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 $\delta f$ 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 $v_2\left(p_T\right)$. We observe that bulk viscosity scales as the second power of conformality breaking $\zeta \sim \eta {(c_s^2-1/3)}^2$, whereas $\delta f$ 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 $\delta f$ 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 $\zeta /s\lesssim 0.05$ near freeze-out. We also find that effects of the bulk viscosity on the $p_T$ integrated $v_2$ are small.

• Received 21 October 2011

DOI:https://doi.org/10.1103/PhysRevC.85.044909