Applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA and Physics Department, Purdue University, West Lafayette, Indiana 47907 (United States)
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{yields}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 {eta}/s{approx_equal}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 {tau}{sub 0}/{lambda}{sub tr,0} > or approx. 2. The same accuracy with NS requires three times larger {tau}{sub 0}/{lambda}{sub tr,0} > or approx. 6. For dynamics driven by a constant cross section, on the other hand, about 50% larger {tau}{sub 0}/{lambda}{sub tr,0} > or approx. 3 (IS) and 9 (NS) are needed. For typical applications at energies currently available at the BNL Relativistic Heavy Ion Collider (RHIC), i.e., {radical}(s{sub NN}){approx}100-200 GeV, these limits imply that even the IS approach becomes marginal when {eta}/s > or approx. 0.15. 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.
- OSTI ID:
- 21199515
- Journal Information:
- Physical Review. C, Nuclear Physics, Vol. 79, Issue 1; Other Information: DOI: 10.1103/PhysRevC.79.014906; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2813
- Country of Publication:
- United States
- Language:
- English
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BROOKHAVEN RHIC
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CONSERVATION LAWS
CROSS SECTIONS
DENSITY
ENTROPY
GEV RANGE 100-1000
HEAVY ION REACTIONS
HEAVY IONS
HYDRODYNAMICS
INTERACTIONS
MATHEMATICAL SOLUTIONS
NAVIER-STOKES EQUATIONS
RELATIVISTIC RANGE
TRANSPORT THEORY
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