The effect of radiation pressure on emission-line profiles and black hole mass determination in active galactic nuclei

We present a new analysis of the motion of pressure-confined, broad-line region (BLR) clouds in active galactic nuclei (AGNs) taking into account the combined influence of gravity and radiation pressure. We calculate cloud orbits under a large range of conditions and include the effect of column density variation as a function of location. The dependence of radiation pressure force on the level of ionization and the column density are accurately computed. The main results are as follows. (1) The mean cloud locations (r_BLR) and line widths (FWHMs) are combined in such a way that the simple virial mass estimate, r_BLR, FWHM²/G, gives a reasonable approximation to M_BH even when radiation pressure force is important. The reason is that L/M rather than L is the main parameter affecting the planar cloud motion. (2) Reproducing the mean observed r_BLR, FWHM, and line intensity of Hβ and C_IV λ 1549 requires at least two different populations of clouds. (3) The cloud location is a function of both L ^1/2 and L/M. Given this, we suggest a new approximation for r _BLR which, when inserted into the BH mass equation, results in a new approximation for M_BH. The new expression involves L^1/2, FWHM, and two constants that are obtained from a comparison with available M-σ* mass estimates. It deviates only slightly from the old mass estimate at all luminosities. (4) The quality of the present black hole mass estimators depends, critically, on the way the present M-σ* AGN sample (29 objects) represents the overall population, in particular the distribution of L/L_Edd.