On the role of initial conditions and final state interactions in ultrarelativistic heavy ion collisions
Abstract
We investigate the rapidity dependence of the elliptical flow in heavy ion collisions at 200 GeV (cms), by employing a threedimensional hydrodynamic evolution, based on different initial conditions, and different freezeout scenarios. It will be shown that the form of pseudorapidity () dependence of the elliptical flow is almost identical to spacetimerapidity () dependence of the initial energy distribution, independent of the freezeout prescriptions.
A hydrodynamical treatment of ultrarelativistic heavy ion collisions requires thermalized matter as an “initial condition” at some early time being of the order of a . Such an initial condition is difficult to access theoretically. There are also considerable uncertainties concerning the evolution of the system, concerning transport coefficients and the equation of state. Finally towards the end of the evolutions, it seems more and more clear that the system will not stay in thermal equilibrium, but interact nevertheless via hadronic rescatterings, before freezing out.
It is therefore desirable to disentangle the different phases, try to understand which kind of observables are sensitive to what feature of the model description. In this paper we are going to investigate the role of the initial condition, and we will in particular focus on the rapidity dependence.
We will compare two options for initial conditions: a parameterization, with parameters chosen in order to optimize final results tetsu , referred to as “PAR” thoughout this paper, and an initial condition obtained from microscopic approach “EPOS”, based on the hypothesis that thermalization happens very quickly and is achieved at some . For both options, we will perform threedimensional hydrodynamic calculations, using the same equation of state, see tetsu . For either of the two scenarios, we will investigate different freezeout (FO) scenarios, to be discussed later. This modular structure allows us to separate initial and final state effects.
The PAR initial condition has been employed in many publications, for details see tetsu . In case of EPOS, the initial scatterings lead to the formation of strings, which break into segments, which are usually identified with hadrons. When it comes to heavy ion collisions, the procedure is modified: one considers the situation at an early proper time , long before the hadrons are formed: one distinguishes between string segments in dense areas (more than some critical density segments per unit volume), from those in low density areas. The high density areas are referred to as core, the low density areas as corona core . The corona is important for certain aspects, not the ones looked at in this paper. So here we simply consider the core part. In any case, it is important to note that initial conditions from EPOS are based on strings, not on partons. Based on the fourmomenta of the string segments which constitute the core, we compute the energy density and the flow velocity .
Having fixed the initial conditions, the system evolves according the equations of ideal hydrodynamics, for details see tetsu . To have a flexible and mudular structure, we make first FO tables (storing FO surface and flows) based on hydro calculations with PAR and EPOS initial conditions (for given ). We then generate particles EbE from the core, using FO tables, based on the CooperFrye prescription.
In the following figures, “EPOS” refers to the hydrodynamic evolution based on EPOS initial conditions, “PAR” refers the parameterized initial conditions of tetsu . Both calculation use fm/c, and the same equation of state.
In fig. 1, we show the spacetime evolutions of the energy density , for a central Au+Au collision (fm), for PAR (upper plots) and EPOS (lower plots) initial conditions. In each plot, the different curves refer to different times, from top to bottom: , , , etc, with fm (4 fm) in case of PAR (EPOS). The left plots show as a function of the spacetime rapidity , for a transverse distance , the middle plots show as a function of the transverse distance , for , the right ones for . Full (dotted) curves refer to (). The most striking difference between the PAR and EPOS curves is the spacetime rapidity dependence of the energy density, at initial time (upper curves on the left plots): Whereas the PAR curve is flat up to , the EPOS curve drops considerably.
In fig. 2, we show the spacetime evolutions of the energy density , for a peripheral Au+Au collision (fm), for PAR (upper plots) and EPOS (lower plots) initial conditions. Again, the most striking difference is the stronger spacetime rapidity dependence of the initial distribution. In transverse direction the curves are quite similar, however, the EPOS results have a bigger eccentricity, as can be seen from the bigger difference between the and the curves.
In the following, we will discuss results concerning the elliptical flow as a function of the pseudorapidity , for Au+Au collisions at 200 GeV. For both PAR and EPOS, we show always three curves:

a dashed one, representing a pure hydrodynamic evolution, with freeze out 100 MeV (FO_100);

a dotted curve, referring to a pure hydrodynamical evolutions, with freeze out at 169 MeV (FO_169);

