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

TL;DR

This paper develops a self-consistent method for converting viscous hydrodynamic fluids to particles using the Cooper-Frye formalism, revealing significant effects on flow coefficients and proposing a power-law correction for improved accuracy.

Contribution

It introduces a linearized Boltzmann equation approach to compute phase space corrections, improving upon the ad-hoc quadratic ansatz in viscous fluid-to-particle conversion.

Findings

Power-law corrections fit momentum dependence better than quadratic.

Significant impact on harmonic flow coefficients $v_2$ and $v_4$.

Analytic solutions for massless gases and numerical results for hadron gases.

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 $v_2$ and $v_4$ are substantial, and should be taken into account when extracting medium properties from experimental data.