We show how accretion rate governs the physical properties of a sample of unobscured broad-line, narrow-line, and lineless active galactic nuclei (AGNs). We avoid the systematic errors plaguing previous studies of AGN accretion rate by using accurate
accretion luminosities (L_int) from well-sampled multiwavelength SEDs from the Cosmic Evolution Survey (COSMOS), and accurate black hole masses derived from virial scaling relations (for broad-line AGNs) or host-AGN relations (for narrow-line and lineless AGNs). In general, broad emission lines are present only at the highest accretion rates (L_int/L_Edd > 0.01), and these rapidly accreting AGNs are observed as broad-line AGNs or possibly as obscured narrow-line AGNs. Narrow-line and lineless AGNs at lower specific accretion rates (L_int/L_Edd < 0.01) are unobscured and yet lack a broad line region. The disappearance of the broad emission lines is caused by an expanding radiatively inefficient accretion flow (RIAF) at the inner radius of the accretion disk. The presence of the RIAF also drives L_int/L_Edd < 10^-2 narrow-line and lineless AGNs to 10 times higher ratios of radio to optical/UV emission than L_int/L_Edd > 0.01 broad-line AGNs, since the unbound nature of the RIAF means it is easier to form a radio outflow. The IR torus signature also tends to become weaker or disappear from L_int/L_Edd < 0.01 AGNs, although there may be additional mid-IR synchrotron emission associated with the RIAF. Together these results suggest that specific accretion rate is an important physical axis of AGN unification, described by a simple model.
In this work we have developed a new stochastic model for the fluctuations in lightcurves of accreting black holes. The model is based on a linear combination of stochastic processes and is also the solution to the linear diffusion equation perturbed
by a spatially correlated noise field. This allows flexible modeling of the power spectral density (PSD), and we derive the likelihood function for the process, enabling one to estimate the parameters of the process, including break frequencies in the PSD. Our statistical technique is computationally efficient, unbiased by aliasing and red noise leak, and fully accounts for irregular sampling and measurement errors. We show that our stochastic model provides a good approximation to the X-ray lightcurves of galactic black holes, and the optical and X-ray lightcurves of AGN. We use the estimated time scales of our stochastic model to recover the correlation between characteristic time scale of the high frequency X-ray fluctuations and black hole mass for AGN, including two new `detections of the time scale for Fairall 9 and NGC 5548. We find a tight anti-correlation between the black hole mass and the amplitude of the driving noise field, which is proportional to the amplitude of the high frequency X-ray PSD, and we estimate that this parameter gives black hole mass estimates to within ~ 0.2 dex precision, potentially the most accurate method for AGN yet. We also find evidence that ~ 13% of AGN optical PSDs fall off flatter than 1 / f^2, and, similar to previous work, find that the optical fluctuations are more suppressed on short time scales compared to the X-rays, but are larger on long time scales, suggesting the optical fluctuations are not solely due to reprocessing of X-rays.
We present black hole masses and accretion rates for 182 Type 1 AGN in COSMOS. We estimate masses using the scaling relations for the broad Hb, MgII, and CIV emission lines in the redshift ranges 0.16<z<0.88, 1<z<2.4, and 2.7<z<4.9. We estimate the a
ccretion rate using an Eddington ratio L_I/L_Edd estimated from optical and X-ray data. We find that very few Type 1 AGN accrete below L_I/L_Edd ~ 0.01, despite simulations of synthetic spectra which show that the survey is sensitive to such Type 1 AGN. At lower accretion rates the BLR may become obscured, diluted or nonexistent. We find evidence that Type 1 AGN at higher accretion rates have higher optical luminosities, as more of their emission comes from the cool (optical) accretion disk with respect to shorter wavelengths. We measure a larger range in accretion rate than previous works, suggesting that COSMOS is more efficient at finding low accretion rate Type 1 AGN. However the measured range in accretion rate is still comparable to the intrinsic scatter from the scaling relations, suggesting that Type 1 AGN accrete at a narrow range of Eddington ratio, with L_I/L_Edd ~ 0.1.
