Using different kinds of velocity tracers derived from the broad Hβ profile (in the mean or rms spectrum) and the corresponding virial factors f, the central supermassive black hole masses ( ) are calculated for a compiled sample of 120 reverberation-mapped (RM) active galactic nuclei (AGNs). For its subsample of RM AGNs with measured stellar velocity dispersion ( ), the multivariate linear regression technique is used to calibrate the mean value f, as well as the variable FWHM-based f. It is found that, whether excluding the pseudobulges or not, the from the Hβ line dispersion in the mean spectrum ( ) has the smallest offset rms with respect to the relation. For the total sample excluding SDSS-RM AGNs, with respect to from or that from the Hβ line dispersion in the rms spectrum ( ), it is found that we can obtain from the with the smallest offset rms of 0.38 or 0.23 dex, respectively. It implies that, with respect to the Hβ FWHM, we prefer to calculate from the single-epoch spectrum. Using the FWHM-based f, we can improve the calculation from FWHM(Hβ) and the mean f, with a decreased offset rms from 0.52 to 0.39 dex with respect to from for the subsample of 36 AGNs with . The value of 0.39 dex is almost the same as that from and the mean f.

Using a sample of 208 broad-line active galactic nuclei (AGNs) from Swift/BAT AGN Spectroscopic Survey in ultra-hard X-ray band (14 − 195 keV), the hot corona properties are investigated, i.e. the fraction of gravitational energy dissipated in the hot corona and the hard X-ray photon index. The bolometric luminosity, L Bol , is calculated from host-corrected luminosity at 5100Å. Virial supermassive black hole masses (SMBH, M BH ) are calculated from the Hβ line width and the corresponding broad line region size-luminosity empirical relation at 5100Å. We find a strong anti-correlation between the fraction of energy released in corona (F X ≡ L 14−195keV /L Bol ) and the Eddington ratio (ε ≡ L Bol /L Edd ), F X ∝ ε −0.60±0.1 . It is found that this fraction also has a correlation with the SMBH mass, BH. Assuming that magnetic buoyancy and feild reconnection lead to the formation of a hot corona, our result favours the shear stress tensor being a proportion of the gas pressure. For our entire sample, it is found that the hard X-ray photon index Γ has a weak but significant correlation with the Eddington ratio, Γ = 2.17 + 0.21 log ε. However, this correlation is not robust because the relation is not statistically significant for its subsample of 32 RM AGNs with relatively reliable M BH or its subsample of 166 AGNs with singleepoch M BH . We do not find a statistically significant relation between the photon index and the Eddington ratio taking into account an additional dependence on F X . disk. Therefore, the fraction of FX ≡ LX/L Bol (LX and L Bol are the X-ray luminosity and the bolometric luminosity respectively) can be obtained if the magnetic stress and energy transportation are assumed (e.g. Merloni & Fabian 2002). This may give us a possible opportunity to test the working magnetic stress from hard X-ray observations. The relation between the fraction of energy dissipated in the corona FX and the Eddington ratio ε (ε ≡ L Bol /L Edd , L Edd is the Eddington luminosity) was investigated by some authors (e.g. Merloni & Fabian 2002;Wang et al. 2004;Yang et al. 2006). For a compiled sample of 56 AGNs from ASCA observation, Wang et al. (2004) found a relation between FX and ε as FX ∝ ε −0.64±0.09 , where the X-ray luminosity in 2 − 10 keV is used. Considering a larger sample of 98 AGNs, Yang et al. (2006) found FX ∝ ε −0.66 . These results supported the magnetic stress tensor being the form of t rφ ∝ Pgas, where Pgas is the gas pressure. In their compiled sample, they only have nine sources with ultra-hard X-ray observations of INTEGRAL and Swift, and for other sources the luminosity in 2 − 150 kev is extrapolated from the 2-10 keV luminosity with a fixed photon index. A sample of more AGNs with direct harder X-ray than 2-10 keV is needed for further investigation, such as Swift/BAT. Another relation between the X-ray photon index Γ and c 0000 The Authors

Using a compiled sample of 34 broad-line active galactic nuclei (AGNs) with measured Hβ 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 Hβ line width or line dispersion from the mean or rms spectrum, there are four kinds of the factor f . Using the Hβ 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-disk BLRs, we also find that, as the tracer of the BLRs velocity, Hβ FWHM has some dependence on the inclination, while the line dispersion σ Hβ 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 BH − σ * relation from high-redshift to low-redshift AGNs.

In this third paper of the series reporting on the reverberation mapping campaign of active galactic nuclei with asymmetric Hβ emission-line profiles, we present results for 15 Palomar–Green quasars using spectra obtained between the end of 2016–2021 May. This campaign combines long time spans with relatively high cadence. For eight objects, both the time lags obtained from the entire light curves and the measurements from individual observing seasons are provided. Reverberation mapping of nine of our targets has been attempted for the first time, while the results for six others can be compared with previous campaigns. We measure the Hβ time lags over periods of years and estimate their black hole masses. The long duration of the campaign enables us to investigate their broad-line region (BLR) geometry and kinematics for different years by using velocity-resolved lags, which demonstrate signatures of diverse BLR geometry and kinematics. The BLR geometry and kinematics of individual objects are discussed. In this sample, the BLR kinematics of Keplerian/virialized motion and inflow is more common than that of outflow.

For a compiled sample of 120 reverberation-mapped AGNs, the bivariate correlations of the broad-line regions (BLRs) size (R BLR ) with the continuum luminosity at 5100Å (L 5100 ) and the dimensionless accretion rates (Ṁ ) are investigated. Using our recently calibrated virial factor f , and the velocity tracer from the Hβ Full-width at half-maximum (FWHM(Hβ )) or the line dispersion (σ Hβ ) measured in the mean spectra, three kinds of SMBH masses andṀ are calculated. An extended R BLR (Hβ) − L 5100 relation includingṀ is found to be stronger than the canonical R BLR (Hβ) − L 5100 relation, showing smaller scatters. The observational parameters, R Fe (the ratio of optical Fe II to Hβ line flux) and the line profile parameter D Hβ (D Hβ = FWHM(Hβ)/σ Hβ ), have relations with three kinds ofṀ . Using R Fe and D Hβ to substituteṀ , extended empirical R BLR (Hβ) − L 5100 relations are presented. R Fe is a better "fix" for the R BLR (Hβ) − L 5100 offset than the Hβ shape D Hβ . The extended empirical R BLR (Hβ) − L 5100 relation including R Fe can be used to calculate R BLR , and thus the single-epoch SMBH mass M BH . Our measured accretion rate dependence is not consistent with the simple model of the accretion disk instability leading the BLRs formation. The BLR may instead form from the inner edge of the torus, or from some other means in which BLR size is positively correlated with accretion rate and the SMBH mass.