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

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