Geometric and Dynamical Models of Reverberation Mapping Data

Abstract

We present a general method to analyze reverberation (or echo) mapping data, that simultaneously provides estimates for the black hole mass and for the geometry and dynamics of the broad line region (BLR) in active galactic nuclei (AGN). While previous methods yield a typical scale size of the broad line region or a reconstruction of the transfer function, our method directly infers the spatial and velocity distribution of the BLR from the data, from which a transfer function can be easily derived. Previous echo mapping analysis requires an independent estimate of a scaling factor known as the virial coefficient to infer the mass of the black hole, but this is not needed in our more direct approach. We use the formalism of Bayesian probability theory and implement a Markov Chain Monte Carlo algorithm to obtain estimates and uncertainties for the parameters of our BLR models. Fitting of models to the data requires knowledge of the continuum flux at all times, not just the measured times. We use Gaussian Processes to interpolate and extrapolate the continuum light curve data in a fully consistent probabilistic manner, taking the associated errors into account. We illustrate our method using simple models of BLR geometry and dynamics and show that we can recover the parameter values of our test systems with realistic uncertainties that depend upon the variability of the AGN and the quality of the reverberation mapping observing campaign. With a geometry model we can recover the mean radius of the BLR to within ∼ 0.1 dex random uncertainty for simulated data with an integrated line flux uncertainty of 1.5%, while with a dynamical model we can recover the black hole mass and the mean radius to within ∼ 0.05 dex random uncertainty, for simulated data with a line profile average signal to noise ratio of 4 per spectral pixel. These uncertainties do not include modeling errors, which are likely to be present in the analysis of real data, and should therefore be considered as lower limits to the accuracy of the method.

Imprints of the quasar structure in time-delay light curves: Microlensing-aided reverberation mapping

“…That technique, originally designed for spectrophotometric data (e.g. Peterson 1993;Kaspi et al 2000;Bentz et al 2009;Denney et al 2010;Pancoast et al 2011), is currently extended to multi-band photometric data (e.g. Chelouche & Daniel 2012;Zu et al 2014).…”

X-ray reverberation around accreting black holes

“…Peterson 1993;Peterson et al 2004;Bentz et al 2009;Denney et al 2010). More recently, stochastic modelling and fitting of light curves has been applied to more accurately model the optical reverberation data (Zu et al 2011;Pancoast et al 2011). The situation for X-ray time-series analysis is different however: here the focus to date has been on Fourier analysis techniques (with just a few exceptions, e.g.…”

“…Such work has culminated in the measurement of black hole masses for a wide range of AGN (e.g. Grier et al 2012 and see Peterson & Bentz 2006 for a review) and is now leading to the measurement of the detailed structure of the BLR, identifying its inclination to the observer as well as whether the gas is simply orbiting, outflowing, inflowing or some combination of all three (Bentz et al 2010;Pancoast et al 2011Pancoast et al , 2013Grier et al 2013).…”

Space Telescope and Optical Reverberation Mapping Project. V. Optical Spectroscopic Campaign and Emission-line Analysis for NGC 5548

“…While the discrepancy between τ Hβ-UV and τ Hβ-opt may not change M BH measurements that use the f factor, dynamical models that directly infer M BH and BLR characteristics (e.g., Pancoast et al 2011;Li et al 2013) using only optical continuum data are affected since they do not depend on this Wandel et al 1999;Kaspi et al 2000Kaspi et al , 2005McLure & Jarvis 2002;Bentz et al 2006Bentz et al , 2009aBentz et al , 2013. If τ Hβ-UV /τ Hβ-opt correlates with AGN luminosity, then the expected value of α would change, and if this ratio is different for all AGNs but is uncorrelated with any other AGN properties, then this would introduce additional scatter to the scaling relation.…”

“…There has been tremendous effort by many groups to recover velocity-delay maps (Rosenblatt & Malkan 1990;Horne et al 1991;Krolik et al 1991;Ulrich & Horne 1996;Bentz et al 2010a;Pancoast et al 2011Pancoast et al , 2014Grier et al 2013;Li et al 2013;Skielboe et al 2015) and velocity-resolved line lags (e.g., Kollatschny 2003;Bentz et al 2009b;Denney et al 2010;Barth et al 2011;Du et al 2016a). In order to obtain Ψ(v, τ), RM campaigns must have a combination of high cadence, long duration, high photometric precision, and high signal-to-noise ratios (S/Ns), which is often not achievable by ground-based programs.…”