The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions

Details The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions

2008-08-07

arxiv.org/abs/0808.0953v1

Phys.Rev.C79:014906,2009

Physics

Nuclear Physics

Nuclear Theory

30 pages, 26 EPS figures, revtex stylefile

Scientific paper

10.1103/PhysRevC.79.014906

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.

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