# Classical and relativistic evolution of an extra-galactic jet with back-reaction

## TL;DR

This paper derives analytical and numerical models for the evolution of extragalactic jets in a specific medium, considering classical and relativistic effects and the impact of radiative losses on jet trajectories.

## Contribution

It provides first-order analytical expressions for jet velocity and trajectory in a Lane-Emden medium, including relativistic effects and back-reaction from radiative losses.

## Key findings

- Analytical velocity expressions for classical and relativistic jets.
- Numerical trajectories accounting for radiative back-reaction.
- Comparison of classical and relativistic jet evolution.

## Abstract

We consider a turbulent jet which is moving in a Lane--Emden ($n=5$) medium. The conserved quantity is the energy flux, which allows finding, to first order, an analytical expression for the velocity and an approximate trajectory. The conservation of the relativistic flux for the energy allows deriving, to first order, an analytical expression for the velocity, and numerically determining the trajectory. The back-reaction due to the radiative losses for the trajectory is evaluated both in the classical and the relativistic case.