Spectroscopic Variability of the Broad H$β$ Emission Line in Sloan Digital Sky Survey Quasars

TL;DR

This work builds a large time-domain spectroscopic catalog of broad $H\beta$ variability for $z<0.8$ SDSS quasars, enabling population-level insights into BLR dynamics. It employs a comprehensive spectral decomposition to isolate broad $H\beta$ and measures changes in centroid velocity, luminosity, and line width across multiple epochs, with rigorous uncertainty treatment that combines MCMC-based forward modeling and short-baseline noise checks. Key findings include that $\Delta v_{rad}$ is non-Gaussian (exponential at short baselines and Lorentzian at long baselines) and that RM-dominated samples sparsely bias the pair statistics, with implications for SMBHB searches and BLR modeling. The paper provides publicly available per-spectrum and per-pair data tables along with two complementary uncertainty estimation approaches, highlighting the importance of cadence and sample composition in time-domain quasar spectroscopy.

Abstract

We present a catalog of broad H$β$ 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$β$ emission. We measure the luminosity, FWHM, equivalent width, centroid, and Pearson skewness coefficient of broad H$β$ 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$β$ emission ($Δv_{rad}$) as well as other derived properties related to broad H$β$ shape variability. We use forward-modeling methods to estimate the uncertainty in our measurements and discuss an improved method for estimating the uncertainty in $Δv_{rad}$ in the case where a spectral decomposition is used to isolate the broad H$β$ emission. We find that $Δv_{rad}$ 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.

Figures (9)

• Figure 1: The distribution of the pairs of spectral observations in our sample as a function of rest frame time between observations. Also plotted are the histograms for the RM and non-RM sub-samples. The RM-targeted pairs dominate the dataset for all but the longest baselines. This is the first sample large enough to statistically characterize BLR profile variability on timescales comparable to BLR dynamical times.
• Figure 2: An example spectral decomposition. Left: The data (gray) are shown with the total decomposition model (red). The model components include a power law for the accretion disk (blue), BLR and NLR emission lines (magenta), host galaxy template (green), Fe II template (orange). Right: A zoom-in highlighting the H$\beta$ region of the decomposition. The data (gray) and total model (red) are plotted along with the individual Gaussians that characterize [O$\,\textsc{iii}]$$\lambda$5007 (pink), [O$\,\textsc{iii}]$$\lambda$4959 (salmon), narrow H$\beta$ (cyan), and broad H$\beta$ (olive).
• Figure 3: Estimates for the uncertainty in radial velocity jitter, $\sigma(\Delta v_{rad})$. The multiple linear regression fit of $\sigma(\Delta v_{rad})$ with SNR(bH$\beta$) and $\Delta v_{rad}$ as the independent variables is plotted in purple. In order to represent the fit on a single independent variable, the sample was binned by SNR(bH$\beta$) and the mean uncertainty value for each bin is plotted. Uncertainty estimates from the $\Delta t<2$ days sample are plotted in blue. For both the MLR and $\Delta t<2$ days plots, horizontal error bars represent the binning and the vertical error bars are estimated with the bootstrap method. The $\Delta t<2$ days bins include 166, 93, 21, 34, and 12 pairs per bin respectively from low to high SNR.
• Figure 4: Left panel shows the number of pairs of spectra in our dataset on a grid of bolometric luminosity and redshift. Right panel shows the same on a grid of bolometric luminosity and black hole mass. Also plotted are lines of constant Eddington ratio.
• Figure 5: Left panel shows the number of pairs of spectra in our sample on a grid of bolometric luminosity and black hole mass. Right panel shows the number of quasars in our sample on the same grid. Because the RM subsample makes up the vast majority of pairs of spectra in our sample and a very small fraction of quasars in our sample, this plot also illustrates the differences in physical properties of the RM and non-RM sub-samples.