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

Abstract

In the Israel-Stewart theory of dissipative hydrodynamics, the scaling properties of elliptic flow in $\mathrm{Au}+\mathrm{Au}$ collisions are studied. The initial energy density of the fluid was fixed to reproduce STAR data on $\ensuremath{\phi}$-meson multiplicity in $0--5%$ $\mathrm{Au}+\mathrm{Au}$ collisions such that, irrespective of fluid viscosity, entropy at the freeze-out is similar in ideal or in viscous evolution. The initial eccentricity or constituent quark number scaling is only approximate in ideal or minimally viscous ($\ensuremath{\eta}/s=1/4\ensuremath{\pi}$) fluid. Eccentricity scaling becomes nearly exact in more viscous fluid ($\ensuremath{\eta}/s\ensuremath{\geqslant}0.12$). However, in more viscous fluid, constituent quark number scaled elliptic flow for mesons and baryons splits into separate scaling functions. Simulated flows also do not exhibit ``universal scaling''; that is, 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 the violation of universal scaling, we obtain an estimate of quark-gluon plasma viscosity, $\ensuremath{\eta}/s=0.12\ifmmode\pm\else\textpm\fi{}0.03$. The error is statistical only. The systematic error in $\ensuremath{\eta}/s$ could be as large.