Multipole solution of hydrodynamics and higher order harmonics

TL;DR

This paper presents new hydrodynamic solutions incorporating higher order asymmetries to explain observed flow coefficients in heavy ion collisions, highlighting the role of initial state fluctuations.

Contribution

It introduces the first analytic solutions that include higher order asymmetries, enabling realistic modeling of higher order flow coefficients $v_n$ in hydrodynamics.

Findings

Higher order flow coefficients $v_n$ can be explained by new solutions with asymmetries.

Different flow patterns can produce similar observed flow coefficients.

Comparison with PHENIX data suggests specific parameter sets.

Abstract

The time evolution of the medium created in heavy ion collisions can be described by hydrodynamical models. After expansion and cooling, the hadrons are created in a freeze-out. Their distribution describes the final state of this medium. In particular their azimuthal asymmetry, characterized by the elliptic flow coefficient $v_2$, is one of the most important observables in heavy ion physics. In recent years it has been revealed that if measuring relative to higher order event planes $\Psi_n$, higher order flow coefficients $v_n$ for $n>2$ can be measured. This is due to initial state fluctuations, previously not described by analytic solutions of relativistic hydrodynamics. In this paper we show the first solutions that utilize higher order asymmetries and thus yield realistic $v_n$ flow coefficients. It is a clear consequence of this that different flow patterns may lead to the same observed flow coefficients. We also compare our results to PHENIX measurements and determine a possible parameter set corresponding to these data.