Weighing black holes from zero to high redshift
  The application of the virial theorem provides a tool to estimate supermassive black hole (BH) masses in large samples of active galactic nuclei (AGN) with broad emission lines at all redshifts and luminosities, if the broad line region (BLR) is gravitationally bound. In this paper we discuss the importance of radiation forces on BLR clouds arising from the deposition of momentum by ionizing photons. Such radiation forces counteract gravitational ones and, if not taken into account, BH masses can be severely underestimated. We provide virial relations corrected for the effect of radiation pressure and we discuss their physical meaning and application. If these corrections to virial masses, calibrated with low luminosity objects, are extrapolated to high luminosities then the BLRs of most quasars might be gravitationally unbound. The importance of radiation forces in high luminosity objects must be thoroughly investigated to assess the reliability of quasar BH masses. 
A. Marconi, D. Axon, R. Maiolino, T. Nagao, P. Pietrini, A. Robinson,   G. Torricelli