Self-consistent Cooper-Frye freeze-out of a viscous fluid to particles

Abstract

Comparing hydrodynamic simulations to heavy-ion data inevitably requires the conversion of the fluid to particles. This conversion, typically done in the Cooper-Frye formalism, is ambiguous for viscous fluids. We compute self-consistent phase space corrections by solving the linearized Boltzmann equation and contrast the solutions to those obtained using the ad-hoc "democratic Grad" ansatz typically employed in the literature where coefficients are independent of particle dynamics. Solutions are calculated analytically for a massless gas and numerically for both a pion-nucleon gas and for the general case of a hadron resonance gas. We find that the momentum dependence of the corrections in all systems investigated is best fit by a power close to 3/2 rather than the typically used quadratic ansatz. The effects on harmonic flow coefficients v2 and v4 are substantial, and should be taken into account when extracting medium properties from experimental data.

Flow harmonics from self-consistent particlization of a viscous fluid

“…The corrections were then used to compute differential harmonic flow coefficients v 2 (p T ), v 4 (p T ), and v 6 (p T ) in Au + Au collisions at top RHIC energy √ s N N = 200 GeV and P b + P b collisions at the LHC energy √ s N N = 2.76 TeV. Expanding upon previous works [1,2], we include early chemical freezeout in the hadron gas and use Cooper-Frye hypersurfaces from real viscous hydrodynamic evolution. We find that self-consistent particlization leads to larger proton elliptic flow at moderately high p T ∼ 2 − 3 GeV compared to that of pions, qualitatively corroborating our prior estimate [1] of the effect on elliptic flow.…”

“…One should also note that using hypersurfaces from realistic viscous hydrodynamic simulations has a dramatic effect on v 4 (p T ), as this observable was roughly zero for protons and negative for pions when estimated from ideal hydrodynamic evolution in Ref. [2]. Finally, Figs.…”

“…In Refs. [1,2], the ambiguity was resolved self-consistently by calculating the distributions from the linearized Boltzmann equation, and shear viscous corrections proportional to p 3/2 power of momentum were found to be favored over the quadratic Grad dependence. Here we expand upon those works by implementing an equation of state for a hadron gas chemically frozen below 175 MeV, as well as hypersurfaces obtained from real viscous hydrodynamic evolution.…”

“…Here, shear viscous phase-space corrections calculated using linearized transport theory are applied in CooperFrye freezeout to quantify the effects on anisotropic flow coefficients vn(pT ) at both RHIC and LHC energies. Expanding upon our previous flow harmonics studies [1,2], we calculate pion and proton v2(pT ), v4(pT ), and v6(pT ), but here we incorporate a hadron gas that is chemically frozen below a temperature of 175 MeV and use hypersurfaces from realistic viscous hydrodynamic simulations. For additive quark model cross sections and relative phase-space corrections with p 3/2 momentum dependence rather than the quadratic Grad form, we find at moderately high transverse momentum noticeably higher v4(pT ) and v6(pT ) for protons than for pions.…”