Initial eccentricity and constituent quark number scaling of elliptic flow in ideal and viscous dynamics

Abstract

In the Israel-Stewart's theory of dissipative hydrodynamics, we study the scaling properties elliptic flow in Au+Au collisions. Initial energy density of the fluid was fixed to reproduce STAR data on $ϕ$ meson multiplicity in 0-5% Au+Au collisions, such that irrespective of fluid viscosity, entropy at the freeze-out is similar in ideal or in viscous evolution. Initial eccentricity or constituent quark number scaling is only approximate in ideal or minimally viscous ($η/s=1/4π$) fluid. Eccentricity scaling become nearly exact in more viscous fluid ($η/s \geq$0.12). However, in more viscous fluid, constituent quark number scaled elliptic flow for mesons and baryons split into separate scaling functions. Simulated flows also do not exhibit 'universal scaling' i.e. elliptic flow scaled by the constituent quark number and charged particles $v_2$ is not a single function of transverse kinetic energy scaled by the quark number. From a study of violation of universal scaling, we obtain an estimate of QGP viscosity, $η/s=0.12 \pm 0.03$.