Simulating elliptic flow with viscous hydrodynamics

TL;DR

This paper models elliptic flow in non-central heavy-ion collisions using viscous hydrodynamics, highlighting the impact of viscous corrections on flow spectra and the limits of hydrodynamic applicability.

Contribution

It applies a viscous hydrodynamical model with a novel approach to freezeout and viscous corrections, analyzing their effects on elliptic flow and stability of the results.

Findings

Viscous corrections modest without distribution function modifications.

Including corrections significantly alters elliptic flow at high transverse momentum.

Hydrodynamics becomes unreliable for η/s > 0.3 due to stress tensor deviations.

Abstract

In this work we simulate a viscous hydrodynamical model of non-central Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance. The model fluid equations were proposed by \"{O}ttinger and Grmela \cite{OG}. Freezeout is signaled when the viscous corrections become large relative to the ideal terms. Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated. When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest. However, when these corrections are included, the elliptic flow is strongly modified at large $p_T$. We also investigate the stability of the viscous results by comparing the non-ideal components of the stress tensor ($\pi^{ij}$) and their influence on the $v_2$ spectrum to the expectation of the Navier-Stokes equations ($\pi^{ij} = -\eta \llangle \partial_i u_j \rrangle$). We argue that when the stress tensor deviates from the Navier-Stokes form the dissipative corrections to spectra are too large for a hydrodynamic description to be reliable. For typical RHIC initial conditions this happens for $\eta/s \gsim 0.3$.