Deceleration of relativistic jets with lateral expansion

TL;DR

This paper introduces a simplified 1D hydrodynamic model for relativistic jets interacting with the circum-stellar medium, enabling efficient simulation of jet dynamics and afterglow emission.

Contribution

The authors develop a new 1D model and code, Jedi, for simulating relativistic jet hydrodynamics and afterglow emission, validated against existing analytical and numerical results.

Findings

The model accurately reproduces jet deceleration and emission across various structures.

Jedi code efficiently simulates afterglow from neutron star merger jets.

The approach simplifies complex 2D problems while maintaining accuracy.

Abstract

We present a model for the hydrodynamics of a relativistic jet interacting with the circum-stellar medium (CSM). The shocked CSM and the jet material are assumed to be in an infinitely thin surface, so the original 2D problem is effectively reduced to 1D. From general conservation laws, we derive the equation of motion for each fluid element along this surface, taking into account the deceleration along the surface normal due to newly swept-up mass and lateral expansion due to pressure gradient in the tangential direction. The pressure and energy density of the shocked CSM are given by the jump conditions at the forward shock. The method is implemented with a finite-differencing numerical scheme, along with calculation of synchrotron emission and absorption from shock-accelerated electrons, in a new code $\mathtt{Jedi}$ (for "jet dynamics"). We present a number of test cases, including top-hat jet, power-law structured jet, "boosted fireball" profile, and CSM with density jump at the wind termination shock. Based on the agreement with other analytical and numerical calculations, we conclude that our simplified method provides a good approximation for the hydrodynamics and afterglow emission for a wide variety of jet structures and CSM density profiles. Efficient modeling of the afterglow from e.g., neutron star mergers, will provide important information on the jet energetics, CSM properties, and the viewing angle.