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Register a new userAn Improved Method for Using MgII to Estimate Black Hole Masses in Active Galactic Nuclei
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We present a method for obtaining accurate black hole (BH) mass estimates from the MgII emission line in active galactic nuclei (AGNs). Employing the large database of AGN measurements from the Sloan Digital Sky Survey (SDSS) presented by Shen et al., we find that AGNs in the redshift range 0.3-0.9, for which a given object can have both H-beta and MgII line widths measured, display a modest but correctable discrepancy in MgII-based masses that correlates with the Eddington ratio. We use the SDSS database to estimate the probability distribution of the true (i.e., H-beta-based) mass given a measured MgII line width. These probability distributions are then applied to the SDSS measurements from Shen et al. across the entire MgII-accessible redshift range (0.3-2.2). We find that accounting for this residual correlation generally increases the dispersion of Eddington ratios by a small factor (~0.09 dex for the redshift and luminosity bins we consider). We continue to find that the intrinsic distribution of Eddington ratios for luminous AGNs is extremely narrow, 0.3-0.4 dex, as demonstrated by Kollmeier et al. Using the method we describe, MgII emission lines can be used with confidence to obtain BH mass estimates.
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We investigate the relationship between the linewidths of broad Mg II lambda2800 and Hbeta in active galactic nuclei (AGNs) to refine them as tools to estimate black hole (BH) masses. We perform a detailed spectral analysis of a large sample of AGNs at intermediate redshifts selected from the Sloan Digital Sky Survey, along with a smaller sample of archival ultraviolet spectra for nearby sources monitored with reverberation mapping. Careful attention is devoted to accurate spectral decomposition, especially in the treatment of narrow-line blending and Fe II contamination. We show that, contrary to popular belief, the velocity width of Mg II tends to be smaller than that of Hbeta, suggesting that the two species are not cospatial in the broad-line region. Using these findings and recently updated BH mass measurements from reverberation mapping, we present a new calibration of the empirical prescriptions for estimating virial BH masses for AGNs using the broad Mg II and Hbeta lines. We show that the BH masses derived from our new formalisms show subtle but important differences compared to some of the mass estimators currently used in the literature.
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 $f$.
Reverberation mapping methods have been used to measure masses in about three dozen AGNs. The consistency of the virial masses computed from line widths and time delays, the relationship between black hole mass and host-galaxy stellar bulge velocity dispersion, and the consistency with black hole masses estimated from stellar dynamics in the two cases in which such determinations are possible all indicate that reverberation mass measurements are robust and are accurate to typically a factor of a few. The reverberation-mapped AGNs are of particular importance because they anchor the scaling relationships that allow black hole mass estimation based on single spectra. We discuss potential sources of systematic error, particularly with regard to how the emission line widths are measured.
The astrophysical origin of gravitational wave (GW) transients is a timely open question in the wake of discoveries by LIGO/Virgo. In active galactic nuclei (AGNs), binaries form and evolve efficiently by interaction with a dense population of stars and the gaseous AGN disk. Previous studies have shown that stellar-mass black hole (BH) mergers in such environments can explain the merger rate and the number of suspected hierarchical mergers observed by LIGO/Virgo. The binary eccentricity distribution can provide further information to distinguish between astrophysical models. Here we derive the eccentricity distribution of BH mergers in AGN disks. We find that eccentricity is mainly due to binary-single (BS) interactions, which lead to most BH mergers in AGN disks having a significant eccentricity at $0.01,mathrm{Hz}$, detectable by LISA. If BS interactions occur in isotropic-3D directions, then $8$--$30%$ of the mergers in AGN disks will have eccentricities at $10,mathrm{Hz}$ above $e_{10,rm Hz}gtrsim 0.03$, detectable by LIGO/Virgo/KAGRA, while $5$--$17%$ of mergers have $e_{10,rm Hz}geq 0.3$. On the other hand, if BS interactions are confined to the AGN-disk plane due to torques from the disk, with 1-20 intermediate binary states during each interaction, or if BHs can migrate to $lesssim10^{-3},mathrm{pc}$ from the central supermassive black hole, then $10$--$70%$ of the mergers will be highly eccentric ($e_{10,rm Hz} geq 0.3$), consistent with the possible high eccentricity in GW190521.
I review how AGN black hole masses are calculated from emission-line reverberation-mapping data, with particular attention to both assumptions and caveats. I discuss the empirical relationship between AGN luminosity and broad-line region radius that underpins the indirect methods by which most AGN masses are estimated. I also discuss how line widths are characterized in this method and illustrate how different ways of measuring the line-widths can lead to systematic errors in the mass scale. I discuss specific implications for NLS1 galaxies and consider whether the NLS1 phenomenon is better explained by source inclination or by Eddington rate, and conclude that there is evidence that both of these effects are contributing factors and that at least the high-Eddington rate NLS1s are physically similar to some high-luminosity quasars.
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