Geometric and Dynamical Models of Reverberation Mapping Data
  We present a general method to analyze reverberation mapping data that
provides both estimates for the black hole mass and for the geometry and
dynamics of the broad line region (BLR) in active galactic nuclei (AGN). Our
method directly infers the spatial and velocity distribution of the BLR from
the data, allowing us to easily derive a velocity-resolved transfer function
and allowing for a self-consistent estimate of the black hole mass without a
virial coefficient. We obtain estimates and reasonable uncertainties of the BLR
model parameters by implementing a Markov Chain Monte Carlo algorithm using the
formalism of Bayesian probability theory. We use Gaussian Processes to
interpolate the the continuum light curve data and create mock light curves
that can be fitted to the data. We test our method by creating simulated
reverberation mapping data-sets with known true parameter values and by trying
to recover these parameter values using our models. We are able to recover the
parameters with realistic uncertainties that depend upon the variability of the
AGN and the quality of the reverberation mapping campaign. With a geometry
model we can recover the mean radius of the BLR to within ~0.1dex 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 ~0.05dex 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.
