How large is the Knudsen number reached in fluid dynamical simulations of ultrarelativistic heavy ion collisions?

TL;DR

This paper assesses the limits of fluid dynamics applicability in ultrarelativistic heavy ion and proton-nucleus collisions by calculating the Knudsen number and shear viscosity thresholds at RHIC and LHC energies.

Contribution

It provides the first detailed estimation of maximum shear viscosity values for which fluid dynamics remains valid in AA and pA collisions at high energies.

Findings

Maximum η/s in AA collisions is about 0.1 to 0.2.

In pA collisions, the viscosity limit is below 0.08.

Fluid dynamics applicability depends on collision centrality and multiplicity.

Abstract

We investigate the applicability of fluid dynamics in ultrarelativistic heavy ion (AA) collisions and high multiplicity proton nucleus (pA) collisions. In order for fluid dynamics to be applicable the microscopic and macroscopic distance/time scales of the system have to be sufficiently separated. The degree of separation is quantified by the ratio between these scales, usually referred to as the Knudsen number. In this work, we calculate the Knudsen numbers reached in fluid dynamical simulations of AA and pA collisions at RHIC and LHC energies. For this purpose, we consider different choices of shear viscosity parametrizations, initial states and initialization times. We then estimate the values of shear viscosity for which the fluid dynamical description of ultrarelativistic AA and pA collisions breaks down. In particular, we study how such values depend on the centrality, in the case of AA collision, and multiplicity, in the case of pA collision. We found that the maximum viscosity in AA collisions is of the order $\eta/s \sim 0.1 \ldots 0.2$, which is similar in magnitude to the viscosities currently employed in simulations of heavy ion collisions. For pA collisions, we found that such limit is significantly lower, being less than $\eta/s=0.08$