Hydrodynamics of Ultra-Relativistic Heavy Ion Collisions. Considerations of Boost Non-invariance and Stopping

Abstract

We investigate the features of boost-invariant hydrodynamics of Bjorken, the boost-non-invariant hydrodynamics of Srivastava et al. and the Landau hydrodynamics corresponding to the so-called stopping scenario for the ultra relativistic collision of heavy nuclei. The chemical potential has been assumed to be small, and a (1 + 1)-dimensional expansion is considered. The fluid rapidity densities for the three cases are found to be quite distinct in nature. It is shown that a rapidity shift parameter can be defined which measures the deviation of the flow from the so-called similarity flow. It is found to be dramatically different for the three hydrodynamic solutions and can be used to characterise the flow. The cooling laws for the three solutions are obtained and they reveal that the cooling is fastest for the Landau solution and slowest for the Bjorken solution. It is also seen that the initial temperatures likely to be attained at a given incident energy are largest for the Landau solution and smallest for the Bjorken solution. A number of alternative general solutions are also discussed.