  Neutrino-cooled hyperaccretion disks around stellar mass black holes are
plausible candidates for the central engine 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, with 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
enlarges the absorption optical depth for neutrinos, and it along with the
neutronization processes favored by high temperature cause the electron
fraction to drop to be below 0.1 in the inner region of the disk. The resulting
neutrino annihilation luminosity is considerably reduced comparing with that
obtained in previous works where 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 and has an anisotropic distribution.
