Stationary Relativistic Jets

TL;DR

This paper introduces a simple, efficient numerical method for studying steady-state relativistic jets using one-dimensional time-dependent simulations, offering a practical alternative to more complex approaches.

Contribution

The authors propose a novel approach that approximates steady-state relativistic jet equations with time-dependent simulations, validated against existing solutions and revealing insights into jet reconfinement and oscillations.

Findings

Validated the method against analytical and numerical solutions.

Identified reasons for failure of self-similar models in flat atmospheres.

Clarified the nature of radial oscillations in jets.

Abstract

In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with v~c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialized code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres and elucidated the nature of radial oscillations of steady-state jets.