We describe a Bayesian approach to estimating quasar black hole mass functions (BHMF) when using the broad emission lines to estimate black hole mass. We show how using the broad line mass estimates in combination with statistical techniques develope
d for luminosity function estimation leads to statistically biased results. We derive the likelihood function for the BHMF based on the broad line mass estimates, and derive the posterior distribution for the BHMF, given the observed data. We develop our statistical approach for a flexible model where the BHMF is modelled as a mixture of Gaussian functions. Statistical inference is performed using markov chain monte carlo (MCMC) methods. Our method has the advantage that it is able to constrain the BHMF even beyond the survey detection limits at the adopted confidence level, accounts for measurement errors and the intrinsic uncertainty in broad line mass estimates, and provides a natural way of estimating the probability distribution of any quantities derived from the BHMF. We conclude by using our method to estimate the local active BHMF using the z < 0.5 Bright Quasar Survey sources. At z = 0.2, the quasar BHMF falls off approximately as a power law with slope ~ 2 for M_{BH} > 10^8. Our analysis implies that z < 0.5 broad line quasars have a typical Eddington ratio of ~ 0.4 and a dispersion in Eddington ratio of < 0.5 dex (abridged).
We describe a Bayesian approach to estimating luminosity functions. We derive the likelihood function and posterior probability distribution for the luminosity function, given the observed data, and we compare the Bayesian approach with maximum-likel
ihood by simulating sources from a Schechter function. For our simulations confidence intervals derived from bootstrapping the maximum-likelihood estimate can be too narrow, while confidence intervals derived from the Bayesian approach are valid. We develop our statistical approach for a flexible model where the luminosity function is modeled as a mixture of Gaussian functions. Statistical inference is performed using Markov chain Monte Carlo (MCMC) methods, and we describe a Metropolis-Hastings algorithm to perform the MCMC. The MCMC simulates random draws from the probability distribution of the luminosity function parameters, given the data, and we use a simulated data set to show how these random draws may be used to estimate the probability distribution for the luminosity function. In addition, we show how the MCMC output may be used to estimate the probability distribution of any quantities derived from the luminosity function, such as the peak in the space density of quasars. The Bayesian method we develop has the advantage that it is able to place accurate constraints on the luminosity function even beyond the survey detection limits, and that it provides a natural way of estimating the probability distribution of any quantities derived from the luminosity function, including those that rely on information beyond the survey detection limits.
In this work we use a sample of 318 radio-quiet quasars (RQQ) to investigate the dependence of the ratio of optical/UV flux to X-ray flux, alpha_ox, and the X-ray photon index, Gamma_X, on black hole mass, UV luminosity relative to Eddington, and X-r
ay luminosity relative to Eddington. Our sample is drawn from the SDSS, with X-ray data from ROSAT and Chandra, and optical data mostly from the SDSS; 153 of these sources have estimates of Gamma_X from Chandra. We estimate M_BH using standard estimates derived from the Hbeta, Mg II, and C IV broad emission lines. Our sample spans a broad range in black hole mass (10^6 < M_BH / M_Sun < 10^10) and redshift (z < 4.8). We find that alpha_ox increases with increasing M_BH and L_UV / L_Edd, and decreases with increasing L_X / L_Edd. In addition, we confirm the correlation seen in previous studies between Gamma_X and M_BH and both L_UV / L_Edd and L_X / L_Edd; however, we also find evidence that the dependence of Gamma_X of these quantities is not monotonic, changing sign at M_BH ~ 3 x 10^8 M_Sun. We argue that the alpha_ox correlations imply that the fraction of bolometric luminosity emitted by the accretion disk, as compared to the corona, increases with increasing accretion rate relative to Eddington. In addition, we argue that the Gamma_X trends are caused by a dependence of X-ray spectral index on accretion rate. We discuss our results within the context of accretion models with comptonizing corona, and discuss the implications of the alpha_ox correlations for quasar feedback. To date, this is the largest study of the dependence of RQQ X-ray parameters on black hole mass and related quantities, and the first to attempt to correct for the large statistical uncertainty in the broad line mass estimates.
I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors, and intrinsic scatter in the regression relationship. The meth
od is based on deriving a likelihood function for the measured data, and I focus on the case when the intrinsic distribution of the independent variables can be approximated using a mixture of Gaussians. I generalize the method to incorporate multiple independent variables, non-detections, and selection effects (e.g., Malmquist bias). A Gibbs sampler is described for simulating random draws from the probability distribution of the parameters, given the observed data. I use simulation to compare the method with other common estimators. The simulations illustrate that the Gaussian mixture model outperforms other common estimators and can effectively give constraints on the regression parameters, even when the measurement errors dominate the observed scatter, source detection fraction is low, or the intrinsic distribution of the independent variables is not a mixture of Gaussians. I conclude by using this method to fit the X-ray spectral slope as a function of Eddington ratio using a sample of 39 z < 0.8 radio-quiet quasars. I confirm the correlation seen by other authors between the radio-quiet quasar X-ray spectral slope and the Eddington ratio, where the X-ray spectral slope softens as the Eddington ratio increases.
