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Using a compiled sample of 34 broad-line active galactic nuclei (AGNs) withmeasured H$\beta$ time lags from the reverberation mapping (RM) method andmeasured bulge stellar velocity dispersions $\sigma_*$, we calculate the virialfactor $f$ by assuming that the RM AGNs intrinsically obey the same $M_{\rmBH}-\sigma_*$ relation as quiescent galaxies, where $M_{\rm BH}$ is the mass ofthe supermassive black hole (SMBH). Considering four tracers of the velocity ofthe broad-line regions (BLRs), i.e., the H$\beta$ line width or line dispersionfrom the mean or rms spectrum, there are four kinds of the factor $f$. Usingthe \hb Full-width at half-maximum (FWHM) to trace the BLRs velocity, we findsignificant correlations between the factor $f$ and some observationalparameters, e.g., FWHM, the line dispersion. Using the line dispersion to tracethe BLRs velocity, these relations disappear or become weaker. It implies theeffect of inclination in BLRs geometry. It also suggests that the variable $f$in $M_{\rm BH}$ estimated from luminosity and FWHM in a single-epoch spectrumis not negligible. Using a simple model of thick-disk BLRs, we also find that,as the tracer of the BLRs velocity, H$\beta$ FWHM has some dependence on theinclination, while the line dispersion $\sigma_{\rm H\beta }$ is insensitive tothe inclination. Considering the calibrated FWHM-based factor $f$ from the meanspectrum, the scatter of the SMBH mass is 0.39 dex for our sample of 34 lowredshift RM AGNs. For a high redshift sample of 30 SDSS RM AGNs with measuredstellar velocity dispersions, we find that the SMBH mass scatter is larger thanthat for our sample of 34 low redshift RM AGNs. It implies the possibility ofevolution of the $M_{\rm BH}-\sigma_*$ relation from high-redshift tolow-redshift AGNs.

Calibration of the virial factor $f$ in supermassive black hole masses of reverberation-mapped AGNs