The unreasonable effectiveness of hydrodynamics in heavy ion collisions

TL;DR

This paper demonstrates that initial spatial eccentricities and flow coefficients in heavy ion collisions are remarkably insensitive to small-scale fluctuations, supporting the robustness of hydrodynamic models even with large local Knudsen numbers.

Contribution

The study shows that initial eccentricities and flow observables are robust against variations in the fluctuation scale, justifying the effectiveness of hydrodynamics despite large local Knudsen numbers.

Findings

Initial eccentricities are stable across a wide range of fluctuation scales.

Flow coefficients are insensitive to small-scale initial energy density variations.

Hydrodynamic models remain valid even when local Knudsen numbers are large.

Abstract

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, $\lambda$. 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 $\lambda$ varies from 0.1 to 1 fm. Given that the local Knudsen number $K_n\approx \frac{1}{\lambda}$, 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 $\frac{1}{\Lambda_{QCD}}\approx 1$ 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.