Transverse expansion of hot magnetized Bjorken flow in heavy ion collisions

TL;DR

This paper explores how an inhomogeneous external magnetic field influences the transverse expansion and energy density of a hot, magnetized fluid in high-energy nuclear collisions, extending the classical Bjorken flow model.

Contribution

It introduces a model incorporating inhomogeneous magnetic fields into Bjorken flow, analyzing their effects on transverse expansion and particle spectra in heavy ion collisions.

Findings

Magnetic fields induce radial flow in the transverse plane.

Inhomogeneous magnetic fields modify the energy density evolution.

The model estimates transverse momentum spectra of produced particles.

Abstract

We argue that the existence of an inhomogeneous external magnetic field can lead to radial flow in transverse plane. Our aim is to show how the introduction of a magnetic field generalizes the Bjorken flow. We investigate the effect of an inhomogeneous weak external magnetic field on the transverse expansion of in-viscid fluid created in high energy nuclear collisions. In order to simplify our calculation and compare with Gubser model, we consider the fluid under investigation to be produced in central collisions, at small impact parameter; azimuthal symmetry has been considered. In our model, we assume an inhomogeneous external magnetic field following the power-law decay in proper time and having radial inhomogeneity perpendicular to the radial velocity of the in-viscid fluid in the transverse plane; then the space time evolution of the transverse expansion of the fluid is obtained. We also show how the existence of an inhomogeneous external magnetic field modifies the energy density. Finally we use the solutions for the transverse velocity and energy density in the presence of a weak magnetic field, to estimate the transverse momentum spectrum of protons and pions emerging from the Magneto-hydrodynamic solutions.