7 research outputs found
Characteristic form of boost-invariant and cylindrically non-symmetric hydrodynamic equations
It is shown that the boost-invariant and cylindrically non-symmetric
hydrodynamic equations for baryon-free matter may be reduced to only two
coupled differential equations. In the case where the system exhibits the
cross-over phase transition, the standard numerical methods may be applied to
solve these equations and the proposed scheme allows for a very convenient
analysis of the cylindrically non-symmetric hydrodynamic expansion.Comment: 8 pages, 3 figures, 3 sets of figure
Temperature dependent sound velocity in hydrodynamic equations for relativistic heavy-ion collisions
We analyze the effects of different forms of the sound-velocity function
cs(T) on the hydrodynamic evolution of matter formed in the central region of
relativistic heavy-ion collisions. At high temperatures (above the critical
temperature Tc) the sound velocity is calculated from the recent lattice
simulations of QCD, while in the low temperature region it is obtained from the
hadron gas model. In the intermediate region we use different interpolations
characterized by the values of the sound velocity at the local maximum (at T =
0.4 Tc) and local minimum (at T = Tc). In all considered cases the temperature
dependent sound velocity functions yield the entropy density, which is
consistent with the lattice QCD simulations at high temperature. Our
calculations show that the presence of a distinct minimum of the sound velocity
leads to a very long (about 20 fm/c) evolution time of the system, which is not
compatible with the recent estimates based on the HBT interferometry. Hence, we
conclude that the hydrodynamic description is favored in the case where the
cross-over phase transition renders the smooth sound velocity function with a
possible shallow minimum at Tc.Comment: 6 pages, 3 figures, talk given at SQM'07 Levoca, Slovaki
On the formation of Hubble flow in Little Bangs
A dynamical appearance of scaling solutions in the relativistic hydrodynamics
applied to describe ultra-relativistic heavy-ion collisions is studied. We
consider the boost-invariant cylindrically symmetric systems and the effects of
the phase transition are taken into account by using a temperature dependent
sound velocity inferred from the lattice simulations of QCD. We find that the
transverse flow acquires the scaling form r/t within the short evolution times,
10 - 15 fm, only if the initial transverse flow originating from the
pre-equilibrium collective behavior is present at the initial stage of the
hydrodynamic evolution. The amount of such pre-equilibrium flow is correlated
with the initial pressure gradient; larger gradients require smaller initial
flow. The results of the numerical calculations support the phenomenological
parameterizations used in the Blast-Wave, Buda-Lund, and Cracow models of the
freeze-out process.Comment: 11 page
THERMINATOR 2: THERMal heavy IoN generATOR 2
We present an extended version of THERMINATOR, a Monte Carlo event generator
dedicated to studies of the statistical production of particles in relativistic
heavy-ion collisions. The increased functionality of the code contains the
following features: The input of any shape of the freeze-out hypersurface and
the expansion velocity field, including the 3+1 dimensional profiles, in
particular those generated externally with various hydrodynamic codes. The
hypersufraces may have variable thermal parameters, which allows for studies
departing significantly from the mid-rapidity region, where the baryon chemical
potential becomes large. We include a library of standard sets of hypersurfaces
and velocity profiles describing the RHIC Au+Au data at sqrt(s_(NN)) = 200 GeV
for various centralities, as well as those anticipated for the LHC Pb+Pb
collisions at sqrt(s_(NN)) = 5.5 TeV. A separate code, FEMTO-THERMINATOR, is
provided to carry out the analysis of femtoscopic correlations which are an
important source of information concerning the size and expansion of the
system. We also include several useful scripts that carry out auxiliary tasks,
such as obtaining an estimate of the number of elastic collisions after the
freeze-out, counting of particles flowing back into the fireball and violating
causality (typically very few), or visualizing various results: the particle
p_T-spectra, the elliptic flow coefficients, and the HBT correlation radii. We
also investigate the problem of the back-flow of particles into the
hydrodynamic region, as well as estimate the elastic rescattering in terms of
trajectory crossings. The package is written in C++ and uses the CERN ROOT
environment.Comment: 51 pages, 12 figures, 4 tables, project web-page:
http://therminator2.ifj.edu.p
Early evolution of transversally thermalized partons
The idea that the parton system created in relativistic heavy-ion collisions (i) emerges in a state with transverse momenta close to thermodynamic equilibrium and (ii) its evolution at early times is dominated by the 2-dimensional (transverse) hydrodynamics of the ideal fluid is investigated. It is argued that this mechanism may help to solve the problem of early equilibration