a full curve, referring to a hydrodynamical evolution with freeze out at 169 MeV, and subsequent hadronic cascade, using UrQMD (FO_169+cascade).
We should keep in mind that the critical temperature is MeV . In fig.3, we show first the results for the PAR initial conditions, for minimum bias (MB) events, as well as for different centrality classes: 315%, 1525%, 2550%, and 040% of the most central collisions, compared to data phobos . The data show for all centralities a more or less pronounced triangular shape, with larger values for more peripheral collisions. The calculations show as well a very similar shape for the different centrality classes, for each of the three freeze out options. The FO_100 option gives the largest values, the shape is quite flat. The FO_169 option (early freeze out) gives significantly smaller values, and the distributions get narrower. Considering finally early freeze out with subsequent hadronic cascade (FO_169+cascade), leads again to some increase of , but it remains considerably lower than the pure hydro results FO_100.
The theoretical curves are identical to those shown in tetsu , in case of the FO_100 and FO_169 options. Concerning the hadronic rescattering, two different approaches have been employed: the UrQMD model in this work, and JAM in ref. tetsu . The results are quite close, though not identical. The JAM curves show a slight dip at midrapidity, which is absent when using UrQMD. It is difficult to pin down the origin of these differences, but it is encouraging that the differences are relatively small, and they may be considered as the “systematic error” of the theoretical treatment of this part.
In fig. 4, we show the corresponding results for the EPOS initial conditions. Here, the shape is completely different compared to the PAR initial conditions, it is more triangular. The different freeze out options differ in magnitude (in the same fashion as for the PAR results), but they all show a similar overall shape.
How can we understand this large difference in the shape of the dependence of , between PAR and EPOS initial conditions, which is even independent of the freeze out prescriptions? From figs. 1,2 we know, that the space time evolution of the energy density in PAR and EPOS are quite similar, apart of the fact that initially the spacetime rapidity dependence in PAR is flat, wheras in EPOS it drops strongly with . Using a linear scale, initial dependence is already almost triangular. So there is a strong correlation between the width of the initial energy density and the pseudorapidity distribution of , which is compatible with earlier findings tetsu2 .
The triangularlike shape of the initial distribution in EPOS is, on the other hand, partly due to the fact that we use strings as a basis of the calculation of the initial energy density. Strings always strech over a certain range in , with fluctuations concerning the length of the string, but always covering , leading thus to a triangularlike shape.
We have seen significant differences in the rapidity dependence of the elliptical flow, when choosing different initial conditions. Do similar differences show up in simple rapidity spectra as well? In fig. 5, we show the rapidity distributions of pions in central Au+Au collisions, for the PAR initial conditions (upper panel), and EPOS initial conditions (lower panel). Again we consider the three different freeze out scenarios, but they provide quite similar results, although the late freeze out (FO_100) gives slightly more particles than the two other options, the latter ones being almost identical. Comparing PAR and EPOS initial conditions, the former one gives a broader distribution, as expected. But, the difference is quite small, much smaller than the difference concerning the v2 rapidity dependencies.
To summarize: we compared two options for initial conditions for 3D hydrodynamical calculations of AuAu collisions: a parameterization, with parameters chosen in order to optimize final results (PAR), and an initial condition obtained from a microscopic approach (EPOS). For both options, we performed the hydrodynamic calculations using the same equation of state. For either of the two scenarios, we investigated three different freezeout options: a pure hydrodynamic evolution, with freeze out 100 MeV, a pure hydrodynamical evolution, with freeze out at 169 MeV, and a hydrodynamical evolution with freeze out at 169 MeV, with subsequent hadronic cascade. We found a fundamentally different shape of the pseudorapidity dependence of for the two different initial conditions PAR and EPOS, independent of the freeze out options. The characteristic triangular shape for the results for EPOS initial conditions is due to a triangular spacetime rapidity dependence of the initial energy density. The latter fact is mainly due to the fact that strings are used to compute initial conditions, not partons. It is interesting to note that rapidity spectra are much less affected by the the choice of initial conditions than the rapidity dependence.
Acknowledgements.
T. H. is supported in part by the GrantsinAid of the Japanese Ministry of Education, Culture, Sports, Science, and Technology (No. 19740130). The research has been carried out within the scope of the ERG (GDRE): Heavy ions at ultrarelativistic energies  a European Research Group comprising IN2P3/CNRS, Ecole des Mines de Nantes, Universite de Nantes, Warsaw University of Technology, JINR Dubna, ITEP Moscow and Bogolyubov Institute for Theoretical Physics NAS of Ukraine. Iu. K. acknowledges the partial support of the Ministry for Education and Science of Ukraine and Fundamental Research State Fund of Ukraine, Agreement No F33/4612009.References
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