Bulk viscosity, particle spectra, and flow in heavy-ion collisions

Abstract

We study the effects of bulk viscosity on ${p}_{T}$ spectra and elliptic flow in heavy-ion collisions. For this purpose, we compute the dissipative correction $\ensuremath{\delta}f$ to the single-particle distribution functions in leading-log QCD, and in several simplified models. We consider, in particular, the relaxation time approximation and a kinetic model for the hadron resonance gas. We implement these distribution functions in a hydrodynamic simulation of Au + Au collisions at the Relativistic Heavy Ion Collider (RHIC). We find significant corrections due to bulk viscosity in hadron ${p}_{T}$ spectra and the differential elliptic flow parameter ${v}_{2}({p}_{T})$. We observe that bulk viscosity scales as the second power of conformality breaking $\ensuremath{\zeta}\ensuremath{\sim}\ensuremath{\eta}{({c}_{s}^{2}\ensuremath{-}1/3)}^{2}$, whereas $\ensuremath{\delta}f$ scales as the first power. Corrections to the spectra are therefore dominated by viscous corrections to the distribution function, and reliable bounds on the bulk viscosity require accurate calculations of $\ensuremath{\delta}f$ in the hadronic resonance phase. Based on viscous hydrodynamic simulations and a simple kinetic model of the resonance phase, which correctly extrapolates to the kinetic description of a dilute pion gas, we conclude that it is difficult to describe the ${v}_{2}$ spectra at RHIC unless $\ensuremath{\zeta}/s\ensuremath{\lesssim}0.05$ near freeze-out. We also find that effects of the bulk viscosity on the ${p}_{T}$ integrated ${v}_{2}$ are small.