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We present a new analysis of the motion of broad line region (BLR) clouds inactive galactic nuclei (AGNs) taking into account the combined influence ofgravity and radiation pressure force. We calculate cloud orbits under a largerange of conditions and include the effect of a changing column density as afunction of location. The dependence of radiation pressure force on the levelof ionization and the column density are accurately computed. The main resultsare: a. The mean cloud location r(BLR) and the line widths (FWHMs) are combinedin such a way that the simple virial mass estimate, r{BLR} FWHM^2/G, gives areasonable approximation to the black hole mass M even when radiation pressureforce is important. The reason is that L/M rather than L is the main parameteraffecting the planar cloud motion. b. Reproducing the observed mean radius,FWHM and intensity of H-beta and CIV 1549 requires at least two differentpopulations of clouds. c. The cloud location is a function of both L^{1/2} andL/M. Given this we suggest a new approximation for r(BLR) which, when insertedinto the BH mass equation, results in a new approximation for M. The newexpression involves L^{1/2}, FWHM and two constants that are obtained from acomparison with available M-sigma mass estimates. It deviates only slightlyfrom the old mass estimate at all luminosities. d. The quality of present blackhole mass estimators depends, critically, on the way the present M-sigma AGNsample (16 objects) represents the AGN population, in particular thedistribution of Eddington ratios.

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