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In this third paper of the series reporting on the reverberation mapping (RM) campaign of active galactic nuclei with asymmetric H$\beta$ emission-line profiles, we present results for 15 Palomar-Green (PG) quasars using spectra obtained between the end of 2016 to May 2021. This campaign combines long time spans with relatively high cadence. For 8 objects, both the time lags obtained from the entire light curves and the measurements from individual observing seasons are provided. Reverberation mapping of 9 of our targets has been attempted for the first time, while the results for 6 others can be compared with previous campaigns. We measure the H$\beta$ 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 outflow., Comment: 35 pages, 18 figures, 8 tables, accepted for publication in The Astrophysical Journal Supplement

Using different kinds of velocity tracers derived from the broad H$\beta$ profile (in the mean or rms spectrum) and the corresponding virial factors $f$, the central supermassive black hole (SMBH) masses ($M_{\rm BH}$) are calculated for a compiled sample of 120 reverberation-mapped (RM) AGNs. For its subsample of RM AGNs with measured stellar velocity dispersion ($\sigma_{\rm \ast}$), 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 pseudo-bulges or not, $M_{\rm BH}$ from the H$\beta$ line dispersion in the mean spectrum ($\sigma_{\rm H\beta,mean}$) has the smallest offset rms with respect to the $M_{\rm BH}-\sigma_{\ast}$ relation. For the total sample excluding SDSS-RM AGNs, with respect to $M_{\rm BH}$ from $\sigma_{\rm \ast}$ or that from the H$\beta$ line dispersion in the rms spectrum ($\sigma_{\rm H\beta,rms}$), it is found that we can obtain $M_{\rm BH}$ from the $\sigma_{\rm H\beta,mean}$ with the smallest offset rms of 0.38 dex or 0.23 dex, respectively. It implies that, with respect to the H$\beta$ FWHM, we prefer $\sigma_{\rm H\beta,mean}$ to calculate $M_{\rm BH}$ from the single-epoch spectrum. Using the FWHM-based $f$, we can improve $M_{\rm BH}$ calculation from FWHM(H$\beta$) and the mean $f$, with a decreased offset rms from 0.52 dex to 0.39 dex with respect to $M_{\rm BH}$ from $\sigma_{\rm \ast}$ for the subsample of 36 AGNs with $\sigma_{\rm \ast}$. The value of 0.39 dex is almost the same as that from $\sigma_{\rm H\beta,mean}$ and the mean $f$., Comment: 20 pages, 5 tables, 8 figures, accepted for publication in ApJ

For a compiled sample of 120 reverberation-mapped AGNs, the bivariate correlations of the broad-line regions (BLRs) size ($R_{\rm BLR}$) with the continuum luminosity at 5100 \AA\ ($L_{5100}$) and the dimensionless accretion rates ($\dot{\mathscr{M}}$) are investigated. Using our recently calibrated virial factor $f$, and the velocity tracer from the H$\beta$ Full-width at half-maximum (FWHM(H$\beta$)) or the line dispersion ($\sigma_{\rm H\beta}$) measured in the mean spectra, three kinds of SMBH masses and $\dot{\mathscr{M}}$ are calculated. An extended \RL relation including $\dot{\mathscr{M}}$ is found to be stronger than the canonical $R_{\rm BLR}({\rm H\beta}) - L_{\rm 5100}$ relation, showing smaller scatters. The observational parameters, $R_{\rm Fe}$ (the ratio of optical Fe II to H$\beta$ line flux) and the line profile parameter $D_{\rm H\beta}$ ($D_{\rm H\beta}=\rm FWHM(H\beta)/\sigma_{\rm H\beta}$), have relations with three kinds of $\dot{\mathscr{M}}$. Using $R_{\rm Fe}$ and $D_{\rm H\beta}$ to substitute $\dot{\mathscr{M}}$, extended empirical $R_{\rm BLR}({\rm H\beta}) - L_{\rm 5100}$ relations are presented. $R_{\rm Fe}$ is a better "fix" for the $R_{\rm BLR}({\rm H\beta}) - L_{\rm 5100}$ offset than the H$\beta$ shape $D_{\rm H\beta}$. The extended empirical $R_{\rm BLR}({\rm H\beta}) - L_{\rm 5100}$ relation including $R_{\rm Fe}$ can be used to calculate $R_{\rm BLR}$, and thus the single-epoch SMBH mass $M_{\rm BH}$. 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., Comment: Accepted for publication in MNRAS, 11 pages, 2 tables, 6 figures

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., Comment: 15 pages, 6 tables, 7 figures, accepted for publication in MNRAS

Incorporating the radiation reaction force into two-fluid plasma in curved space, we get a set of one-fluid general relativistic magnetohydrodynamics (GRMHD) equations with the Landau-Lifshitz radiation reaction force. We analyze the importance of the radiation reaction acting on plasma around an astrophysical compact object., Comment: 11 pages, 1 figure, ApJ, in press

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, \lb, is calculated from host-corrected luminosity at 5100 \AA. Virial supermassive black hole masses (SMBH, \mbh) are calculated from the $\rm H\beta$ line width and the corresponding broad line region size-luminosity empirical relation at 5100 \AA. We find a strong anti-correlation between the fraction of energy released in corona ($F_x \equiv L_{14-195 keV}/L_{\rm Edd}$) and the Eddington ratio ($ \varepsilon \equiv L_{\rm Bol}/L_{\rm Edd}$), $F_x \propto \varepsilon^{-0.60\pm 0.1}$. It is found that this fraction also has a correlation with the SMBH mass, $F_x \propto \varepsilon^{-0.74\pm 0.14} M_{\rm BH}^{-0.30\pm 0.03}$. 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 $\Gamma$ has a weak but significant correlation with the Eddington ratio, $ \Gamma=2.17+0.21\log \varepsilon$. However, this correlation is not robust because the relation is not statistically significant for its subsample of 32 RM AGNs with relatively reliable $M_{\rm BH}$ or its subsample of 166 AGNs with single-epoch $M_{\rm BH}$. We do not find a statistically significant relation between the photon index and the Eddington ratio taking into account an additional dependence on $F_x$., Comment: Accepted for publication in MNRAS, 4 Figures, 1 Table

For the sample from Ge et al. of 87 low-$z$ Palomar--Green (PG) quasi-stellar objects (QSOs) and 130 high-$z$ QSOs ($0