The unreasonable effectiveness of hydrodynamics in heavy ion collisions

Event-by-event hydrodynamic simulations of AA and pA collisions involve initial energy densities with large spatial gradients. This is associated with the presence of large Knudsen numbers ($K_n\approx 1$) at early times, which may lead one to question the validity of the hydrodynamic approach in these rapidly evolving, largely inhomogeneous systems. A new procedure to smooth out the initial energy densities is employed to show that the initial spatial eccentricities, $\varepsilon_n$, are remarkably robust with respect to variations in the underlying scale of initial energy density spatial gradients, $λ$. For $\sqrt{s_{NN}}=2.76$ TeV LHC initial conditions generated by the MCKLN code, $\varepsilon_n$ (across centralities) remains nearly constant if the fluctuation scale varies by an order of magnitude, i.e., when $λ$ varies from 0.1 to 1 fm. Given that the local Knudsen number $K_n\approx \frac{1}λ$, the robustness of the initial eccentricities with respect to changes in the fluctuation scale suggests that the vn's cannot be used to distinguish between events with large $K_n$ from events where $K_n$ is in the hydrodynamic regime. We use the 2+1 Lagrangian hydrodynamic code v-USPhydro to show that this is indeed the case: anisotropic flow coefficients computed within event-by-event viscous hydrodynamics are only sensitive to long wavelength scales of order $\frac{1}{Λ_{QCD}}\approx 1$ fm and are incredibly robust with respect to variations in the initial local Knudsen number. This robustness can be used to justify the somewhat unreasonable effectiveness of the nearly perfect fluid paradigm in heavy ion collisions.

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