Relativistic Hydrodynamics for Heavy--Ion Collisions: Freeze--Out and Particle Spectra

We investigate freeze--out in hydrodynamic models for relativistic heavy--ion collisions. In particular, instantaneous freeze--out across a hypersurface of constant temperature (``isothermal'' freeze--out) is compared with that across a hypersurface at constant time in the center-of-momentum frame (``isochronous'' freeze--out). For one--dimensional (longitudinal) expansion the rapidity distributions are shown to differ significantly in the two scenarios, while the transverse momentum spectra are remarkably similar. We also investigate the rapidity distribution in greater detail and show that the Gaussian-like shape of this distribution commonly associated with the Landau expansion model in general emerges only if one neglects contributions from time-like parts of the isothermal freeze--out hypersurface.Comment: 12 figure

Experimental investigation of corrosion of IG-110 graphite by steam

In the framework of a cooperation between the Japan Atomic Energy Research Institute (JAERI) and the Research Centre of Julien (KFA) experiments on the corrosion of the Japanese graphite IG-110 by water vapour were carried out. The temperature of the graphite samples and the water vapour partial pressure were kept constant at 1000°C/474 mbar. The total pressure in the test loop using helium as carrier gas was varied between 3 and 55 bar. Burn-off and pressure dependent reaction rates and density profiles in corroded samples were measured. As expected, the burn-off dependence of the reaction rate decreased with increasing pressure, while only a comparably low pressure dependence of the reaction rate was found. The latter indicates that the influence of the Knudsen diffusion is giveneven for the highest pressure. This finding is in fair agreement with the results of density profile measurements carried out at a couple of corroded samples, which also revealed a relatively small pressure dependence of the "penetration depth". Correlations for the caculation of reaction rates and the penetration depth are given

Thermal photons as a measure for the rapidity dependence of the temperature

The rapidity distribution of thermal photons produced in Pb+Pb collisions at CERN-SPS energies is calculated within scaling and three-fluid hydrodynamics. It is shown that these scenarios lead to very different rapidity spectra. A measurement of the rapidity dependence of photon radiation can give cleaner insight into the reaction dynamics than pion spectra, especially into the rapidity dependence of the temperature.Comment: 3 Figure

Relativistic Hydrodynamics for Heavy--Ion Collisions -- I. General Aspects and Expansion into Vacuum

We present algorithms to solve relativistic hydrodynamics in 3+1--dimensional situations without apparent symmetry to simplify the solution. In simulations of heavy--ion collisions, these numerical schemes have to deal with the physical vacuum and with equations of state with a first order phase transition between hadron matter and a quark--gluon plasma. We investigate their performance for the one--dimensional expansion of baryon-free nuclear matter into the vacuum, which is an analytically solvable test problem that incorporates both the aspect of the vacuum as well as that of a phase transition in the equation of state. The dependence of the lifetime of the mixed phase on the initial energy density is discussed.Comment: 31 pages, 16 uuencoded figure

The Maximum Lifetime of the Quark-Gluon Plasma

The width $\Delta T$ of the deconfinement transition region is shown to influence strongly the flow structure in the (Landau-) hydrodynamical expansion of a quark-gluon plasma. For a sharp first order transition ($\Delta T=0$) the mixed phase is rather long-lived, with a lifetime that has a maximum when the initial energy density is at the phase boundary between mixed and pure quark-gluon matter. For increasing $\Delta T$, however, the lifetime decreases rapidly. Hadronic matter, however, remains long-lived as a consequence of the rapid change in the degrees of freedom in the transition region and the corresponding ``softening'' of the equation of state.Comment: 22 pages, latex, 12 uuencoded figure

Second Order Dissipative Fluid Dynamics for Ultra-Relativistic Nuclear Collisions

The M\"uller-Israel-Stewart second order theory of relativistic imperfect fluids based on Grad's moment method is used to study the expansion of hot matter produced in ultra-relativistic heavy ion collisions. The temperature evolution is investigated in the framework of the Bjorken boost-invariant scaling limit. The results of these second-order theories are compared to those of first-order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler.Comment: 5 pages, 4 figures, size of y-axis tick marks for Figs. 3 and 4 fixe

