Analytic Bjorken flow in one-dimensional relativistic magnetohydrodynamics

TL;DR

This paper analytically investigates the evolution of relativistic fluid flow in heavy-ion collisions under strong magnetic fields, revealing that the classic Bjorken flow behavior persists regardless of magnetic field strength and decay rate.

Contribution

It provides new analytic solutions for magnetohydrodynamic flow in heavy-ion collisions, demonstrating the robustness of Bjorken flow in magnetic fields and offering insights for future research and numerical modeling.

Findings

Fluid energy density decay matches classic Bjorken flow regardless of magnetic field strength.

Two classes of solutions depending on magnetic field decay rate $ au^{-a}$.

Bjorken flow is more general than previously understood.

Abstract

In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density $e$ with proper time $\tau$ is the same as for the time-honored "Bjorken flow" without magnetic field. Furthermore, when the magnetic field is assumed to decay $\sim \tau^{-a}$, where $a$ is an arbitrary number, two classes of analytic solutions can be found depending on whether $a$ is larger or smaller than one. In summary, the analytic solutions presented here highlight that the Bjorken flow is far more general than formerly thought. These solutions can serve both to gain insight on the dynamics of heavy-ion collisions in the presence of strong magnetic fields and as testbeds for numerical codes.