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 broad line region (BLR) clouds in active galactic nuclei (AGNs) taking into account the combined influence of gravity and radiation pressure force. We calculate cloud orbits under a large range of conditions and include the effect of a changing column density 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: a. The mean cloud location r(BLR) and the line widths (FWHMs) are combined in such a way that the simple virial mass estimate, r{BLR} FWHM^2/G, gives a reasonable approximation to the black hole mass M 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. b. Reproducing the observed mean radius, FWHM and intensity of H-beta and CIV 1549 requires at least two different populations of clouds. c. 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. The new expression involves L^{1/2}, FWHM and two constants that are obtained from a comparison with available M-sigma mass estimates. It deviates only slightly from the old mass estimate at all luminosities. d. The quality of present black hole mass estimators depends, critically, on the way the present M-sigma AGN sample (16 objects) represents the AGN population, in particular the distribution of Eddington ratios.