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

## TL;DR

This study calibrates the virial factor $f$ for supermassive black hole mass estimates in AGNs using reverberation mapping data, revealing the influence of BLR geometry and inclination, and suggesting possible evolution of the $M_{BH}-\sigma_*$ relation.

## Contribution

It provides a detailed analysis of the virial factor $f$ calibration considering different BLR velocity tracers and inclination effects, and compares low and high redshift AGN samples to explore evolutionary trends.

## Key findings

- Significant correlation between $f$ and FWHM when using FWHM as velocity tracer.
- Line dispersion $\sigma_{Heta}$ shows weaker or no correlation with $f$, indicating inclination effects.
- Higher SMBH mass scatter in high-redshift AGNs suggests evolution of the $M_{BH}-\sigma_*$ relation.

## Abstract

Using a compiled sample of 34 broad-line active galactic nuclei (AGNs) with measured H$\beta$ time lags from the reverberation mapping (RM) method and measured bulge stellar velocity dispersions $\sigma_*$, we calculate the virial factor $f$ by assuming that the RM AGNs intrinsically obey the same $M_{\rm BH}-\sigma_*$ relation as quiescent galaxies, where $M_{\rm BH}$ 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$\beta$ line width or line dispersion from the mean or rms spectrum, there are four kinds of the factor $f$. Using the \hb 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 $M_{\rm BH}$ estimated from luminosity and FWHM in a single-epoch spectrum is 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 the inclination, while the line dispersion $\sigma_{\rm H\beta }$ 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 SDSS 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 $M_{\rm BH}-\sigma_*$ relation from high-redshift to low-redshift AGNs.