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

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.

Comments: 11 pages, 11 figures, Version to appear in Physical Review C, typos corrected, a brief discussion about the centrality dependence and Gamow criterion added