Viscosity, non-conformal equation of state and sound velocity in Landau hydrodynamics

TL;DR

This paper presents an analytical solution to relativistic viscous hydrodynamics for non-conformal systems, fitting experimental rapidity spectra and extracting the speed of sound, showing viscosity's negligible effect on spectra.

Contribution

It introduces a new analytical solution for non-conformal Landau hydrodynamics with viscosity, improving data fit and enabling extraction of the speed of sound from heavy-ion collision data.

Findings

Viscous corrections do not affect rapidity spectra at freeze-out.

Non-conformal Landau flow yields better data agreement than conformal ideal models.

Speed of sound decreases monotonically with collision energy.

Abstract

We find an analytical solution to relativistic viscous hydrodynamics for a 1+1 dimensional Landau flow profile. We consider relativistic Navier-Stokes form of the dissipative hydrodynamic equation, for a non-conformal system with a constant speed of sound, and employ the obtained solution to fit rapidity spectrum of observed pions in $\sqrt{s_{NN}}=$ 200, 17.3, 12.3, 8.76, 7.62, 6.27, 4.29, 3.83, 3.28 and 2.63 GeV collision energies. We find that at the freeze-out hypersurface with improved Landau's freeze-out prescription, the viscous corrections do not affect the rapidity spectra. We demonstrate that the solution of the non-conformal Landau flow lead to a better agreement with the experimental data compared to the conformal ideal solution. We also extract speed of sound from fit to the rapidity spectra for various collision energies and find a monotonous decrease with decreasing collision energies. Appealing to the fact that viscosity has negligible effect on rapidity spectra for Landau's freeze-out scenario, we argue that our calculations provides a framework for extracting the average value of speed of sound in relativistic heavy-ion collisions.