On the Deceleration and Spreading of Relativistic Jets I: Jet Dynamics

TL;DR

This paper introduces a semi-analytical model for relativistic jet deceleration and spreading in gamma-ray bursts, based on numerical simulations, improving the understanding of jet break phenomena in afterglow observations.

Contribution

A new semi-analytical model derived from relativistic numerical calculations that accurately describes jet deceleration and spreading, surpassing previous analytical models.

Findings

The model accurately predicts Lorentz factor and opening angle evolution.

Comparison shows good agreement with numerical simulations.

Provides a foundation for efficient synthetic afterglow calculations.

Abstract

Jet breaks in gamma ray burst (GRB) afterglows provide a direct probe of their collimation angle. Modeling a jet break requires an understanding of the "jet spreading" process, whereby the jet transitions from a collimated outflow into the spherical Sedov-Taylor solution at late times. Currently, direct numerical calculations are the most accurate way to capture the deceleration and spreading process, as analytical models have previously given inaccurate descriptions of the dynamics. Here (in paper I) we present a new, semi-analytical model built empirically by performing relativistic numerical jet calculations and measuring the relationship between Lorentz factor and opening angle. We then calculate the Lorentz factor and jet opening angle as a function of shock radius and compare to the numerical solutions. Our analytic model provides an efficient means of computing synthetic GRB afterglow light curves and spectra, which is the focus of paper II.