Hybrid model with viscous relativistic hydrodynamics: a role of constraints on the shear-stress tensor

Abstract

We present the hybrid hadron string dynamic (HydHSD) model connecting the parton-hadron-string dynamic model (PHSD) and a hydrodynamic model taking into account shear viscosity within the Israel-Stewart approach. The performance of the code is tested on the pion and proton rapidity and transverse mass distributions calculated for Au+Au and Pb+Pb collision at AGS--SPS energies. The influence of the switch time from transport to hydro models, the viscous parameter, and freeze-out time are discussed. Since the applicability of the Israel-Stewart hydrodynamics assumes the perturbative character of the viscous stress tensor, ${\pi }^{\mu \nu }$, which should not exceed the ideal energy-momentum tensor, $T_{\mathrm{id}}^{\mu \nu }$, hydrodynamical codes usually rescale the shear stress tensor if the inequality $\Vert {\pi }^{\mu \nu }\Vert \ll \Vert T_{\mathrm{id}}^{\mu \nu }\Vert$ is not fulfilled in some sense. We show that the form of the corresponding condition plays an important role in the sensitivity of hydrodynamic calculations to the viscous parameter -- a ratio of the shear viscosity to the entropy density, $\eta /s$. It is shown that the constraints used in the vHLLE and MUSIC models give the same results for the observables. With these constraints, the rapidity distributions and transverse momentum spectra are most sensitive to a change of the $\eta /s$ ratio. As an alternative, a strict condition is used. We performed global fits the rapidity and transverse mass distribution of pion and protons. It was also found that $\eta /s$ as a function of the collision energy monotonically increases from $E_{\mathrm{lab}}=6A$GeV up to $E_{\mathrm{lab}}=40A$GeV and saturates for higher SPS energies. We observe that it is difficult to reproduce simultaneously pion and proton rapidity distribution within our model with the present choice of the equation of state without a phase transition.

This paper is the essentially revised version of our paper arXiv:1810.10303

References in corpus (13)

• Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics
• Fully integrated transport approach to heavy ion reactions with an intermediate hydrodynamic stage
• Suppression of elliptic flow in a minimally viscous quark-gluon plasma
• Relativistic hydrodynamics for heavy-ion collisions
• Estimation of the shear viscosity at finite net-baryon density from A+A collision data at $\sqrt{s_{\mathrm{NN}}}=7.7-200$ GeV
• Relativistic Dynamics of Non-ideal Fluids: Viscous and heat-conducting fluids I. General Aspects and 3+1 Formulation for Nuclear Collisions
• Do nuclear collisions create a locally equilibrated quark-gluon plasma?
• A Fast Hadron Freeze-out Generator
• Centrality dependence of proton and antiproton spectra in Pb+Pb collisions at 40A GeV and 158A GeV measured at the CERN SPS
• Directed flow at mid-rapidity in event-by-event hydrodynamics
• Influence of temperature dependent shear viscosity on elliptic flow at back- and forward rapidities in ultrarelativistic heavy-ion collisions
• Relativistic Dissipative Hydrodynamic Equations at the Second Order for Multi-Component Systems with Multiple Conserved Currents
• Comparing the first and second order theories of relativistic dissipative fluid dynamics using the 1+1 dimensional relativistic flux corrected transport algorithm