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Register a new userCalibration of the virial factor $f$ in supermassive black hole masses of reverberation-mapped AGNs
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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 $sigma_{rm Hbeta }$ 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.
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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 ($sigma_{rm Hbeta,mean}$) 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 ($sigma_{rm Hbeta,rms}$), it is found that we can obtain $M_{rm BH}$ from the $sigma_{rm Hbeta,mean}$ 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 $sigma_{rm Hbeta,mean}$ 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 $sigma_{rm Hbeta,mean}$ and the mean $f$.
X-ray reverberation mapping has emerged as a powerful probe of microparsec scales around AGN, and with high sensitivity detectors, its full potential in echo-mapping the otherwise inaccessible disk-corona at the black hole horizon scale will be revealed.
Based on the gravitational redshift, one prediction of Einsteins general relativity theory, of broad optical emission lines in active galactic nuclei (AGNs), a new method is proposed to estimate the virial factors $f$ in measuring black hole masses $M_{rm{RM}}$ by the reverberation mapping of AGNs. The factors $f$ can be measured on the basis of two physical quantities, i.e. the gravitational redshifts $z_{rm{g}}$ and full widths at half maxima $v_{rm{FWHM}}$ of broad lines. In the past it has been difficult to determine the factors $f$ for individual AGNs. We apply this new method to several reverberation mapped Seyfert 1 galaxies. There is a correlation between $f$ and broad-line region (BLR) radius $r_{rm{BLR}}$, $f=5.4 r_{rm{BLR}}^{0.3}$, for the gravitationally redshifted broad lines He II, He I, H$beta$ and H$alpha$ in narrow-line Seyfert 1 galaxy (NLS1) Mrk 110. This correlation results from the radiation pressure influence of the accretion disc on the BLR clouds. The radiation pressure influence seems to be more important than usually thought in AGNs. Mrk 110 has $f approx$ 8--16, distinctly larger than the mean $langle frangle approx 1$, usually used to estimate $M_{rm{RM}}$ in the case of $v_{rm{FWHM}}$. NGC 4593 and NLS1 Mrk 486 has $fapprox 3$ and $fapprox 9$, respectively. Higher $f$ values of several tens are derived for three other NLS1s. There is a correlation between $f$ and accretion rate $mathscr{dot M}_{f=1}$, $f=6.8mathscr{dot M}^{0.4}_{f=1}$ for five objects, where $mathscr{dot M}_{f=1}=dot M_{bullet}/L_{rm{Edd}}c^{-2}$ as $f=1$ is assumed to estimate $M_{rm{RM}}$ used in the Eddington luminosity $L_{rm{Edd}}$, $dot M_{bullet}$ is the mass accretion rate, and $c$ is the speed of light. These larger $f$ values will produce higher $M_{rm{RM}}$ values and lower Eddington ratios.
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 ($sigma_{rm Hbeta}$) 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 $R_{rm BLR}({rm Hbeta}) - L_{rm 5100}$ 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 $D_{rm Hbeta}$ ($D_{rm Hbeta}=rm FWHM(Hbeta)/sigma_{rm Hbeta}$), have relations with three kinds of $dot{mathscr{M}}$. Using $R_{rm Fe}$ and $D_{rm Hbeta}$ to substitute $dot{mathscr{M}}$, extended empirical $R_{rm BLR}({rm Hbeta}) - L_{rm 5100}$ relations are presented. $R_{rm Fe}$ is a better fix for the $R_{rm BLR}({rm Hbeta}) - L_{rm 5100}$ offset than the H$beta$ shape $D_{rm Hbeta}$. The extended empirical $R_{rm BLR}({rm Hbeta}) - L_{rm 5100}$ 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.
Megamaser disks provide the most precise and accurate extragalactic supermassive black hole masses. Here we describe a search for megamasers in nearby galaxies using the Green Bank Telescope (GBT). We focus on galaxies where we believe that we can resolve the gravitational sphere of influence of the black hole and derive a stellar or gas dynamical measurement with optical or NIR observations. Since there are only a handful of super massive black holes (SMBH) that have direct black hole mass measurements from more than one method, even a single galaxy with a megamaser disk and a stellar dynamical black hole mass would provide necessary checks on the stellar dynamical methods. We targeted 87 objects from the Hobby-Eberly Telescope Massive Galaxy Survey, and detected no new maser disks. Most of the targeted objects are elliptical galaxies with typical stellar velocity dispersions of 250 km/s and distances within 130 Mpc. We discuss the implications of our non-detections, whether they imply a threshold X-ray luminosity required for masing, or possibly reflect the difficulty of maintaining a masing disk around much more massive (>10^8 Msun) black holes at low Eddington ratio. Given the power of maser disks at probing black hole accretion and demographics, we suggest that future maser searches should endeavour to remove remaining sample biases, in order to sort out the importance of these covariant effects.
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