General Relativistic Ray-Tracing Method for Estimating the Energy and Momentum Deposition by Neutrino Pair Annihilation in Collapsars

TL;DR

This paper introduces a general relativistic ray-tracing code to estimate neutrino pair annihilation energy deposition near black hole accretion disks, showing relativistic effects significantly enhance energy transfer relevant for gamma-ray burst models.

Contribution

We developed a novel numerical scheme for relativistic neutrino transfer using ray-tracing, enabling accurate estimation of energy deposition in collapsar environments.

Findings

Relativistic effects increase local energy deposition by about tenfold.

Net energy deposition rate increases by several tens of percent with black hole spin.

Neutrino heating can be faster than dynamical timescales, influencing GRB fireball formation.

Abstract

Bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs), we develop a numerical scheme and code for estimating the deposition of energy and momentum due to the neutrino pair annihilation ($\nu + {\bar \nu} \rightarrow e^{-} + e^{+}$) in the vicinity of accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic neutrino transfer by a ray-tracing method. To solve the collisional Boltzmann equation in curved spacetime, we numerically integrate the so-called rendering equation along the null geodesics. For the neutrino opacity, the charged-current $\beta$-processes are taken into account, which are dominant in the vicinity of the accretion tori. The numerical accuracy of the developed code is certificated by several tests, in which we show comparisons with the corresponding analytic solutions. Based on the hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. Increasing the Kerr parameter from 0 to 1, it is found that the general relativistic effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percents. After the accretion disk settles into a stationary state (typically later than $\sim 9$ s from the onset of gravitational collapse), we point out that the neutrino-heating timescale in the vicinity of the polar funnel region can be shorter than the dynamical timescale. Our results suggest the neutrino pair annihilation has a potential importance equal to the conventional magnetohydrodynamic mechanism for igniting the GRB fireballs.