[Paper Review] Bulk viscosity in heavy ion collision

Victor Roy, Asim Chaudhuri|arXiv (Cornell University)|Jan 20, 2012

High-Energy Particle Collisions Research1 references3 citations

TL;DR

This study investigates the impact of temperature-dependent bulk viscosity to entropy density ratio (ζ/s) on relativistic viscous hydrodynamic simulations of heavy ion collisions using the Israel-Stewart formalism. The authors find that Grad’s 14-moment method for freezeout correction remains valid only for ζ/s < 0.004, with bulk viscosity causing relative corrections of up to ~10% in pion pT spectra and ~3% in v2, indicating limited but measurable effects on observables when ζ/s is small.

ABSTRACT

The effect of a temperature dependent bulk viscosity to entropy density ratio~($ζ/s$) along with a constant shear viscosity to entropy density ratio~($η/s$) on the space time evolution of the fluid produced in high energy heavy ion collisions have been studied in a relativistic viscous hydrodynamics model. The boost invariant Israel-Stewart theory of causal relativistic viscous hydrodynamics is used to simulate the evolution of the fluid in 2 spatial and 1 temporal dimension. The dissipative correction to the freezeout distribution for bulk viscosity is calculated using Grad's fourteen moment method. From our simulation we show that the method is applicable only for $ζ/s&lt;0.004$.

Motivation & Objective

• To assess the influence of temperature-dependent bulk viscosity (ζ/s) on fluid evolution in relativistic heavy ion collisions.
• To evaluate the validity of Grad’s 14-moment method for calculating dissipative corrections to the freezeout distribution function under varying ζ/s values.
• To quantify the impact of bulk viscosity on key observables such as pion transverse momentum spectra and elliptic flow (v2).
• To determine the upper limit of ζ/s for which the freezeout correction procedure remains physically reliable.

Proposed method

• Employed the causal relativistic viscous hydrodynamics framework based on the Israel-Stewart theory to simulate fluid evolution in 2+1 dimensions.
• Used a hybrid equation of state combining lattice QCD data for the QGP phase and a hadronic resonance gas model for the hadronic phase, joined at Tc = 174 MeV.
• Implemented a temperature-dependent ζ/s using pQCD-based formula ζ/s = 15(η/s)(1/3 - c²s)², with c²s derived from lattice data.
• Applied the 14-moment method of Grad to compute non-equilibrium corrections to the freezeout distribution function.
• Simulated fluid evolution with initial energy density ε₀ = 30 GeV/fm³ from a two-component Glauber model and set freezeout at Tfo = 130 MeV using the Cooper-Freely algorithm.
• Solved the energy-momentum conservation equation ∂μTμν = 0 alongside relaxation equations for shear and bulk stresses, with initial viscous stresses set to Navier-Stokes estimates.

Experimental results

Research questions

• RQ1 How does a temperature-dependent bulk viscosity (ζ/s) affect the space-time evolution of the quark-gluon plasma in heavy ion collisions?
• RQ2 To what extent do bulk viscosity corrections alter the pion transverse momentum spectra and elliptic flow (v2) compared to ideal hydrodynamics?
• RQ3 What is the maximum value of ζ/s for which the freezeout correction via Grad’s 14-moment method remains physically valid?
• RQ4 How do the relative corrections to pT spectra and v2 scale with increasing ζ/s, and are they consistent with experimental observability?

Key findings

• The relative correction to the pion invariant yield due to bulk viscosity remains within approximately 10% across the pT range studied, indicating a moderate but measurable effect.
• The relative correction to elliptic flow (v2) due to bulk viscosity is less than 3%, showing a small but non-negligible influence on anisotropic flow.
• The freezeout correction procedure based on Grad’s 14-moment method breaks down when the relative correction to the yield exceeds 50%, limiting its applicability to ζ/s < 0.004.
• The method remains valid only for ζ/s values below 0.004, as higher values lead to unphysical corrections exceeding the threshold for reliability.
• Bulk viscosity reduces the spatially averaged transverse velocity ⟨⟨vT⟩⟩ compared to ideal hydrodynamics, due to reduced pressure in the fluid.
• Both shear and bulk viscosity suppress momentum-space anisotropy εp, which correlates with reduced v2, consistent with viscous damping of flow gradients.