Thermal noise in non-boost-invariant dissipative hydrodynamics

TL;DR

This paper investigates how thermal noise affects the longitudinal expansion of matter in relativistic heavy ion collisions, revealing that it produces ridge-like rapidity correlations sensitive to dissipative models and equations of state.

Contribution

It formulates a second-order viscous hydrodynamics framework for thermal noise in non-boost-invariant flow and develops a numerical simulation to analyze resulting rapidity correlations.

Findings

Thermal noise induces ridge-like rapidity correlations.

Correlations are dominated by temperature at small rapidity separation.

Pattern of correlations varies with dissipative formalism and equation of state.

Abstract

We study the effects of hydrodynamic fluctuations in non-boost-invariant longitudinal expansion of matter formed in relativistic heavy ion collisions. We formulate the theory of thermal noise within second-order viscous hydrodynamics treating noise as a perturbation on top of the non-boost-invariant flow. We develop a numerical simulation model to treat the (1+1)-dimension hydrodynamic evolution. The code is tested to reproduce the analytic results for the Riemann solver for expansion of matter in vacuum. For viscous hydrodynamic expansion, the initial energy density distribution are obtained by reproducing the measured charged hadron rapidity distribution at the RHIC energies. We show that the longitudinal rapidity correlations arising from space-time dependent thermal noise and from an induced thermal perturbation have distinct structures. In general, the rapidity correlations are found to be dominated by temperature fluctuations at small rapidity separation and velocity fluctuations at large rapidities. We demonstrate that thermal noise produce ridge-like two-particle rapidity correlations which persist at moderately large rapidities. The magnitude and pattern of the correlations are quite sensitive to various second-order dissipative formalisms and to the underlying equations of state, especially at large rapidities. The short-range part of the rapidity correlation is found to be somewhat enhanced as compared to that in boost-invariant flow of matter.