Self-consistent conversion of a viscous fluid to particles

Abstract

Comparison of hydrodynamic and "hybrid" hydrodynamics+transport calculations to heavy-ion data inevitably requires the conversion of the fluid to particles. For dissipative fluids the conversion is ambiguous without additional theory input complementing hydrodynamics. We obtain self-consistent shear viscous phase space corrections from linearized Boltzmann transport theory for a gas of hadrons. These corrections depend on the particle species, and incorporating them in Cooper-Frye freezeout affects identified particle observables. For example, with additive quark model cross sections, proton elliptic flow is larger than pion elliptic flow at moderately high pT in Au + Au collisions at RHIC. This is in contrast to Cooper-Frye freezeout with the commonly used "democratic Grad" ansatz that assumes no species dependence. Various analytic and numerical results are also presented for massless and massive two-component mixtures to better elucidate how species dependence arises. For convenient inclusion in pure hydrodynamic and hybrid calculations, Appendix G contains self-consistent viscous corrections for each species both in tabulated and parameterized form.

Flow harmonics from self-consistent particlization of a viscous fluid

“…This requires knowledge of the local distribution functions of each hadron species in momentum space. If the fluid is in local thermal equilibrium, i.e., an ideal fluid, then the distributions are uniquely determined by the hydrodynamic variables [1,8]. For viscous fluids, however, an infinite number of particle distributions will match the hydrodynamic fields (see discussion in Sec.…”

“…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.…”

“…[1]. In Section III A and B particle distributions are calculated for a chemically frozen effective hadron gas.…”

“…[1] by calculating the distribution functions using the linearized Boltzmann equation. In this way, the collision rates between particles that keep the hadron gas near equilibrium are taken into account, and no ad-hoc assumptions about the momentum dependence of the corrections are necessary [35].…”

“…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.…”