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

• Published in: The Astrophysical journal Vol. 720; no. 1; p. 614
• Main Authors: Harikae, Seiji, Kotake, Kei, Takiwaki, Tomoya, Sekiguchi, Yu-ichiro
• Format: Journal Article
• Language: English
• Published: United States IOP Publishing 01.09.2010
• Subjects: ACCRETION DISKS; ALGEBRAIC CURRENTS; ANALYTICAL SOLUTION; ANNIHILATION; ANTILEPTONS; ANTIMATTER; ANTINEUTRINO REACTIONS; ANTINEUTRINOS; ANTIPARTICLES; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BINARY STARS; BLACK HOLES; BOLTZMANN EQUATION; CALCULATION METHODS; CHARGED CURRENTS; COSMIC GAMMA BURSTS; COSMIC NEUTRINOS; COSMIC RADIATION; CURRENTS; DIFFERENTIAL EQUATIONS; ELEMENTARY PARTICLES; ENERGY DEPENDENCE; ENERGY RANGE; EQUATIONS; ERUPTIVE VARIABLE STARS; FERMIONS; FLUID MECHANICS; GRAVITATIONAL COLLAPSE; HYDRODYNAMICS; INTEGRO-DIFFERENTIAL EQUATIONS; INTERACTIONS; IONIZING RADIATIONS; ITERATIVE METHODS; KINETIC EQUATIONS; LEPTON-LEPTON INTERACTIONS; LEPTONS; MAGNETOHYDRODYNAMICS; MASSLESS PARTICLES; MATHEMATICAL SOLUTIONS; MATTER; MECHANICS; NEUTRINO-NEUTRINO INTERACTIONS; NEUTRINOS; NUCLEAR REACTIONS; NUMERICAL SOLUTION; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE INTERACTIONS; PRIMARY COSMIC RADIATION; RADIATIONS; RELATIVISTIC RANGE; RUNGE-KUTTA METHOD; SPACE-TIME; STARS; SUPERNOVAE; VARIABLE STARS
• ISSN: 0004-637X; 1538-4357
• DOI: 10.1088/0004-637X/720/1/614

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}+{nu}-bar{yields}e{sup -}+e{sup +}) in the vicinity of an accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic (GR) 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. We employ the Fehlberg (4,5) adaptive integrator in the Runge-Kutta method to perform the numerical integration accurately. For the neutrino opacity, the charged-current {beta}-processes, which are dominant in the vicinity of the accretion tori, are taken into account. The numerical accuracy of the developed code is certified by several tests in which we show comparisons with the corresponding analytical solutions. In order to solve the energy-dependent ray-tracing transport, we propose that an adaptive-mesh-refinement approach, which we take for the two radiation angles ({theta}, {phi}) and the neutrino energy, is useful in reducing the computational cost significantly. 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 GR effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percent. After the accretion disk settles into a stationary state (typically later than {approx}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 that the neutrino pair annihilation is potentially as important as the conventional magnetohydrodynamic mechanism for igniting the GRB fireballs.