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Comparison of results from a 2+1D relativistic viscous hydrodynamic model to elliptic and hexadecapole flow of charged hadrons measured in Au-Au collisions at $\sqrt{s_{\rm {NN}}}$ = 200 GeV

Simulated results from a 2+1D relativistic viscous hydrodynamic model have been compared to the experimental data on the centrality dependence of invariant yield, elliptic flow ($v_{2}$), and hexadecapole flow ($v_{4}$) as a function of transverse momentum ($p_{T}$) of charged hadrons in Au-Au collisions at $\sqrt{s_{\rm {NN}}}$ = 200 GeV. Results from two types of initial transverse energy density profile, one based on the Glauber model and other based on Color-Glass-Condensate (CGC) are presented. We observe no difference in the simulated results on the invariant yield of charged hadrons for the calculations with different initial conditions. The comparison to the experimental data on invariant yield of charged hadrons supports a shear viscosity to entropy density ratio ($η/s$) between 0 to 0.12 for the 0-10% to 40-50% collision centralities. The simulated $v_{2}(p_{T})$ is found to be higher for a fluid with CGC based initial condition compared to Glauber based initial condition for a given collision centrality. Consequently the Glauber based calculations when compared to the experimental data requires a lower value of $η/s$ relative to CGC based calculations. In addition, a centrality dependence of the estimated $η/s$ is observed from the $v_{2}(p_{T})$ study. The $v_{4}(p_{T})$ for the collision centralities 0-10% to 40-50% supports a $η/s$ value between 0 - 0.08 for a CGC based initial condition. While simulated results using the Glauber based initial condition for the ideal fluid evolution under estimates the $v_{4}(p_{T})$ for collision centralities 0-10% to 30-40%.