Modeling reverberation mapping data I: improved geometric and dynamical models and comparison with cross-correlation results

We present an improved and expanded simply parameterized phenomenological model of the broad line region (BLR) in active galactic nuclei (AGN) for modeling reverberation mapping data. By modeling reverberation mapping data directly, we can constrain the geometry and dynamics of the BLR and measure the black hole mass without relying on the normalization factor needed in the traditional analysis. For realistic simulated reverberation mapping datasets of high-quality, we can recover the black hole mass to $0.05-0.25$ dex uncertainty and distinguish between dynamics dominated by elliptical orbits and inflowing gas. While direct modeling of the integrated emission line light curve allows for measurement of the mean time lag, other details of the geometry of the BLR are better constrained by the full spectroscopic dataset of emission line profiles. We use this improved model of the BLR to explore possible sources of uncertainty in measurements of the time lag using cross-correlation function (CCF) analysis and in measurements of the black hole mass using the virial product. Sampling the range of geometries and dynamics in our model of the BLR suggests that the theoretical uncertainty in black hole masses measured using the virial product is on the order of 0.25 dex. These results support the use of the CCF to measure time lags and the virial product to measure black hole masses when direct modeling techniques cannot be applied, provided the uncertainties associated with the interpretation of the results are taken into account.