Elliptic flow scaling in ideal and viscous hydrodynamics.

Abstract

STAR and PHENIX measurements of elliptic flow, in Au+Au collisions at RHIC,revealed an interesting scaling property: elliptic flow, of different particle species at differentcollisions centrality, when scaled by the initial eccentricity and constituent quark numbers ($n_q$)is a singlefunction of $KE_T/n_q$, $KE_T=m_T-m$. Initial eccentricity scaling suggests that elliptic flow is driven by the initial spatial asymmetry. Constituentquark number scaling indicate existence of initial collective partonic state. Elliptic flow is best explained in ahydrodynamic model. In non-zero impact parameter collisions, the reaction zone is spatially asymmetric.Differential pressure gradient convert the spatial asymmetry to momentum asymmetry, resulting in elliptic flow. Inthe Israel-Stewart’s theory of 2nd order dissipative hydrodynamics, we study the universal scaling of ellipticflow in ideal and viscous fluid evolution. Initial eccentricity scaling is only approximate in ideal hydrodynamicsand gets better with viscosity. Ideal or viscous hydrodynamic do not indicate constituent quarks number scaling anduniversal scaling is only approximate,violated by $sim\% or more in ideal or viscous fluid evolution. We also showthat RHIC data on elliptic flowdemand very small QGP viscosity, $eta/s ~0.08$, indicating nearly ideal fluid isproduced in Au+Au collisions