Does the Slim-Disk Model Correctly Consider Photon-Trapping Effects?

Abstract

We investigate the photon-trapping effects in the super-critical black hole accretion flows by solving radiation transfer as well as the energy equations of radiation and gas. It is found that the slim-disk model generally overestimates the luminosity of the disk at around the Eddington luminosity (L_E) and is not accurate in describing the effective temperature profile, since it neglects time delay between energy generation at deeper inside the disk and energy release at the surface. Especially, the photon-trapping effects are appreciable even below L ~ L_E, while they appear above ~ 3L_E according to the slim disk. Through the photon-trapping effects, the luminosity is reduced and the effective temperature profile becomes flatter than r^{-3/4} as in the standard disk. In the case that the viscous heating is effective only around the equatorial plane, the luminosity is kept around the Eddington luminosity even at very large mass accretion rate, Mdot>>L_E/c^2. The effective temperature profile is almost flat, and the maximum temperature decreases in accordance with rise in the mass accretion rate. Thus, the most luminous radius shifts to the outer region when Mdot/(L_E/c^2) >> 10^2. In the case that the energy is dissipated equally at any heights, the resultant luminosity is somewhat larger than in the former case, but the energy-conversion efficiency still decreases with increase of the mass accretion rate, as well. The most luminous radius stays around the inner edge of the disk in the latter case. Hence, the effective temperature profile is sensitive to the vertical distribution of energy production rates, so is the spectral shape. Future observations of high L/L_E objects will be able to test our model.