Causal Viscous Hydrodynamics for Relativistic Heavy Ion Collisions

Abstract

The viscosity of the QGP is a presently hotly debated subject. Since its computation from first principles is difficult, it is desirable to try to extract it from experimental data. Viscous hydrodynamics provides a tool that can attack this problem and which may work in regions where ideal hydrodynamics begins to fail. This thesis focuses on viscous hydrodynamics for relativistic heavy ion collisions. We first review the 2nd order viscous equations obtained from different approaches, and then report on the work of the Ohio State University group on setting up the equations for causal viscous hydrodynamics in 2+1 dimensions and solving them numerically for central and noncentral Cu+Cu and Au+Au collisions at RHIC energies and above. We discuss shear and bulk viscous effects on the hydrodynamic evolution of entropy density, temperature, collective flow, and flow anisotropies, and on the hadron multiplicity, single particle spectra and elliptic flow. Viscous entropy production and its influence on the centrality dependence of hadron multiplicities and the multiplicity scaling of eccentricity-scaled elliptic flow are studied in viscous hydrodynamics and compared with experimental data. The dynamical effects of using different versions of the Israel-Stewart second order formalism for causal viscous fluid dynamics are discussed, resolving some of the apparent discrepancies between early results reported by different groups. Finally, we assess the present status of constraining the shear viscosity to entropy ratio of the hot and dense matter created at RHIC.