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

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.Comment: 33 pages, 15 figures, accepted to the Ap

Gravitational Wave Signatures of Hyperaccreting Collapsar Disks

By performing two-dimensional special relativistic (SR) magnetohydrodynamic simulations, we study possible signatures of gravitational waves (GWs) in the context of the collapsar model for long-duration gamma-ray bursts. In our SR simulations, the central black hole is treated as an absorbing boundary. By doing so, we focus on the GWs generated by asphericities in neutrino emission and matter motions in the vicinity of the hyperaccreting disks. We compute nine models by adding initial angular momenta and magnetic fields parametrically to a precollapse core of a $35 M_{\odot}$ progenitor star. As for the microphysics, a realistic equation of state is employed and the neutrino cooling is taken into account via a multiflavor neutrino leakage scheme. To accurately estimate GWs produced by anisotropic neutrino emission, we perform a ray-tracing analysis in general relativity by a post-processing procedure. By employing a stress formula that includes contributions both from magnetic fields and special relativistic corrections, we study also the effects of magnetic fields on the gravitational waveforms. We find that the GW amplitudes from anisotropic neutrino emission show a monotonic increase with time, whose amplitudes are much larger than those from matter motions of the accreting material. We show that the increasing trend of the neutrino GWs stems from the excess of neutrino emission in the direction near parallel to the spin axis illuminated from the hyperaccreting disks. We point out that a recently proposed future space-based interferometer like Fabry-Perot type DECIGO would permit the detection of these GW signals within $\approx$ 100 Mpc.Comment: 38 pages, 14 figures, ApJ in pres