Gamma-Ray Burst Dynamics and Afterglow Radiation from Adaptive Mesh Refinement, Special Relativistic Hydrodynamic Simulations

TL;DR

This paper introduces Mezcal-SRHD, a new adaptive mesh refinement code for simulating relativistic hydrodynamics in gamma-ray bursts, demonstrating its accuracy and revealing new insights into jet and blast wave dynamics.

Contribution

The paper presents a novel SRHD code with adaptive mesh refinement and applies it to study relativistic blast waves and jets, providing new understanding of their deceleration and afterglow radiation.

Findings

Deceleration to non-relativistic speeds occurs at larger scales than the Sedov length.

Stratification delays the transition to non-relativistic speeds.

Simulated afterglow light curves match analytical models and previous simulations.

Abstract

We report on the development of Mezcal-SRHD, a new adaptive mesh refinement, special relativistic hydrodynamics (SRHD) code, developed with the aim of studying the highly relativistic flows in Gamma-Ray Burst sources. The SRHD equations are solved using finite volume conservative solvers. The correct implementation of the algorithms is verified by one-dimensional (1D) shock tube and multidimensional tests. The code is then applied to study the propagation of 1D spherical impulsive blast waves expanding in a stratified medium with $\rho \propto r^{-k}$, bridging between the relativistic and Newtonian phases, as well as to a two-dimensional (2D) cylindrically symmetric impulsive jet propagating in a constant density medium. It is shown that the deceleration to non-relativistic speeds in one-dimension occurs on scales significantly larger than the Sedov length. This transition is further delayed with respect to the Sedov length as the degree of stratification of the ambient medium is increased. This result, together with the scaling of position, Lorentz factor and the shock velocity as a function of time and shock radius, is explained here using a simple analytical model based on energy conservation. The method used for calculating the afterglow radiation by post-processing the results of the simulations is described in detail. The light curves computed using the results of 1D numerical simulations during the relativistic stage correctly reproduce those calculated assuming the self-similar Blandford-McKee solution for the evolution of the flow. The jet dynamics from our 2D simulations and the resulting afterglow lightcurves, including the jet break, are in good agreement with those presented in previous works. Finally, we show how the details of the dynamics critically depend on properly resolving the structure of the relativistic flow.