Spectroscopic Variability of the Broad H$\beta$ Emission Line in Sloan Digital Sky Survey Quasars
We present a catalog of broad H$\beta$ variability properties for all spectra of quasars with $z<0.8$ and at least two observations included in the Sloan Digital Sky Survey (SDSS) Data Release 16 quasar catalog. For each spectrum, we perform a spectral decomposition to isolate the broad H$\beta$ emission. We measure the luminosity, FWHM, equivalent width, centroid, and Pearson skewness coefficient of broad H$\beta$ and provide derived physical properties such as the single-epoch black hole mass and the bolometric luminosity. For each pair of spectra in the sample, we calculate the change in radial velocity of the centroid of broad H$\beta$ emission ($\Delta v_{rad}$) as well as other derived properties related to broad H$\beta$ shape variability. We use forward-modeling methods to estimate the uncertainty in our measurements and discuss an improved method for estimating the uncertainty in $\Delta v_{rad}$ in the case where a spectral decomposition is used to isolate the broad H$\beta$ emission. We find that $\Delta v_{rad}$ is not normally distributed and that the shape of the distribution depends on the interval between observations. We discuss the effect of the predominance of the Reverberation Mapping subsample in the sample of pairs of spectra in SDSS.