Neutrino Pair Annihilation in Collapsars; Ray-Tracing Method in Special Relativity

TL;DR

This paper develops a special relativistic ray-tracing scheme to estimate neutrino pair annihilation energy and momentum transfer in collapsar models, highlighting its potential role in gamma-ray burst outflows.

Contribution

The authors introduce a novel numerical method for calculating neutrino pair annihilation in relativistic collapsar environments, validated with analytical tests.

Findings

Neutrino energy deposition peaks near the accretion disk's inner edge.

Relativistic beaming effects significantly alter annihilation rates in the polar funnel.

Neutrino heating timescales can be shorter than hydrodynamical timescales, enabling outflow launching.

Abstract

We develop a numerical scheme and code for estimating the energy and momentum transfer via neutrino pair annihilation ($\nu + {\bar \nu} \to e^{-}+ e^{+}$), bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs). To calculate the neutrino flux illuminated from the accretion disk, we perform a ray-tracing calculation in the framework of special relativity. The numerical accuracy of the developed code is certificated by several tests, in which we show comparisons with the corresponding analytical solutions. Using hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. We show that the neutrino energy deposition and momentum transfers are strongest near the inner edge of the accretion disk. The beaming effects of special relativity are found to change the annihilation rates by several factors in the polar funnel region. After the accretion disk settles into a stationary state (typically later than $\sim 9$ s from the onset of gravitational collapse), we find that the neutrino-heating timescale in the vicinity of the polar funnel ($\lesssim 80$ km) can become shorter than the hydrodynamical timescale, indicating that the neutrino-heated outflows can be launched there. We point out that the momentum transfer can play as important role as the energy deposition for the efficient acceleration of neutrino-driven outflows. Our results suggest that the neutrino pair annihilation has a potential importance equal to the conventional magnetohydrodynamic mechanism for igniting the GRB fireballs.