Critical radiation fluxes and luminosities of black holes and relativistic stars

Abstract

The critical luminosity at which the outward force of radiation balances the inward force of gravity plays an important role in many astrophysical systems. We present expressions for the radiation force on particles with arbitrary cross sections and analyze the radiation field produced by radiating matter, such as a disk, ring, boundary layer, or stellar surface, that rotates slowly around a slowly rotating gravitating mass. We then use these results to investigate the critical radiation flux and, where possible, the critical luminosity of such a system in general relativity. We demonstrate that if the radiation source is axisymmetric and emission is back-front symmetric with respect to the local direction of motion of the radiating matter, as seen in the comoving frame, then the radial component of the radiation flux and the diagonal components of the radiation stress-energy tenser outside the source are the same, to first order in the rotation rates, as they would be if the radiation source and gravitating mass were not rotating. If the opacity is independent of frequency and direction, the critical flux for matter at the surface of a star or in orbit around a star or black hole is the same, at least to first order, as it would be if the matter, radiation source, and gravitating mass were static. In this case the critical flux measured at the radiation source is also the same to first order as it would be if the matter, source, and mass were static. We argue that the critical radiation flux for matter at rest in the locally nonrotating frame is often satisfactory as an astrophysical benchmark flux and show that if this benchmark is adopted, many of the complications potentially introduced by rotation of the radiation source and the gravitating mass are avoided. If instead the opacity is frequency- or direction-dependent, the critical flux generally depends on the angular size and spectrum of the source and is affected by rotation of the source and mass and orbital motion of the matter to first order. We show that if the radiation field in the absence of rotation would be spherically symmetric and the opacity is independent of frequency and direction, one can define a critical luminosity for the system that is independent of the spectrum and angular size of the radiation source and is unaffected by rotation of the source and mass and orbital motion of the matter, to first order. Finally, we analyze the conditions under which the maximum possible luminosity of a star or black hole powered by steady spherically symmetric radial accretion is the same in general relativity as in the Newtonian limit.