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

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 the ideal hydrodynamical description of heavy-ion collisions at the Relativistic Heavy Ion Collider at BNL ($\sqrt{s_{\mathrm{NN}}}=200$ GeV) and the Large Hadron Collider ($\sqrt{s_{\mathrm{NN}}}=2760$ 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.

Figure 1

The scattering rate of pions in both chemically equilibrated (CE, red solid line) and chemically frozen (PCE, blue dashed line) hadron resonance gas compared with the parametrization [30] of the rate evaluated in Ref. [24] (PPVW, black dotted line).

Figure 2

Constant-temperature (solid red curve) and constant-Knudsen-number (dashed blue curve) freeze-out surfaces in $\sqrt{s_{\mathit{NN}}}=200$ GeV 20%–30% central $\text{Au}+\text{Au}$ collisions. Surfaces are shown along the $x$ and $y$ axes.

Figure 3

Transverse momentum spectra of positive pions and protons in $\sqrt{s_{\mathit{NN}}}=200$ GeV 20%–30% central $\text{Au}+\text{Au}$ collisions assuming (a) chemically equilibrated or (b) chemically frozen EoS. The solid red line corresponds to the results obtained by using freeze-out at constant temperature and the dashed blue line by using freeze-out at constant Knudsen number. The data are from the PHENIX Collaboration [40].

Figure 4

Elliptic flow of positively charged pions and protons in $\sqrt{s_{\mathit{NN}}}=200$ GeV 20%–30% central $\text{Au}+\text{Au}$ collisions assuming (a) chemical or (b) partial chemical equilibrium in the EoS. The solid red line corresponds to the results obtained by using freeze-out at constant temperature and the dashed blue line by using freeze-out at constant Knudsen number. Error bars depict estimated statistical errors.

Figure 5

Transverse momentum spectra of positively charged pions and protons in $\sqrt{s_{\mathit{NN}}}=200$ GeV 20%–30% central $\text{Au}+\text{Au}$ collisions from event-by-event hydrodynamical simulations. The solid red line corresponds to the results obtained by using freeze-out at constant temperature and the dashed blue line by using freeze-out at constant Knudsen number. The data are from the PHENIX Collaboration [40].

Figure 6

(a) Elliptic and (b) triangular flow of positive pions and protons in $\sqrt{s_{\mathit{NN}}}=200$ GeV 20%–30% central $\text{Au}+\text{Au}$ collisions from event-by-event hydrodynamical simulations. The solid red line corresponds to the results obtained by using freeze-out at constant temperature and the dashed blue line by using freeze-out at constant Knudsen number. Error bars depict estimated statistical errors.

Figure 7

Transverse momentum spectra of positive pions and protons in $\sqrt{s_{\mathit{NN}}}=2760$ GeV 0-5% central $\text{Pb}+\text{Pb}$ collisions. The solid red line corresponds to the results obtained by using freeze-out at constant temperature and the dashed blue line by using freeze-out at constant Knudsen number. The data are from the ALICE Collaboration [50].

Figure 8

Elliptic flow of positive pions and protons in $\sqrt{s_{\mathit{NN}}}=2760$ GeV 20%–30% central $\text{Pb}+\text{Pb}$ collisions. The solid red line corresponds to the results obtained by using freeze-out at constant temperature and the dashed blue line by using freeze-out at constant Knudsen number. Error bars depict estimated statistical errors.