The Sloan Digital Sky Survey Reverberation Mapping Project:
  Low-Ionization Broad-Line Widths and Implications for Virial Black Hole Mass
  Estimation
  The width of the broad emission lines in quasars is commonly characterized
either by the full-width-at-half-maximum (FWHM) or the square root of the
second moment of the line profile ($\sigma_{\rm line}$), and used as an
indicator of the virial velocity of the broad-line region (BLR) in the
estimation of black hole (BH) mass. We measure FWHM and $\sigma_{\rm line}$ for
H$\alpha$, H$\beta$ and Mg II broad lines in both the mean and root-mean-square
(rms) spectra of a large sample of quasars from the Sloan Digital Sky Survey
Reverberation Mapping (SDSS-RM) project. We introduce a new quantitative recipe
to measure $\sigma_{\rm line}$ that is reproducible, less susceptible to noise
and blending in the wings, and scales with the intrinsic width of the line. We
compare the four definitions of line width (FWHM and $\sigma_{\rm line}$ in
mean and rms spectra, respectively) for each of the three broad lines and among
different lines. There are strong correlations among different width
definitions for each line, providing justification for using the line width
measured in single-epoch spectroscopy as a virial velocity indicator. There are
also strong correlations among different lines, suggesting alternative lines to
H$\beta$ can be used to estimate virial BH masses. We further investigate the
correlations between virial BH masses using different line width definitions
and the stellar velocity dispersion of the host galaxies, and the dependence of
line shape (characterized by the ratio FWHM/$\sigma_{\rm line}$) on physical
properties of the quasar. Our results provide further evidence that FWHM is
more sensitive to the orientation of a flattened BLR geometry than $\sigma_{\rm
line}$, but the overall comparison between the virial BH mass and host stellar
velocity dispersion does not provide conclusive evidence that one particular
width definition is significantly better than the others.
