatment of Roche geometry \citep{kop69,avn75}. It uses the NextGen model atmospheres integrated over a specified filter (in this case, the relatively broad ``white-light'' \emph{Kepler} bandpass).
To characterize the binary, we compute two sets of ELC models. The first
set is done before any constraints uses all eclipses from
Section \ref{atm} are known. We use the
full folded light curve together with all radial velocity points and employ ELC's ``fast analytic mode.'' This
first set of and subsequent models
uses use the equations in
%\citet{gim06} \citet{man02}
and treats the two to treat both stars as
perfect spheres, which is
a reasonable
assumption for a well-detached
binary. binary like KIC 9246715. We use the parameters from
these prelimiary models this model to
guide inform the spectral disentangling process described in Section \ref{atm}.
The second set of ELC models breaks the light curves into ``chunks'' to investigate how stellar activity affects the model results. One ``chunk'' is a portion of the light curve that includes one primary and one secondary eclipse.
The second set of \subsection{All-Eclipse ELC
models uses constraints from atmosphere modeling, and breaks the light curves into ``chunks'' to search for stellar activity. One ``chunk'' is a portion of the light curve that includes one primary and one secondary eclipse and has length of order one orbital period (about 171 days for KIC 9246715). This allows us to search for stellar activity that may appear during one eclipse event only. % We keep the spherical assumption?? Or not??? Model}
\subsection{Preliminary ELC Model} We initially use ELC to solve for
16 19 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 $R_2/a$ (where $a$ is the average orbital seperation), the \emph{Kepler} contamination
factor, factor for each of four spacecraft configurations, and stellar limb darkening parameters for the quadratic limb darkening law. Because all binaries obey the relation
\begin{equation}
\frac{M_1}{M_2} = \frac{K_2}{K_1},
\end{equation}
the
final result from the ELC model includes masses and radii for both stars.
Error bars for each fit parameter are estimated by scaling the measured error values so that an otherwise identical ELC model yields an overall reduced $\chi^2 = 1$. One-sigma errors for each parameter then correspond to the value that gives $\Delta \chi^2 = 1$. The results for the All-Eclipse ELC Model are presented in Table TABLEREFHERE.
Maybe %Maybe talk about how we are suspicious of a spot during one of the primary eclipses, which we investigate in the next round of modeling.