The Sloan Digital Sky Survey Reverberation Mapping Project: How Broad Emission Line Widths Change When Luminosity Changes

Quasar broad emission lines are largely powered by photoionization from the accretion continuum. Increased central luminosity will enhance line emissivity in more distant clouds, leading to increased average distance of the broad-line-emitting clouds and decreased averaged line width, known as the broad-line region (BLR) "breathing". However, different lines breathe differently, and some high-ionization lines, such as C IV, can even show "anti-breathing" where the line broadens when luminosity increases. Using multi-year photometric and spectroscopic monitoring data from the Sloan Digital Sky Survey Reverberation Mapping project, we quantify the breathing effect ($\Delta$log W=$\alpha\Delta$log L) of broad H$\alpha$, H$\beta$, Mg II, C IV, and C III] for statistical quasar samples over $z\approx 0.1-2.5$. We found that H$\beta$ displays the most consistent normal breathing expected from the virial relation ($\alpha\sim-0.25$), Mg II and H$\alpha$ on average show no breathing ($\alpha\sim 0$), and C IV (and similarly C III] and Si IV mostly shows anti-breathing ($\alpha>0$). The anti-breathing of C IV can be well understood by the presence of a non-varying core component in addition to a reverberating broad-base component, consistent with earlier findings. The deviation from canonical breathing introduces extra scatter (a luminosity-dependent bias) in single-epoch virial BH mass estimates due to intrinsic quasar variability, which underlies the long argued caveats of C IV single-epoch masses. Using the line dispersion instead of FWHM leads to less, albeit still substantial, deviations from canonical breathing in most cases. Our results strengthen the need for reverberation mapping to provide reliable quasar BH masses, and quantify the level of variability-induced bias in single-epoch BH masses based on various lines.