Structure and Luminosity of Neutrino‐cooled Accretion Disks

Neutrino-cooled hyperaccretion disks around stellar mass black holes areplausible candidates for the central engine of gamma-ray bursts. We calculatethe one-dimensional structure and the annihilation luminosity of such disks.The neutrino optical depth is of crucial importance in determining the neutrinocooling rate and is in turn dependent on the electron fraction, the freenucleon fraction, and the electron degeneracy, with given density andtemperature of the disk matter. We construct a bridging formula for theelectron fraction that works for various neutrino optical depths, and giveexact definitions for the free proton fraction and free neutron fraction. Weshow that the electron degeneracy has important effects in the sense that itenlarges the absorption optical depth for neutrinos, and it along with theneutronization processes favored by high temperature cause the electronfraction to drop to be below 0.1 in the inner region of the disk. The resultingneutrino annihilation luminosity is considerably reduced comparing with thatobtained in previous works where the electron degeneracy was not considered andthe electron fraction was simply taken to be 0.5, but it is still likely to beadequate for gamma-ray bursts, and it is ejected mainly from the inner regionof the disk and has an anisotropic distribution.Comment: 32 pages, 13 figures, accepted by Ap