Aspects of causal viscous hydrodynamics

TL;DR

This paper compares causal Israel-Stewart viscous hydrodynamics with acausal ELNS hydrodynamics in modeling expanding fluids, highlighting differences in thermalization, entropy production, and fluctuation behavior, with implications for initial energy density estimates.

Contribution

It provides a detailed analysis of viscous hydrodynamics, defining thermalization time, constructing solutions for boost-invariant flows, and studying fluctuation damping and wave phenomena.

Findings

Viscous fluids expand slower than ideal fluids, producing entropy.

Late-time flows are well approximated by ELNS solutions.

Fluctuations are damped in ELNS but can form sound waves in IS hydrodynamics.

Abstract

We investigate the phenomenology of freely expanding fluids, with different material properties, evolving through the Israel-Stewart (IS) causal viscous hydrodynamics, and compare our results with those obtained in the relativistic Eckart-Landau-Navier-Stokes (ELNS) acausal viscous hydrodynamics. Through the analysis of scaling invariants we give a definition of thermalization time which can be self-consistently determined in viscous hydrodynamics. Next we construct the solutions for one-dimensional boost-invariant flows. Expansion of viscous fluids is slower than that of one-dimensional ideal fluids, resulting in entropy production. At late times, these flows are reasonably well approximated by solutions obtained in ELNS hydrodynamics. Estimates of initial energy densities from observed final values are strongly dependent on the dynamics one chooses. For the same material, and the same final state, IS hydrodynamics gives the smallest initial energy density. We also study fluctuations about these one-dimensional boost-invariant backgrounds; they are damped in ELNS hydrodynamics but can become sound waves in IS hydrodynamics. The difference is obvious in power spectra due to clear signals of wave-interference in IS hydrodynamics, which is completely absent in ELNS dynamics.