On freeze-out problem in relativistic hydrodynamics
Yu. B. Ivanov, V. N. Russkikh
备注：
6 pages, 2 figures, references are corrected and updated, to be published in the issue of Phys. Atom. Nucl. dedicated to S.T. Belyaev on the occasion of his birthday
A finite unbound system which is equilibrium in one reference frame is in general nonequilibrium in another frame. This is a consequence of the relative character of the time synchronization in the relativistic physics. This puzzle was a prime motivation of the Cooper--Frye approach to the freeze-out in relativistic hydrodynamics. Solution of the puzzle reveals that the Cooper--Frye recipe is far not a unique phenomenological method that meets requirements of energy-momentum conservation. Alternative freeze-out recipes are considered and discussed.
In hydrodynamical modeling of the ultrarelativistic heavy-ion collisions the freeze-out is typically performed at a constant temperature or density. In this work we apply a dynamical freeze-out criterion, which compares the hydrodynamical expansion rate with the pion scattering rate. Recently many calculations have been done using event-by-event hydrodynamics where the initial density profile fluctuates from event to event. In these event-by-event calculations the expansion rate fluctuates strongly as well, and thus it is interesting to check how the dynamical freeze-out changes hadron distrib…
We argue that a detailed analysis of the spin alignement of vector mesons can serve as a probe of two little-understood aspects of spin dynamics in the vortical fluid: The degree of relaxation between vorticity and parton spin polarization, and the degree of coherence of the hadron wavefunction at freeze-out. We illustrate these with a coalescence model.
In hydrodynamical modelling of ultrarelativistic heavy-ion collisions the freeze-out is typically assumed to take place on a surface of constant temperature or energy density. In this work we apply a dynamical freeze-out criterion, which compares the hydrodynamical expansion rate with the pion scattering rate, to an event-by-event ideal hydrodynamics at the full RHIC collision energy. We present hadron spectra and elliptic flow calculated using (2+1)-dimensional ideal hydrodynamics, and show the differences between constant temperature and dynamical freeze-out criteria. We find that when the f…
The kinetic freeze-out for the hydrodynamical description of relativistic heavy ion collisions is discussed using a background-fluctuation splitting of the hydrodynamical fields. For a single event, the particle spectrum, or its logarithm, can be written as the sum of background part that is symmetric with respect to azimuthal rotations and longitudinal boosts and a part containing the contribution of fluctuations or deviations from the background. Using a complete orthonormal basis to characterize the initial state allows one to write the double differential harmonic flow coefficients determi…
In hydrodynamical modeling of ultrarelativistic heavy-ion collisions, the freeze-out is typically assumed to take place at a surface of constant temperature or energy density. A more physical approach is to assume that freeze-out takes place at a surface of constant Knudsen number. We evaluate the Knudsen number as a ratio of the expansion rate of the system to the pion scattering rate, and apply the constant Knudsen number freeze-out criterion to ideal hydrodynamical description of heavy-ion collisions at RHIC ($\sqrt{s_\mathrm{NN}}=200$ GeV) and the LHC ($\sqrt{s_\mathrm{NN}}=2760$ GeV) ener…
We analyze hadrochemical freeze-out in central Pb+Pb collisions at CERN SPS energies, employing the hybrid version of the Ultrarelativistic Quantum Molecular Dynamics model, which describes the transition from a hydrodynamic stage to hadrons by the Cooper-Frye mechanism, and matches to a final hadron-resonance cascade. We fit the results both before and after the cascade stage using the Statistical Model, to assess the effect of the cascade phase. We observe a strong effect on antibaryon yields except anti-Omega, resulting in a shift in T and mu_B of the freeze-out curve. We discuss indication…
Global evolution of the matter in relativistic collisions of heavy nuclei and the resulting global freeze-out parameters are analyzed in a wide range of incident energies 2.7 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The analysis is performed within the three-fluid model employing three different equations of state (EoS): a purely hadronic EoS, an EoS with the first-order phase transition and that with a smooth crossover transition. Global freeze-out parameters deduced from experimental data within the statistical model are well reproduced within the crossover scenario. The 1st-order-transition scena…
We study the rapidity spectra in ultra-relativistic heavy ion collisions in the framework of the Landau hydrodynamical model. We find that thermal smearing effects improve the agreement with experimental results on pion rapidity spectra. We describe a simple model of the hadronization and discuss its consequences regarding the pion multiplicity and the increasing entropy condition.
This proceeding briefly summarizes our recent work on calculating the correlated fluctuations of net protons on the hydrodynamic freeze-out surface near the QCD critical point. For both Poisson and Binomial baselines, our calculations could roughly reproduce the energy dependent cumulant $C_4$ and $κσ^2$ of net protons, but always over-predict $C_2$ and $C_3$ due to the positive contributions from the static critical fluctuations.
We investigate an effective relativistic equation of state at finite values of temperature and baryon chemical potential with the inclusion of the full octet of baryons, the Delta-isobars and the lightest pseudoscalar and vector meson degrees of freedom. These last particles have been introduced within a phenomenological approach by taking into account of an effective chemical potential and mass depending on the self-consistent interaction between baryons. In this framework, we study of the hadron yield ratios measured in central heavy ion collisions over a broad energy range and present the b…
We investigate the form of the viscous correction to the equilibrium distribution function in the context of a Cooper-Frye freeze out prescription for viscous hydrodynamic simulations of relativistic heavy ion collisions. The standard quadratic ansatz used by all groups for the case of shear viscosity is found to be disfavored by experimental data for v4/(v2)^2 at the Relativistic Heavy Ion Collider, and is unlikely to be correct for the hadron resonance gas present at freeze out. Instead, data for v2(pt) along with v4/(v2)^2 favor a momentum dependence between linear and quadratic.
