# Conservation of the Flux of Energy in Extra-Galactic Jets

## TL;DR

This paper investigates energy flux conservation in turbulent extragalactic jets across different intergalactic medium profiles, deriving analytical and numerical models for jet velocity and trajectory, with applications to radio galaxy observations.

## Contribution

It introduces a method to derive jet motion laws from energy flux conservation considering various IGM density profiles, including relativistic effects and radiative losses.

## Key findings

- Derived analytical velocity expressions for different IGM profiles.
- Numerically determined jet trajectories in various media.
- Applied models to radio galaxy 3C31's synchrotron emission and magnetic field evolution.

## Abstract

The conservation of the energy flux in turbulent jets that propagate in the intergalactic medium (IGM) allows us to deduce the law of motion in the classical and relativistic cases. Four types of IGM are considered: constant density, hyperbolic decrease of density, inverse power law decrease of density and a Lane--Emden ($n=5$) profile. The conservation of the relativistic flux for the energy allows us to derive, to the first order, an analytical expression for the velocity. It also allows us to numerically determine the trajectory for the four types of medium. In the case of a Lane--Emden ($n=5$) profile, the back-reaction due to the radiative losses for the trajectory is evaluated both in the classical and the relativistic case. Astrophysical applications are made to the centerline intensity of the synchrotron emission and to the evolution of the magnetic field in the case of the radio-galaxy 3C31.