Exact solution of one dimensional relativistic jet with relativistic equation of state

TL;DR

This paper derives an exact analytical solution for the evolution of one-dimensional relativistic jets with a relativistic equation of state, considering jet composition, cross-section variation, and interaction with ambient media.

Contribution

It provides the first exact solution for relativistic jet evolution incorporating variable cross-section and composition effects using relativistic fluid dynamics.

Findings

Jet propagation speed varies with jet composition.

Reverse shock behavior depends on jet and ambient medium properties.

Jet-head cross-section variation influences jet dynamics.

Abstract

We study the evolution of one-dimensional relativistic jets, using the exact solution of the Riemann problem for relativistic flows. For this purpose, we solve equations for the ideal special relativistic fluid composed of dissimilar particles in flat space-time and the thermodynamics of fluid is governed by a relativistic equation of state. We obtain the exact solution of jets impinging on denser ambient media. The time variation of the cross-section of the jet-head is modeled and incorporated. We present the initial condition that gives rise to a reverse shock. If the jet-head cross-section increases in time, the jet propagation speed slows down significantly and the reverse-shock may recede opposite to the propagation direction of the jet. We show that the composition of jet and ambient medium can affect the jet solution significantly. For instance, the propagation speed depends on the composition and is maximum for a pair-dominated jet, rather than a pure electron-positron or electron-proton jet. The propagation direction of the reverse-shock may also strongly depend on the composition of the jet.