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Register a new userThe Black Hole Mass-Bulge Luminosity Relationship for Active Galactic Nuclei from Reverberation Mapping and Hubble Space Telescope Imaging
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Misty C. Bentz
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We investigate the relationship between black hole mass and bulge luminosity for AGNs with reverberation-based black hole mass measurements and bulge luminosities from two-dimensional decompositions of Hubble Space Telescope host galaxy images. We find that the slope of the relationship for AGNs is 0.76-0.85 with an uncertainty of ~0.1, somewhat shallower than the M_BH propto L^{1.0+/-0.1} relationship that has been fit to nearby quiescent galaxies with dynamical black hole mass measurements. This is somewhat perplexing, as the AGN black hole masses include an overall scaling factor that brings the AGN M_BH-sigma relationship into agreement with that of quiescent galaxies. We discuss biases that may be inherent to the AGN and quiescent galaxy samples and could cause the apparent inconsistency in the forms of their M_BH-L_bulge relationships.
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We have measured the stellar velocity dispersions (sigma_*) and estimated the central black hole (BH) masses for over 900 broad-line active galactic nuclei (AGNs) observed with the Sloan Digital Sky Survey. The sample includes objects which have redshifts up to z=0.452, high quality spectra, and host galaxy spectra dominated by an early-type (bulge) component. The AGN and host galaxy spectral components were decomposed using an eigenspectrum technique. The BH masses (M_BH) were estimated from the AGN broad-line widths, and the velocity dispersions were measured from the stellar absorption spectra of the host galaxies. The range of black hole masses covered by the sample is approximately 10^6 < M_BH < 10^9 M_Sun. The host galaxy luminosity-velocity dispersion relationship follows the well-known Faber-Jackson relation for early-type galaxies, with a power-law slope 4.33+-0.21. The estimated BH masses are correlated with both the host luminosities (L_{H}) and the stellar velocity dispersions (sigma_*), similar to the relationships found for low-redshift, bulge-dominated galaxies. The intrinsic scatter in the correlations are large (~0.4 dex), but the very large sample size allows tight constraints to be placed on the mean relationships: M_BH ~ L_H^{0.73+-0.05} and M_BH ~ sigma_*^{3.34+-0.24}. The amplitude of the M_BH-sigma_* relation depends on the estimated Eddington ratio, such that objects with larger Eddington ratios have smaller black hole masses than expected at a given velocity dispersion.
Reverberation mapping is a proven technique that is used to measure the size of the broad emission-line region and central black hole mass in active galactic nuclei. More ambitious reverberation mapping programs that are well within the capabilities of Hubble Space Telescope could allow us to determine the nature and flow of line-emitting gas in active nuclei and to assess accurately the systematic uncertainties in reverberation-based black hole mass measurements.
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 $f$.
We have investigated the relationship between the 2-10 keV X-ray variability amplitude and black hole mass for a sample of 46 radio-quiet active galactic nuclei observed by ASCA. Thirty-three of the objects in our sample exhibited variability over a time-scale of ~40 ks, and we found a significant anti-correlation between excess variance and mass. Unlike most previous studies, we have quantified the variability using nearly the same time-scale for all objects. Moreover, we provide a prescription for estimating the uncertainties in excess variance which accounts both for measurement uncertainties and for the stochastic nature of the variability. We also present an analytical method to predict the excess variance from a model power spectrum accounting for binning, sampling and windowing effects. Using this, we modelled the variance-mass relation assuming all objects have a universal twice-broken power spectrum, with the position of the breaks being dependent on mass. This accounts for the general form of the relationship but there is considerable scatter. We investigated this scatter as a function of the X-ray photon index, luminosity and Eddington ratio. After accounting for the dependence of excess variance on mass, we find no significant correlation with either luminosity or X-ray spectral slope. We do find an anti-correlation between excess variance and the Eddington ratio, although this relation might be an artifact owing to the uncertainties in the mass measurements. It remains to be established that enhanced X-ray variability is a property of objects with steep X-ray slopes or large Eddington ratios.
Black hole masses for samples of active galactic nuclei (AGN) are currently estimated from single-epoch optical spectra. In particular, the size of the broad-line emitting region needed to compute the black hole mass is derived from the optical or ultraviolet continuum luminosity. Here we consider the relationship between the broad-line region size, R, and the near-infrared (near-IR) AGN continuum luminosity, L, as the near-IR continuum suffers less dust extinction than at shorter wavelengths and the prospects for separating the AGN continuum from host-galaxy starlight are better in the near-IR than in the optical. For a relationship of the form R propto L^alpha, we obtain for a sample of 14 reverberation-mapped AGN a best-fit slope of alpha=0.5+/-0.1, which is consistent with the slope of the relationship in the optical band and with the value of 0.5 naively expected from photoionisation theory. Black hole masses can then be estimated from the near-IR virial product, which is calculated using the strong and unblended Paschen broad emission lines (Pa alpha or Pa beta).
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