A GENERAL RELATIVISTIC RAY-TRACING METHOD FOR ESTIMATING THE ENERGY AND MOMENTUM DEPOSITION BY NEUTRINO PAIR ANNIHILATION IN COLLAPSARS

Journal Article · Wed Sep 01 00:00:00 EDT 2010 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/720/1/614· OSTI ID:21460104

Harikae, Seiji ^[1]; Kotake, Kei; Sekiguchi, Yu-ichiro ^[2]; Takiwaki, Tomoya ^[3]

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1. Department of Astronomy, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)
2. Division of Theoretical Astronomy, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588 (Japan)
3. Center for Computational Astrophysics, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588 (Japan)

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.

• OSTI ID: 21460104
• Journal Information: Astrophysical Journal, Vol. 720, Issue 1; Other Information: DOI: 10.1088/0004-637X/720/1/614; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
ACCRETION DISKS
ANALYTICAL SOLUTION
ANNIHILATION
ANTINEUTRINO REACTIONS
ANTINEUTRINOS
BLACK HOLES
BOLTZMANN EQUATION
CHARGED CURRENTS
COSMIC GAMMA BURSTS
COSMIC NEUTRINOS
ENERGY DEPENDENCE
GRAVITATIONAL COLLAPSE
MAGNETOHYDRODYNAMICS
NEUTRINO-NEUTRINO INTERACTIONS
RELATIVISTIC RANGE
RUNGE-KUTTA METHOD
SPACE-TIME
SUPERNOVAE
ALGEBRAIC CURRENTS
ANTILEPTONS
ANTIMATTER
ANTIPARTICLES
BINARY STARS
CALCULATION METHODS
COSMIC RADIATION
CURRENTS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
ENERGY RANGE
EQUATIONS
ERUPTIVE VARIABLE STARS
FERMIONS
FLUID MECHANICS
HYDRODYNAMICS
INTEGRO-DIFFERENTIAL EQUATIONS
INTERACTIONS
IONIZING RADIATIONS
ITERATIVE METHODS
KINETIC EQUATIONS
LEPTON-LEPTON INTERACTIONS
LEPTONS
MASSLESS PARTICLES
MATHEMATICAL SOLUTIONS
MATTER
MECHANICS
NEUTRINOS
NUCLEAR REACTIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS
PRIMARY COSMIC RADIATION
RADIATIONS
STARS
VARIABLE STARS