The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions

TL;DR

This paper assesses the validity of causal dissipative hydrodynamics models, specifically Israel-Stewart and Navier-Stokes theories, in describing relativistic heavy ion collisions, identifying their accuracy limits under various conditions.

Contribution

The study provides quantitative validity ranges for Israel-Stewart and Navier-Stokes hydrodynamics in relativistic heavy ion collision scenarios, including analytic solutions and tests for numerical codes.

Findings

Israel-Stewart theory is 10% accurate when expansion timescale exceeds half the mean free path.

Navier-Stokes requires three times larger timescale for similar accuracy.

Israel-Stewart becomes marginal for eta/s > ~0.15 at RHIC energies.

Abstract

We utilize nonequilibrium covariant transport theory to determine the region of validity of causal Israel-Stewart dissipative hydrodynamics (IS) and Navier-Stokes theory (NS) for relativistic heavy ion physics applications. A massless ideal gas with 2->2 interactions is considered in a 0+1D Bjorken scenario, appropriate for the early longitudinal expansion stage of the collision. In the scale invariant case of a constant shear viscosity to entropy density ratio eta/s ~ const, we find that Israel-Stewart theory is 10% accurate in calculating dissipative effects if initially the expansion timescale exceeds half the transport mean free path tau0/lambda0 > ~2. The same accuracy with Navier-Stokes requires three times larger tau0/lambda0 > ~6. For dynamics driven by a constant cross section, on the other hand, about 50% larger tau0/lambda0 > ~3 (IS) and ~9 (NS) are needed. For typical applications at RHIC energies s_{NN}**(1/2) ~ 100-200 GeV, these limits imply that even the Israel-Stewart approach becomes marginal when eta/s > ~0.15. In addition, we find that the 'naive' approximation to Israel-Stewart theory, which neglects products of gradients and dissipative quantities, has an even smaller range of applicability than Navier-Stokes. We also obtain analytic Israel-Stewart and Navier-Stokes solutions in 0+1D, and present further tests for numerical dissipative hydrodynamics codes in 1+1, 2+1, and 3+1D based on generalized conservation laws.