Scaling of the higher-order flow harmonics: implications for initial-eccentricity models and the "viscous horizon"

The scaling properties of the flow harmonics for charged hadrons $v_{n}$ and their ratios $[ v_n/(v_2)^{n/2}]_{n\geq 3}$, are studied for a broad range of transverse momenta ($p_T$) and centrality selections in Au+Au and Pb+Pb collisions at $\sqrt{s_{NN}}=0.2 \text{and} 2.76$ TeV respectively. At relatively low $p_T$, these scaling properties are found to be compatible with the expected growth of viscous damping for sound propagation in the plasma produced in these collisions. They also provide important constraints for distinguishing between the two leading models of collision eccentricities, as well as a route to constrain the relaxation time and make estimates for the ratio of viscosity to entropy density $\eta/s$, and the "viscous horizon" or length-scale which characterizes the highest harmonic which survives viscous damping.