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.

We first refine the fixed concept in the literature that the usage of the Newtonian potential in studies of black hole accretion is invalid and the general relativistic effect must be considered. As our main results, we then show that the energy released by neutrino annihilation in neutrino-dominated accretion flows is sufficient for gammaray bursts when the contribution from the optically thick region of the flow is included, and that in the optically thick region advection does not necessarily dominate over neutrino cooling because the advection factor is relevant to the geometrical depth rather than the optical depth of the flow.

No abstract

Neutrino-dominated accretion flows (NDAFs) around rotating stellar-mass black holes are plausible candidates for the central engines of gamma-ray bursts (GRBs). We investigate one-dimensional global solutions of NDAFs, taking account of general relativity in Kerr metric, neutrino physics and nucleosynthesis more precisely than previous works. We calculate sixteen solutions with different characterized accretion rates and black hole spins to exhibit the radial distributions of various physical properties in NDAFs. We confirm that the electron degeneracy has important effects in NDAFs and we find that the electron fraction is about 0.46 in the outer region for all the sixteen solutions. From the perspective of the mass fraction, free nucleons, 4 He, and 56 Fe dominate in the inner, middle, and outer region, respectively. The influence of neutrino trapping on the annihilation is of importance for the superhigh accretion (Ṁ = 10M ⊙ s −1 ) and most of the sixteen solutions have an adequate annihilation luminosity for GRBs.