Meredith L. Rawls edited Stellar atmosphere model.tex  about 9 years ago

Commit id: f76ba9202abee842881d6d1463c0d9d241352232

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To accomplish this, we use the FDBinary tool \citep{ili04} on the spectral window 5402--6750 \AA. Following the approach in \citet{bec14}, we break the window into 25 pieces that each span about 10 \AA. FDBinary does not require a template spectrum, and instead uses the orbital parameters of a binary system to separate spectra in Fourier space. We tested FDBinary's capabilities by creating a set of fake double-lined spectra from a weighted sum of two identical spectra of Arcturus. When the orbital solution and flux ratio is correctly specified, the program returns a pair of single-lined spectra that are indistinguishable from the original.  FDBinary requires six parameters to define the shape of the radial velocity curve: orbital period, time of periastron passage (zeropoint), eccentricity, longitude of periastron, and amplitudes of each star's radial velocity curve. We set these to 171.277 days, 319.7 days\footnote{Units of BJD--2454833}, 0.35, 17.3 deg, 33.1 km s$^{-1}$, and 33.4 km s$^{-1}$, respectively. While FDBinary does include an optimization algorithm for any subset of these parameters, we use more robust fixed values from the photodynamical model described in Section \ref{model}. However, some of measured radial velocity points from Figure \ref{rvfig} \ref{fig:rvfig}  deviate as much as $\pm 2$ km s$^{-1}$ from the FDBinary model velocity curve. WHAT DO WE DO ABOUT THIS? ANYTHING? FDBinary also requires the flux ratio of the two stars. WRITE MORE HERE.  %Because KIC 9246715 contains two similar red giants (though the oscillating giant is larger than its companion), we initially set the flux ratio to 1. However, as it became clear that the oscillating giant is nearly 2x as large as its companion, we estimated a flux ratio of 4:1. THIS IS ACTUALLY WRONG, FLUX RATIO IS CLOSER TO 1.