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

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 ($\nu +\bar{\nu }\to e^{-}+e^{+}$) 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.

33 pages, 15 figures, accepted to the ApJ

References in corpus (17)

• The Supernova -- Gamma-Ray Burst Connection
• Theory of Core-Collapse Supernovae
• Neutrino signatures and the neutrino-driven wind in Binary Neutron Star Mergers
• Special Relativistic Simulations of Magnetically-dominated Jets in Collapsing Massive Stars
• Disk-Jet Coupling in Black Hole Accretion Systems I: General Relativistic Magnetohydrodynamical Models
• Stellar explosions powered by the Blandford-Znajek mechanism
• Neutrino pair annihilation near accreting, stellar-mass black holes
• Angular Energy Distribution of Collapsar-Jets
• Numerical Study on GRB-Jet Formation in Collapsars
• Magnetar-energized supernova explosions and GRB-jets
• Development of General Relativistic Magnetohydrodynamic Code and its Application to Central Engine of Long Gamma-Ray Bursts
• Magnetar-Driven Magnetic Tower as a Model for Gamma-Ray Bursts and Asymmetric Supernovae
• Magnetohydrodynamics of Neutrino-Cooled Accretion Tori around a Rotating Black Hole in General Relativity
• Magnetohydrodynamic Simulations of A Rotating Massive Star Collapsing to A Black Hole
• Long-Term Evolution of Slowly Rotating Collapsar in Special Relativistic Magnetohydrodynamics
• Eclipsing light curves for accretion flows around a rotating black hole and atmospheric effects of the companion star
• Neutrino oscillations in magnetically driven supernova explosions

Cited by in corpus (17)

• Comprehensive nucleosynthesis analysis for ejecta of compact binary mergers
• Multiple physical elements to determine the gravitational-wave signatures of core-collapse supernovae
• Hyper-accreting black hole as GRB central engine. I: Baryon loading in GRB jets
• Neutrino Transfer in Three Dimensions for Core-Collapse Supernovae. I. Static Configurations
• Black Hole-Neutron Star Mergers with a Hot Nuclear Equation of State: Outflow and Neutrino-Cooled Disk for a Low-Mass, High-Spin Case
• Model of extended emission of short Gamma-ray Bursts
• Formation of black hole and accretion disk in a massive high-entropy stellar core collapse
• Monte Carlo Neutrino Transport Through Remnant Disks from Neutron Star Mergers
• The Transient Gravitational-Wave Sky
• Rotating BHs as Central Engines of Long GRBs: Faster is Better
• Spontaneous Lorentz symmetry breaking effects on GRBs jets arising from neutrino pair annihilation process near a black hole
• Evolutions of stellar-mass black hole hyperaccretion systems in the center of gamma-ray bursts
• Gravitational Wave Signatures of Hyperaccreting Collapsar Disks
• Pion Production via Proton Synchrotron Radiation in Strong Magnetic Fields in Relativistic Field Theory: Scaling Relations and Angular Distributions
• Elastic Scattering in General Relativistic Ray Tracing for Neutrinos
• Neutrino pair annihilation above black-hole accretion disks in modified gravity
• The propagation of neutrino-driven jets in Wolf-Rayet stars