[Paper Review] Thermalization of dense hadronic matter in Au + Au collisions at the energies available at FAIR

Somnath De, Sudipan De+1 more|arXiv (Cornell University)|Oct 6, 2015

High-Energy Particle Collisions Research3 citations

TL;DR

This study uses the UrQMD transport model to investigate thermalization timescales in dense hadronic matter formed in central Au+Au collisions at FAIR energies (10–40 A GeV). It finds that local thermodynamic equilibrium is achieved within ~1–2 fm/c, with pressure isotropization and energy spectrum thermalization occurring nearly simultaneously, and entropy evolution closely resembling ideal hydrodynamics at 30 A GeV, indicating fluid-like behavior in dense baryonic matter.

ABSTRACT

The conditions of local thermodynamic equilibrium of baryons (non-strange, strange) and mesons (strange) are presented for central Au + Au collisions at FAIR energies using the microscopic transport model UrQMD. The net particle density, longitudinal-to-transverse pressure anisotropy and inverse slope parameters of the energy spectra of non-strange and strange hadrons are calculated inside a cell in the central region within rapidity window $|y| < 1.0$ at different time steps after the collision. We observed that the strangeness content is dominated by baryons at all energies, however contribution from mesons become significant at higher energies. The time scale obtained from local pressure (momentum) isotropization and thermalization of energy spectra are nearly equal and found to decrease with increase in laboratory energy. The equilibrium thermodynamic properties of the system are obtained with statistical thermal model. The time evolution of the entropy densities at FAIR energies are found very similar with the ideal hydrodynamic behaviour at top RHIC energy.

Motivation & Objective

• To determine the time scale for local thermal equilibration in dense baryonic matter produced in central Au+Au collisions at FAIR energies.
• To assess whether the dense hadronic matter formed at high baryon density achieves local thermodynamic equilibrium, as required by hydrodynamic models.
• To compare the thermalization dynamics of non-strange and strange baryons and mesons in the central rapidity region.
• To evaluate the entropy density evolution and compare it with ideal hydrodynamic behavior to infer fluidity of the system.
• To extract thermodynamic parameters (T, μB, μS) using a statistical thermal model post-equilibrium.

Proposed method

• Employed the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model in default cascade mode to simulate central Au+Au collisions at 10A, 20A, 30A, and 40A GeV.
• Analyzed time evolution of net baryon and meson densities, longitudinal-to-transverse pressure anisotropy, and inverse slope parameters of energy spectra within a 8 fm³ cell at |y| < 1.0.
• Used the pressure anisotropy ratio (P_L/P_T) to track momentum isotropization as a proxy for thermalization onset.
• Tracked the inverse slope parameter of the energy spectra to assess thermalization of particle momentum distributions.
• Applied a statistical thermal model to extract temperature (T), baryon chemical potential (μB), and strangeness chemical potential (μS) from particle spectra after equilibration.
• Compared the time evolution of entropy density with a parameterized ideal hydrodynamic model (τ⁻².⁶ scaling) at √sNN = 200 GeV to assess fluid-like behavior.

Experimental results

Research questions

• RQ1 What is the time scale for local thermal equilibration of dense hadronic matter in central Au+Au collisions at FAIR energies?
• RQ2 How do the thermalization times for non-strange and strange baryons and mesons compare, and is there a hierarchy in equilibration speed?
• RQ3 To what extent does the entropy density evolution of the system resemble ideal hydrodynamic behavior, particularly at high baryon density?
• RQ4 How do the extracted thermodynamic parameters (T, μB, μS) from the statistical thermal model compare with empirical freeze-out relations?
• RQ5 Does the shear viscosity to entropy density ratio (η/s) influence the observed fluid-like behavior, and how does it vary with beam energy?

Key findings

• Local thermodynamic equilibrium is achieved within ~1–2 fm/c in the central region, with pressure anisotropy (P_L/P_T) approaching unity.
• The time scale for pressure isotropization and thermalization of energy spectra (via inverse slope parameters) is nearly identical, with a small delay (~0.5 fm/c) in strange baryons compared to non-strange baryons.
• The net baryon density peaks at 30–40 A GeV, and strangeness is dominated by baryons at all energies, though mesons (kaons) contribute significantly at higher energies.
• Entropy density evolution at 30 A GeV closely follows the τ⁻².⁶ scaling of ideal hydrodynamics at √sNN = 200 GeV, indicating fluid-like behavior.
• At 10 A GeV, entropy density decreases even faster than the ideal hydrodynamic limit, suggesting a lower η/s ratio and potentially more ideal fluid behavior.
• Thermodynamic parameters extracted via the statistical thermal model (T, μB, μS) are consistent with empirical freeze-out trends in the T–μB plane.