2019MNRAS.488.1519Y

Using a compiled sample of 34 broad-line active galactic nuclei (AGNs) with measured H β time lags from the reverberation mapping (RM) method and measured bulge stellar velocity dispersions σ_*, we calculate the virial factor f by assuming that the RM AGNs intrinsically obey the same M_BH-σ_* relation as quiescent galaxies, where M_BH is the mass of the supermassive black hole (SMBH). Considering four tracers of the velocity of the broad-line regions (BLRs), i.e. the H β line width or line dispersion from the mean or rms spectrum, there are four kinds of the factor f. Using the H β full width at half-maximum (FWHM) to trace the BLRs velocity, we find significant correlations between the factor f and some observational parameters, e.g. FWHM, the line dispersion. Using the line dispersion to trace the BLRs velocity, these relations disappear or become weaker. It implies the effect of inclination in BLRs geometry. It also suggests that the variable f in M_BH estimated from luminosity and FWHM in a single-epoch spectrum is not negligible. Using a simple model of thick-disc BLRs, we also find that, as the tracer of the BLRs velocity, H β FWHM has some dependence on the inclination, while the line dispersion σ_H β_ is insensitive to the inclination. Considering the calibrated FWHM-based factor f from the mean spectrum, the scatter of the SMBH mass is 0.39 dex for our sample of 34 low-redshift RM AGNs. For a high-redshift sample of 30 Sloan Digital Sky Survey RM AGNs with measured stellar velocity dispersions, we find that the SMBH mass scatter is larger than that for our sample of 34 low-redshift RM AGNs. It implies the possibility of evolution of the M_BH-σ_* relation from high-redshift to low-redshift AGNs.