Hydrodynamical assessment of 200 AGeV collisions

We are analyzing the hydrodynamics of 200 A GeV S+S collisions using a new approach which tries to quantify the uncertainties arising from the specific implementation of the hydrodynamical model. Based on a previous phenomenological analysis we use the global hydrodynamics model to show that the amount of initial flow, or initial energy density, cannot be determined from the hadronic momentum spectra. We additionally find that almost always a sizeable transverse flow deve- lops, which causes the system to freeze out, thereby limiting the flow velocity in itself. This freeze-out dominance in turn makes a distinction between a plasma and a hadron resonance gas equation of state very difficult, whereas a pure pion gas can easily be ruled out from present data. To complete the picture we also analyze particle multiplicity data, which suggest that chemical equilibrium is not reached with respect to the strange particles. However, the over- population of pions seems to be at most moderate, with a pion chemical potential far away from the Bose divergence.Comment: 19 pages, 11 figs in separate uuencoded file, for LateX, epsf.tex, dvips, TPR-94-5 and BNL-(no number yet

1+1 Dimensional Hydrodynamics for High-energy Heavy-ion Collisions

A 1+1 dimensional hydrodynamical model in the light-cone coordinates is used to describe central heavy-ion collisions at ultrarelativistic bombarding energies. Deviations from Bjorken's scaling are taken into account by choosing finite-size profiles for the initial energy density. The sensitivity of fluid dynamical evolution to the equation of state and the parameters of initial state is investigated. Experimental constraints on the total energy of produced particles are used to reduce the number of model parameters. Spectra of secondary particles are calculated assuming that the transition from the hydrodynamical stage to the collisionless expansion of matter occurs at a certain freeze-out temperature. An important role of resonances in the formation of observed hadronic spectra is demonstrated. The calculated rapidity distributions of pions, kaons and antiprotons in central Au+Au collisions at the c.m. energy 200 GeV per NN pair are compared with experimental data of the BRAHMS Collaboration. Parameters of the initial state are reconstructed for different choices of the equation of state. The best fit of these data is obtained for a soft equation of state and Gaussian-like initial profiles of the energy density, intermediate between the Landau and Bjorken limits.Comment: 43 pages, 27 figure

Hydrodynamical analysis of symmetric nucleus-nucleus collisions at CERN/SPS energies

We present a coherent theoretical study of ultrarelativistic heavy-ion data obtained at the CERN/SPS by the NA35/NA49 Collaborations using 3+1-dimensional relativistic hydrodynamics. We find excellent agreement with the rapidity spectra of negative hadrons and protons and with the correlation measurements in two experiments: $S+S$ at 200 $AGeV$ and $Pb+Pb$ at 160 $AGeV$ (preliminary results). Within our model this implies that for $Pb+Pb$ ($S+S$) a quark-gluon-plasma of initial volume 174 $fm^3$ (24 $fm^3$) with a lifetime 3.4 $fm/c$ (1.5 $fm/c$) was formed. It is found that the Bose-Einstein correlation measurements do not determine the maximal effective radii of the hadron sources because of the large contributions from resonance decay at small momenta. Also within this study we present an NA49 acceptance corrected two-pion Bose-Einstein correlation function in the invariant variable, $Q_{inv}$.Comment: 21 pages, 11 Postscript figures (1 File, 775654 Bytes, has to be requested for submission via e.mail from [email protected]

Nonequilibrium fluid-dynamics in the early stage of ultrarelativistic heavy-ion collisions

To describe ultrarelativistic heavy-ion collisions we construct a three-fluid hydrodynamical model. In contrast to one-fluid hydrodynamics, it accounts for the finite stopping power of nuclear matter, i.e. for nonequilibrium effects in the early stage of the reaction. Within this model, we study baryon dynamics in the BNL-AGS energy range. For the system Au+Au we find that kinetic equilibrium between projectile and target nucleons is established only after a time $t_{CM}^{eq}\approx 5~fm/c\simeq 2R_{Au}/\gamma_{CM}$. Observables which are sensitive to the early stage of the collision (like e.g. nucleon flow) therefore differ considerably from those calculated in the one-fluid model.Comment: 36 pages, Late