Neutrino trapping and accretion models for gamma-ray bursts

Many models of gamma-ray bursts (GRBs) invoke a central engine consisting of a black hole of a few solar masses accreting matter from a disk at a rate of a fraction to a few solar masses per second. Popham et al. and Narayan et al. have shown that, for ̇M ≲ 0.1 M_⊙ s^-1, accretion proceeds via neutrino cooling and neutrinos can carry away a significant amount of energy from the inner regions of the disks. We improve on these calculations by including a simple prescription for neutrino transfer and neutrino opacities in such regions. We find that the flows become optically thick to neutrinos inside a radius R ∼ 6R_S-40R_S for Ṁ in the range of 0.1-10 M_⊙ s^-1, where R _S is the black hole Schwarzchild radius. Most of the neutrino emission comes from outside this region, and the neutrino luminosity stays roughly constant at a value L_μv ∼ 10⁵³ ergs s ^-1. We show that, for ̇M ≳ 1 M_⊙ s ^-1, neutrinos are sufficiently trapped that energy advection becomes the dominant cooling mechanism in the flow. These results imply that μvv̄ annihilation in hyperaccreting black holes is an inefficient mechanism for liberating large amounts of energy. Extraction of rotational energy by magnetic processes remains the most viable mechanism.