Test of Ideal Hydrodynamical Limit at RHIC

Elliptic flow ($v_2$) is one of the most prominent observables to study collective properties of the hot and dense medium created in relativistic heavy ion collisions. It has been found that the ratio of $v_2$ to the initial spatial anisotropy $\varepsilon$ scales as transverse number density $1/S dN/dy$ for different collision energies and systems from AGS ($\sqrt{s_{_{NN}}} \sim$ 5 GeV) to RHIC ($\sqrt{s_{_{NN}}}$ = 200 GeV). Eventually, the linear dependence of $v_2/\varepsilon$ vs. $1/S dN/dy$ is expected to be saturated when the system reaches local thermal equilibrium. However, till now there is no sign of saturation of $v_2/\varepsilon$ at top RHIC energy. It is natural to ask the question to what extent the system has reached the ideal hydrodynamical limit. It is also important to understand how the $v_2/\varepsilon$ behaves at higher transverse number density. Compared to Au nucleus, uranium is a heavier and naturally deformed. The planned U~+~U collisions at RHIC (2012) could provide higher densities than that achieved in Au~+~Au collisions. In this talk, we present the results of a test on ideal hydrodynamical limit. The $v_2$ data from Au~+~Au collisions at $\sqrt{s_{_{NN}}}$~=~200~GeV are used. It has been found that even at most central Au~+~Au collisions the ideal hydrodynamical limit has not been reached. In addition, we present the prediction of $v_2$ in U~+~U collisions at $\sqrt{s_{_{NN}}}$~=~200~GeV by extrapolating the measured $v_2$ in Au~+~Au collisions at RHIC.