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Register a new userConstraints on shear stress tensor in viscous relativistic hydrodynamics
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We extend our hybrid model HydHSD by taking into account shear viscosity within the Israel-Stewart hydrodynamics. The influence of different forms of $pi^{mu u}$ constraints on observables is analyzed. We show that the form of the corresponding condition plays an important role for the sensitivity of viscous hydrodynamics to the ratio of shear viscosity to the entropy density, $eta/s$. It is shown that the constraint used in the vHLLE model, results in most sensitivity of rapidity distributions and transverse momentum spectra to a change of the $eta/s$ ratio; however, their applicability for large values of $eta/s$ is doubtful. On the contrary, the strict constraints from cite{MNR2010} are very strong but most established. We also found that $eta/s$ as a function of the collision energy probably has an extremum at $E_{rm lab}=10.7$ AGeV. However, we obtain that any considered condition does not allow to reproduce simultaneously pion and proton experimental data within our model.
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We present the hybrid hadron string dynamic (HydHSD) model connecting the parton-hadron-string dynamic model (PHSD) and a hydrodynamic model taking into account shear viscosity within the Israel-Stewart approach. The performance of the code is tested on the pion and proton rapidity and transverse mass distributions calculated for Au+Au and Pb+Pb collision at AGS--SPS energies. The influence of the switch time from transport to hydro models, the viscous parameter, and freeze-out time are discussed. Since the applicability of the Israel-Stewart hydrodynamics assumes the perturbative character of the viscous stress tensor, $pi^{mu u}$, which should not exceed the ideal energy-momentum tensor, $T_{rm id}^{mu u}$, hydrodynamical codes usually rescale the shear stress tensor if the inequality $|pi^{mu u}|ll |T_{rm id}^{mu u}|$ is not fulfilled in some sense. We show that the form of the corresponding condition plays an important role in the sensitivity of hydrodynamic calculations to the viscous parameter -- a ratio of the shear viscosity to the entropy density, $eta/s$. It is shown that the constraints used in the vHLLE and MUSIC models give the same results for the observables. With these constraints, the rapidity distributions and transverse momentum spectra are most sensitive to a change of the $eta/s$ ratio. As an alternative, a strict condition is used. We performed global fits the rapidity and transverse mass distribution of pion and protons. It was also found that $eta/s$ as a function of the collision energy monotonically increases from $E_{rm lab}=6A$GeV up to $E_{rm lab}=40A$GeV and saturates for higher SPS energies. We observe that it is difficult to reproduce simultaneously pion and proton rapidity distribution within our model with the present choice of the equation of state without a phase transition.
Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of various macroscopic physical systems, with its equations based on conservation laws such as energy-momentum conservation and charge conservation. Recently there has been significant interest in understanding the implications of angular momentum conservation for a corresponding hydrodynamic theory. In this work, we examine the key conceptual issues for such a theory in the relativistic regime where the orbital and spin components get entangled. We derive the equations for relativistic viscous hydrodynamics with angular momentum through Navier-Stokes type of gradient expansion analysis.
Event-by-event viscous hydrodynamics is combined with heavy quark energy loss models to compute heavy flavor flow cumulants $v_2{2}$, $v_3{2}$, and $v_2{4}$ as well as the nuclear modification factors of $D^0$ and $B^0$ mesons in PbPb collisions at 2.76 TeV. Our results indicate that bottom quarks can flow as much as charm quarks in the $p_T$ range 8--30 GeV.
Recently it has been shown that a realistic description of the medium via event-by-event viscous hydrodynamics plays an important role in the long-standing $R_text{AA}$ vs. $v_2$ puzzle at high $p_T$. In this proceedings we begin to extend this approach to the heavy flavor sector by investigating the effects of full event-by-event fluctuating hydrodynamic backgrounds on the nuclear suppression factor and $v_2{2}$ of heavy flavor mesons and non-photonic electrons at intermediate to high $p_T$. We also show results for $v_3{2}$ of $B^0$ and D$^0$ for PbPb collisions at $sqrt{s}=2.76$ TeV.
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.
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