The LHC data on event-by-event harmonic flow coefficients measured in PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair are analyzed and interpreted within the HYDJET++ model. To compare the model results with the experimental data the unfolding procedure is employed. The essentially dynamical origin of the flow fluctuations in hydro-inspired freeze-out approach has been established. It is shown that the simple modification of the model via introducing the distribution over spatial anisotropy parameters permits HYDJET++ to reproduce both elliptic and triangular flow fluctuatio…
A brief review is presented of the status of the thermal model and chemical freeze-out in relativistic heavy-ion collisions. Some interewsting aspects at lower energies are emphasized.
We introduce a novel approach based on elastic and inelastic scattering rates to extract the hyper-surface of the chemical freeze-out from a hadronic transport model in the energy range from E$_\mathrm{lab}=1.23$ AGeV to $\sqrt{s_\mathrm{NN}}=62.4$ GeV. For this study, the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model combined with a coarse-graining method is employed. The chemical freeze-out distribution is reconstructed from the pions through several decay and re-formation chains involving resonances and taking into account inelastic, pseudo-elastic and string excitation reacti…
We assume that the early evolution of matter produced in relativistic heavy-ion collisions is described by the transverse hydrodynamics. In this approach only transverse degrees of freedom are thermalized, while the longitudinal motion is described by free streaming. When the energy density of the system drops to a certain value, the system becomes isotropic (locally, in the momentum space) and freezes out. The sudden isotropization transition is described with the help of the Landau matching conditions, and the freeze-out is modeled with THERMINATOR. Within this scenario one is able to reprod…
The space-time structure of the multipion system created in central relativistic heavy-ion collisions is investigated. Using the microscopic transport model UrQMD we determine the freeze-out hypersurface from equation on pion density n(t,r)=n_c. It turns out that for proper value of the critical energy density ε_c equation ε(t,r)=ε_c gives the same freeze-out hypersurface. It is shown that for big enough collision energies E_kin > 40A GeV/c (sqrt(s) > 8A GeV/c) the multipion system at a time moment τ ceases to be one connected unit but splits up into two separate spatial parts (drops), which m…
We present calculations of the chemical freeze-out temperature (T_ch) based on particle yields from STAR and ALICE measured at collision energies ranging from sqrt{s_{NN}} = 11.5 GeV to 5.02 TeV. Employing the Grand Canonical Ensemble approach using the Thermal-FIST Hadron Resonance Gas model package, we show evidence for a flavour-dependent chemical freeze-out in the crossover region of the QCD phase diagram. At a vanishing baryochemical potential, we calculate light and strange flavour freeze-out temperatures T_L = 150.2 +- 2.6 MeV and T_S = 165.1 +- 2.7 MeV, respectively.
Comment on "Evaluation of kinetic freeze-out properties in different relativistic heavy-ion collision systems at \sqrtsNN = 200 GeV'' (Eur. Phys. J. Plus (2025) 140:179) https://doi.org/10.1140/epjp/s13360-025-06119-0
An expanding fireball model with two freeze-outs, which assumes that the chemical freeze-out occurs earlier at higher temperature and the thermal freeze-out occurs later at lower temperature, is developed and successfully applied to fit simultaneously the hadron ratios, transverse momentum spectra of measured hadrons and rapidity distribution of charged hadrons measured in Au+Au collision at 200 A$\cdot$GeV by STAR, PHENIX and PHOBOS collaborations. The quality of all the fittings is very good and the resulting parameters are in agreement with published values.
A spheroidal anisotropic local momentum distribution is implemented in the statistical model of hadron production. We show that this form leads to exactly the same ratios of hadronic abundances as the equilibrium distributions, if the temperature is identified with a characteristic transverse-momentum scale. Moreover, to a very good approximation the transverse-momentum spectra of hadrons are the same for isotropic and anisotropic systems, provided the size of the system at freeze-out is appropriately adjusted. We further show that this invariance may be used to improve the agreement between t…
One surprising result in relativistic heavy-ion collisions is that the abundance of various particles measured in experiments is consistent with the picture that they reach chemical equilibrium at a temperature much higher than the temperature they freeze out kinetically. Using a multiphase transport model to study particle production in these collisions, we find that the above result is due to the constancy of the entropy per particle during the evolution of the hadronic matter from the chemical to the kinetic freeze-out. We further use a hadron resonance gas model to illustrate the result fr…
The single-freeze-out model with parametrized hypersurface and flow geometry is employed to analyze the transverse-momentum spectra of hadrons produced in the Pb+Pb collisions at the collision energy of {$\sqrt{s_{\rm NN}}=2.76$ TeV} at the CERN Large Hadron Collider (LHC). With the notable exception for protons and antiprotons, we find a very good agreement between the model results and the data for the measured hadron species. The additional analysis of the HBT radii of pions helps us to select, from several different types of freeze-out studied in this work, the most realistic form of the f…
