Temperature dependent sound velocity in hydrodynamic equations for relativistic heavy-ion collisions

TL;DR

This study investigates how different temperature-dependent sound velocity profiles influence the hydrodynamic evolution in relativistic heavy-ion collisions, emphasizing the importance of a smooth sound velocity function with a shallow minimum at the critical temperature.

Contribution

It introduces various models of the sound velocity function based on lattice QCD and hadron gas data, analyzing their impact on hydrodynamic evolution and experimental observables.

Findings

A distinct minimum in sound velocity causes unrealistically long evolution times.

Smooth sound velocity functions with shallow minima are consistent with experimental data.

Hydrodynamics favor models with a crossover transition and smooth sound velocity profiles.

Abstract

We analyze the effects of different forms of the sound-velocity function cs(T) on the hydrodynamic evolution of matter formed in the central region of relativistic heavy-ion collisions. At high temperatures (above the critical temperature Tc) the sound velocity is calculated from the recent lattice simulations of QCD, while in the low temperature region it is obtained from the hadron gas model. In the intermediate region we use different interpolations characterized by the values of the sound velocity at the local maximum (at T = 0.4 Tc) and local minimum (at T = Tc). In all considered cases the temperature dependent sound velocity functions yield the entropy density, which is consistent with the lattice QCD simulations at high temperature. Our calculations show that the presence of a distinct minimum of the sound velocity leads to a very long (about 20 fm/c) evolution time of the system, which is not compatible with the recent estimates based on the HBT interferometry. Hence, we conclude that the hydrodynamic description is favored in the case where the cross-over phase transition renders the smooth sound velocity function with a possible shallow minimum at Tc.