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Meredith L. Rawls edited Radial Velocities.tex
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\section{Radial velocities}\label{rvs}
To extract radial velocities from the spectra, we use the broadening function (BF) technique as outlined by \citet{ruc02}. The BF is a function that transforms a sharp-line spectrum of a standard star into a Doppler-broadened spectrum. In practice, it can be used to describe any deviation of an observed spectrum from an idealized sharp-line spectrum: various forms of line broadening, shifted lines due to Doppler radial velocity shifts, two sets of lines in the case of a spectroscopic binary, etc. The BF convolution is solved with singular value decomposition as described in \citet{ruc02}. This technique is generally preferred over the more familiar cross-correlation function (CCF), because the BF is a true linear deconvolution while the CCF is a non-linear proxy and is less suitable for double-lined spectra. For this analysis, we adapted the IDL routines provided by Rucinski\footnote{\url{http://www.astro.utoronto.ca/~rucinski/SVDcookbook.html}} into python\footnote{\url{https://github.com/mrawls/BF-rvplotter}}.
% We use a
PHOENIX model spectrum
CITATION HERE of
Arcturus taken a star with
ARCES in 2004 PHYSICAL PARAMETERS HERE as a BF
template. Since the BF handles line broadening between template
for and target robustly, we do not adjust the resolution of the
optical spectra
We use a PHOENIX
template. A model spectrum
CITATION HERE was used instead of
a an actual star
to avoid inconsistencies between the optical and IR regimes, additional barycentric corrections, spurious telluric line BF peaks, and uncertainties in a template star's systemic RV. However, when we tested the BF with
PHYSICAL PARAMETERS HERE an observation of Arcturus as a
BF template,
the peaks were narrower and had larger amplitudes. The advantages that come from using an observed stellar spectrum as a template may be critical for future work, especially when measuring the RVs of main-sequence companions which
has been CONVOLVED SOMEHOW to have contribute only a
similar resolution as ARCES. few percent of the flux to an RG/EB.
%
OR, Are the peaks broader because it's part of the BROADENING function solution, i.e., is
it showing the
Arcturus template better??!! discrepancy in resolution?!
For the optical spectra we consider the wavelength range 5400--6700 \AA. This region is chosen because it has a high signal-to-noise ratio and minimal telluric features. For the near-IR APOGEE spectra, we consider the wavelength range 15150--16950 A. We first smooth the BF with a Gaussian to remove un-correlated, small-scale noise below the size of the spectrograph slit, and then fit Gaussian profiles to measure the location of the BF peaks in velocity space. The geocentric (raw) results from the BF technique are shown for the optical spectra in Figure \ref{fig:bffig}. The results look similar for the near-IR spectra. The final derived radial velocity curve with barycentric corrections is shown in Figure \ref{fig:rvfig}.
%Radial velocities for the two near-IR APOGEE spectra are obtained in the same way, using an APOGEE spectrum of Arcturus taken in 2014 as the BF template.