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.
