A Timescale-Resolved Analysis of the Breathing Effect in Quasar Broad Line Regions

TL;DR

This study tests the breathing effect—the luminosity-driven change of broad-line widths—as a constraint on single-epoch black hole mass estimates, extending beyond reverberation-mapped AGNs. Using a large, multi-epoch SDSS DR16 quasar sample, the authors measure line-width responses for H$\alpha$, H$\beta$, MgII, and CIV and analyze their dependence on rest-frame timescales scaled by $R_{\mathrm{BLR}}$–$L$ relations $R_{\mathrm{BLR}} \propto L^{\beta}$ to reveal a timescale-resolved breathing pattern. They find no significant breathing for H$\alpha$, H$\beta$, or MgII, while CIV shows a statistically significant anti-breathing that is strongest at intermediate timescales; H$\beta$ breathing appears only in a small subset with measurable BLR lags, suggesting episodic behavior linked to optical–ionizing continuum coupling. Across two epochs, black hole mass differences typically lie around $0.1$–$0.2$ dex (up to $\sim0.3$ dex), implying modest average impact on single-epoch masses but possible larger deviations for a fraction of sources. Collectively, these results refine our understanding of BLR variability, the structure of the CIV-emitting region, and the uncertainties in virial mass estimates used for studying SMBH growth and co-evolution.

Abstract

The single-epoch virial method is a fundamental tool for estimating supermassive black hole (SMBH) masses in large samples of AGNs and has been extensively employed in studies of SMBH-galaxy co-evolution across cosmic time. However, since this method is calibrated using reverberation-mapped AGNs, its validity across the entire AGN population remains uncertain. 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. We construct an unprecedentedly large multi-epoch spectroscopic dataset of quasars from SDSS DR16, focusing on four key broad emission lines (Ha, Hb, MgII, and CIV). We assess how breathing behavior evolves with the rest-frame time interval between observations. We detect no significant breathing signal in Ha, Hb, or MgII at any observed timescale. In contrast, CIV exhibits a statistically significant anti-breathing trend, most prominent at intermediate timescales. Notably, for Hb, which has shown breathing in previous reverberation-mapped samples, we recover the effect only in the small subset of quasars with clearly detected 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.

Figures (7)

• Figure 1: Distribution of sources in our samples by the number of repeated spectroscopic observations. The x-axis shows the number of observations per source, while the y-axis indicates the number of sources with that observation count. Only sources with more than one spectroscopic observation are shown, as those with a single observation are not included in our analysis.
• Figure 2: Variation in emission line FWHM as a function of the change in continuum luminosity, for H$\alpha$, H$\beta$, $\textrm{Mg\,ii}$, and $\textrm{C\,iv}$ , respectively. No significant breathing effect is detected in H$\alpha$, H$\beta$, or $\textrm{Mg\,ii}$, with regression slopes consistent with zero. A weak but statistically significant anti-breathing is observed in $\textrm{C\,iv}$ . In each panel, the black solid line denotes the best-fit regression slope (with the best-fit slope and correlation coefficient $R$ provided), and the error bar at the center represents the median statistical uncertainty of the data points. Interestingly, the H$\beta$ panel shows a clear excess of data points in the upper-left and lower-right regions, suggesting that strong breathing is present in a small subset of pairs, even though the sample as a whole shows no average breathing signal.
• Figure 3: The breathing effect slope as a function of the rest-frame time interval between observations for all four broad emission lines. The bar plot shows the number of observation pairs in each bin, with black error bars indicating the scatter in the pair counts, estimated via bootstrapping.
• Figure 4: Same as the second panel of Fig. \ref{['fig:all_line_BE']}, but for different SDSS-RM quasar subsamples. Top: 31 SDSS-RM quasars with well-measured H$\beta$ lags from Wang2020, using only 2014 observations. A clear increase in the breathing slope is seen with increasing timescale. Middle: The same SDSS-RM quasar sample as above, but using all available SDSS-RM observations. The breathing trend disappears. Bottom: All RM quasars with more than 20 spectroscopic epochs. No breathing effect is detected either across all timescales.
• Figure 5: The x-axis shows the number of spectroscopic observations per SDSS RM quasar, and the y-axis shows the variation amplitude (excess variance). Red circles represent RM quasars with significant H$\beta$ lag detections from Wang2020, while green triangles represent all RM quasars in our parent sample, including those without detectable lags. Both samples are based on data from the 2014 monitoring season. There is no clear distinction in either the number of observations or the excess variance between quasars with detected lags and those without.