Structure and luminosity of neutrino-cooled accretion disks

Neutrino-cooled hyperaccretion disks around stellar-mass black holes are plausible candidates for the central engines of gamma-ray bursts. We calculate the one-dimensional structure and the annihilation luminosity of such disks. The neutrino optical depth is of crucial importance in determining the neutrino cooling rate and is in turn dependent on the electron fraction, the free nucleon fraction, and the electron degeneracy, for a given density and temperature of the disk matter. We construct a bridging formula for the electron fraction that works for various neutrino optical depths and give exact definitions for the free proton fraction and free neutron fraction. We show that the electron degeneracy has important effects, in the sense that it increases the absorption optical depth for neutrinos and, along with the neutronization processes favored by high temperature, causes the electron fraction to drop below 0.1 in the inner region of the disk. The resulting neutrino annihilation luminosity is considerably reduced in comparison with that obtained in previous works in which the electron degeneracy was not considered and the electron fraction was simply taken to be 0.5, but it is still likely to be adequate for gamma-ray bursts, and it is ejected mainly from the inner region of the disk with an anisotropic distribution.