A simple family of solutions of relativistic viscous hydrodynamics for fireballs with Hubble flow and ellipsoidal symmetry

TL;DR

This paper introduces new analytic solutions to relativistic viscous hydrodynamics for fireballs with Hubble flow and ellipsoidal symmetry, highlighting the role of bulk viscosity in energy density and temperature evolution.

Contribution

The paper presents a simple family of analytic solutions where shear viscosity does not affect evolution, enabling focused study on bulk viscosity effects in heavy-ion collision models.

Findings

Bulk viscosity slows down energy density decrease.

Temperature evolution is affected by bulk viscosity.

Shear viscosity has negligible influence in these solutions.

Abstract

New, analytic solutions of relativistic viscous hydrodynamics are presented, describing expanding fireballs with Hubble-like velocity profile and ellipsoidal symmetry, similar to fireballs created in heavy ion collisions. We find that with these specifications, one obtains solutions where the shear viscosity essentially does not influence the time evolution of the system, thus these solutions are particularly adept tools to study the effect of bulk viscosity alone, which always results in a slower decrease of energy density as well as temperature compared to the case of perfect fluid. We investigate different scenarios for the bulk viscosity and find qualitatively different effects on the time evolution which suggests that there is a possibility to infer the value of bulk viscosity from energy density and temperature measurements in high-energy heavy-ion collisions.