Hubble Expansion and Freeze-Out at RHIC-BES Energies from UrQMD

TL;DR

This study uses the UrQMD transport model to analyze the freeze-out process in heavy ion collisions at RHIC-BES energies, confirming that decoupling is governed by the competition between expansion and scattering rates.

Contribution

It provides the first microscopic simulation confirmation that the decoupling hypersurface is determined by the balance of expansion and scattering rates.

Findings

Hubble expansion rate at kinetic decoupling aligns with previous models.

Decoupling hypersurface is shaped by the competition of expansion and scattering.

Expansion shape is between spherical and longitudinal.

Abstract

The freeze-out process in heavy ion collisions is driven by the competition between the scattering rate and the expansion rate of the matter. We analyse the expansion rate $\Theta$ (often called Hubble flow) in relativistic heavy ion collisions in the FAIR and RHIC-BES energy regimes and compare it to the scattering rate $\Gamma$ using the UrQMD transport model. We observe that the time evolution of the system is clearly separated into a compression phase and an expansion phase with time dependent $\Theta_\parallel$ and $\Theta_\perp$. The calculated values of the Hubble expansion at kinetic decoupling are in line with previous simple estimates by statistical hadronization models with a Siemens-Rasmussen type emission source. However, the actual shape of the expanding matter is, as expected, found to be between a spherically symmetric and a purely longitudinal expansion. We confirm for the first time in a microscopic simulation that the decoupling hypersurface is indeed determined by the competition of the expansion rate $\Theta$ and the scattering rate $\Gamma$ as suggested previously. This suggests that, in the range of collision energies explored in this study, simple iso-thermal/iso-energy density criteria that are often used in hybrid models to couple hydrodynamic and transport simulations may not capture the true decoupling hyper-surface.