Viscous fluid dynamics in Au+Au collisions at RHIC

We have studied the space-time evolution of minimally viscous ($\frac{\eta}{s}$=0.08) QGP fluid, undergoing boost-invariant longitudinal motion and arbitrary transverse expansion. Relaxation equations for the shear stress tensor components, derived from the phenomenological Israel-Stewart's theory of dissipative relativistic fluid, are solved simultaneously with the energy-momentum conservation equations. Comparison of evolution of ideal and viscous fluid, both initialized under the similar conditions, e.g. same equilibration time, energy density and velocity profile, indicate that in viscous fluid, energy density or temperature of the fluid evolve slowly than in an ideal fluid. Transverse expansion is also more in viscous evolution. We have also studied particle production in viscous dynamics. Compared to ideal dynamics, in viscous dynamics, particle yield at high $p_T$ is increased. Elliptic flow on the other hand decreases. Minimally viscous QGP fluid, initialized at entropy density $s_{ini}$=110 $fm^{-3}$ at the initial time $\tau_i$=0.6 fm, if freeze-out at temperature $T_F$=130 MeV, explains the centrality dependence of $p_T$ spectra of identified particles. Experimental $p_T$ spectra of $\pi^-$, $K^+$ and protons in 0-5%, 5-10%, 10-20%, 20-30%, 30-40% and 40-50% Au+Au collisions are well reproduced through out the experimental $p_T$ range. This is in contrast to ideal dynamics, where, the spectra are reproduced only up to $p_T\approx$1.5 GeV. Minimally viscous QGP fluid, also explain the elliptic flow in mid-central (10-20%, 16-23%, 20-30%) collisions. The minimum bias elliptic flow is also explained. However, the model under-predict/over-predict the elliptic flow in very central/peripheral collisions.