Dynamical freeze-out criterion in a hydrodynamical description of Au + Au collisions at $\sqrt{s_\mathrm{NN}}=200$ GeV and Pb + Pb collisions at $\sqrt{s_\mathrm{NN}}=2760$ GeV

TL;DR

This paper proposes a physically motivated freeze-out criterion based on a constant Knudsen number in hydrodynamical models of heavy-ion collisions, and shows it reproduces flow anisotropies at RHIC and LHC energies.

Contribution

It introduces a constant Knudsen number freeze-out criterion and demonstrates its effectiveness in describing flow anisotropies in heavy-ion collisions.

Findings

The Knudsen number-based freeze-out yields similar flow anisotropies as traditional temperature-based methods.

The approach is consistent across RHIC and LHC energies.

Flow observables are insensitive to the specific freeze-out surface when calibrated properly.

Abstract

In hydrodynamical modeling of ultrarelativistic heavy-ion collisions, the freeze-out is typically assumed to take place at a surface of constant temperature or energy density. A more physical approach is to assume that freeze-out takes place at a surface of constant Knudsen number. We evaluate the Knudsen number as a ratio of the expansion rate of the system to the pion scattering rate, and apply the constant Knudsen number freeze-out criterion to ideal hydrodynamical description of heavy-ion collisions at RHIC ($\sqrt{s_\mathrm{NN}}=200$ GeV) and the LHC ($\sqrt{s_\mathrm{NN}}=2760$ GeV) energies. We see that once the numerical values of freeze-out temperature and freeze-out Knudsen number are chosen to produce similar $p_T$ distributions, the elliptic and triangular anisotropies are similar too, in both event-by-event and averaged initial state calculations.