Relativistic expansion of a magnetized fluid

TL;DR

This paper derives semi-analytical solutions for the relativistic expansion of a magnetized fluid from a spherical source, revealing how magnetic field ratios and energy distribution influence the flow dynamics.

Contribution

It presents novel semi-analytical models for relativistic MHD expansion, incorporating uniform expansion, polytropic fluid relations, and velocity approaching light speed.

Findings

Solutions depend on magnetic field ratios

Flow velocity approaches the speed of light

Density and magnetic flux are self-consistently determined

Abstract

We study semi-analytical time-dependent solutions of the relativistic magnetohydrodynamic (MHD) equations for the fields and the fluid emerging from a spherical source. We assume uniform expansion of the field and the fluid and a polytropic relation between the density and the pressure of the fluid. The expansion velocity is small near the base but approaches the speed of light at the light sphere where the flux terminates. We find self-consistent solutions for the density and the magnetic flux. The details of the solution depend on the ratio of the toroidal and the poloidal magnetic field, the ratio of the energy carried by the fluid and the electromagnetic field and the maximum velocity it reaches.