Radial Velocities

The Adopted Radial Velocities Used by the SSPP

The spZbest fits file, which is generated from the SDSS spectroscopic reduction pipeline, provides two estimated radial velocities. One is an absorption-line redshift derived from a cross-correlation procedure using templates that were obtained from SDSS commissioning spectra (Stoughton et al. 2002). Another estimate comes from performing a "best-match'' procedure that compares the observed spectra with externally measured templates (in this case, the ELODIE library high-resolution spectra, as described by Prugniel & Soubiran 2001 and Moultaka et al. 2004), degraded to the resolving power of SDSS spectra.

Previous experience with the analysis of SDSS stellar spectra suggested that the radial velocity estimated from the ELODIE template matches is often the best available estimate, in the sense that it is the most repeatable based on spectra of "quality assurance'' stars with multiple determinations. However, there are some cases where the quoted error of an ELODIE spectral match velocity is larger than expected, so we also make use of the cross-correlation radial velocity, in the following manner:

1. If the velocity determined by comparison with the ELODIE templates has a reported error of 20 km s^-1 or less, then this velocity is adopted and the radial velocity flag is set to `RVOK(20)'.
2. If the error from the ELODIE template comparison is larger than 20 km s^-1 and the relative difference between the two reported radial velocities is less than 40 km s^-1, then we take an average of the two techniques, and the radial velocity flag is set to `RVOK(40) '.
3. If the error in the reported ELODIE velocity is larger than 20 km s^-1, and the difference of between the two estimates is between 40 and 100 km s^-1, we take an average of the two and the radial velocity flag is set to `RVOK(100)'.
4. If none of the above conditions are satisfied (which happens only rarely, and mainly for quite low S/N spectra, or for hot/cool stars without adequate templates), then we obtain an independent estimate of the radial velocity based on our own IDL routines. The calculation of the radial velocity is carried out by determining wavelength shifts for several strong absorption line features (Ca II K, Ca II H, Hδ, Ca I, Hγ, Hβ, Na I, Hα, the Ca~II triplet). After ignoring the calculated velocity above +500 km s^-1 or below -500 km s^-1 from the individual lines (which are very often spurious), we obtain a 3σ clipped average of the remaining radial velocities. If this computed average falls between -500 km s^-1 and +500 km s^-1, we take the calculated radial velocity as the adopted radial velocity and set the radial velocity flag to `RVCALOK'.

It should be noted that many of the techniques used for atmospheric parameter estimation in the SSPP work well even when the velocity determination for a given star has errors of up to 100 km s^-1 or more. Hence, we choose not to ignore spectra with high velocity errors, but rather simply indicate caution with the appropriate radial velocity flag.

If none of the above methods yield an acceptable estimate of radial velocity, or if the reported velocity is apparently spurious (greater than 1000 km s^-1 or less than -1,000 km s^-1), we simply ignore the spectrum of the star in our subsequent analysis, and set the radial velocity flag to `RVNOTOK'.

Checks on Radial Velocities − Zero Points and Scatter

To check on the accuracy of the SSPP radial velocities, we compare with the sample of over 150 high-resolution spectra of SDSS-I/SEGUE stars that have been obtained in order to calibrate and validate the stellar atmospheric parameters obtained by the SSPP.

After rejecting problematic spectra (e.g., low S/N high-resolution spectra, or stars that appear to be spectroscopic binaries at high spectral resolution), 137 stars remain to compare with the radial velocity results obtained for the medium-resolution SDSS spectra with the SSPP. A consistent offset of about -6.6 km s^-1 (with a standard deviation of 5.2 km s^-1) is obtained from a Gaussian fit to the residuals; this offset appears constant over the color range 0.1 &le: g-r ≤ 0.9.

An additional comparison with the radial velocity distribution of likely member stars in the Galactic globular clusters M~15 and M~13 reveals similar offsets (-6.8 km s^-1 and -8.6 km s^-1, respectively; see Lee et al. 2007 for a more detailed analysis).

The origin of this velocity offset has not yet been identified, but we expect that it may be tied to the wavelength solutions obtained for the individual fibers. However, in order to account for its presence, we apply an empirical +7.3 km s^-1 shift (the mean of the offsets from analysis of the high-resolution and the globular-cluster data), to each radial velocity obtained by the SSPP. For the time being, we conclude that the zero-point uncertainties in the corrected radial velocities determined by the SSPP (and the SDSS spectroscopic reduction pipeline it depends on) should be close to zero, with scatter on the order of 5 km s^-1.

Note that the scatter in the determination of radial velocities, based on the average displacements of the `quality assurance' stars with multiple measurements, varies from 3.5 km s^-1 (for brighter stars) to 20 km s^-1 (for fainter stars).