Applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions

We utilize nonequilibrium covariant transport theory to determine the region of validity of causal Israel-Stewart (IS) dissipative hydrodynamics and Navier-Stokes (NS) theory for relativistic heavy ion physics applications. A massless ideal gas with 2→2 interactions is considered in a Bjorken scenario in 0 + 1 dimension (D) appropriate for the early longitudinal expansion stage of the collision. In the scale-invariant case of a constant shear viscosity to entropy density ratio η/s≈const, we find that IS theory is accurate within 10% in calculating dissipative effects if initially the expansion time scale exceeds half the transport mean free path τ₀/λtr,02. The same accuracy with NS requires three times larger τ₀/λtr,06. For dynamics driven by a constant cross section, on the other hand, about 50% larger τ₀/λtr,03 (IS) and 9 (NS) are needed. For typical applications at energies currently available at the BNL Relativistic Heavy Ion Collider (RHIC), i.e., √sNN~100-200 GeV, these limits imply that even the IS approach becomes marginal when η/s0.15. In addition, we find that the ``naive'' approximation to IS theory, which neglects products of gradients and dissipative quantities, has an even smaller range of applicability than Navier-Stokes. We also obtain analytic IS and NS 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.