A timescale-resolved analysis of the breathing effect in quasar broad-line regions

Context. The single-epoch virial method is a fundamental tool for estimating supermassive black hole (SMBH) masses in large samples of active galactic nuclei (AGNs) and has been extensively employed in studies of SMBH–galaxy coevolution across cosmic time. However, since this method is calibrated using reverberation-mapped AGNs, its validity across the entire AGN population remains uncertain. Aims. We aim to examine the breathing effect–the variability of emission line widths with continuum luminosity–beyond reverberation-mapped AGNs, to assess the validity and estimate potential systematic uncertainties of single-epoch virial black hole mass estimates. Methods. We constructed an unprecedentedly large multi-epoch spectroscopic dataset of quasars from Sloan Digital Sky Survey data release 16 (SDSS DR16), focusing on four key broad emission lines (Hα, Hβ, Mg <ns0:sc>II</ns0:sc>, and C <ns0:sc>IV</ns0:sc>). We assessed how breathing behavior evolves with the rest-frame time interval between observations. Results. We detect no significant breathing signal in Hα, Hβ, or Mg <ns0:sc>II</ns0:sc> at any observed timescale. In contrast, C <ns0:sc>IV</ns0:sc> exhibits a statistically significant anti-breathing trend, most prominent at intermediate timescales. Notably, for Hβ, which has shown breathing in previous reverberation-mapped samples, we recover the effect only in the small subset of quasars with clearly detected broad-line region (BLR) lags and only during the epochs when such lags are measurable–suggesting that both the lag and breathing signals are intermittent, possibly due to a weak correlation between optical and ionizing continua. These results highlight the complex, variable, and timescale-dependent nature of line profile variability and underscore its implications for single-epoch black hole mass estimates.