SIMBAD references

Determining the virial factor of the broad-line region gas is crucial for calibrating active galactic nucleus black hole mass estimators, since the measured line-of-sight velocity needs to be converted into the intrinsic virial velocity. The average virial factor has been empirically calibrated based on the M_BH-σ_* relation of quiescent galaxies, but the claimed values differ by a factor of two in recent studies. We investigate the origin of the difference by measuring the M_BH-σ_* relation using an updated galaxy sample from the literature and explore the dependence of the virial factor on various fitting methods. We find that the discrepancy is primarily caused by the sample selection, while the difference stemming from the various regression methods is marginal. However, we generally prefer the FITEXY and Bayesian estimators based on Monte Carlo simulations for the M_BH-σ_* relation. In addition, the choice of independent variable in the regression leads to ∼0.2 dex variation in the virial factor inferred from the calibration process. Based on the determined virial factor, we present the updated M _BH-σ_* relation of local active galaxies.