On an exact hydrodynamic solution for the elliptic flow

TL;DR

This paper derives exact hydrodynamic solutions for elliptic flow in relativistic perfect fluids, linking theoretical models with observed heavy-ion collision phenomena.

Contribution

It introduces a solvable hydrodynamic potential framework for describing elliptic flow, incorporating entropy conservation and temperature-driven expansion.

Findings

Derived exact solutions for flow coefficients v_2

Matched temperature dependence of anisotropy with experimental data

Demonstrated quasi-stationary expansion governs elliptic flow

Abstract

Looking for the underlying hydrodynamic mechanisms determining the elliptic flow we show that for an expanding relativistic perfect fluid the transverse flow may derive from a solvable hydrodynamic potential, if the entropy is transversally conserved and the corresponding expansion "quasi-stationary", that is mainly governed by the temperature cooling. Exact solutions for the velocity flow coefficients $v_2$ and the temperature dependence of the spatial and momentum anisotropy are obtained and shown to be in agreement with the elliptic flow features of heavy-ion collisions.