FIAS Scientific Report 2011 - Frankfurt Institute for Advanced Studies ...

Effects of temperature dependent shear viscosity over the entropy density ratio on elliptic flow
in ultrarelativistic heavy-ion collisions
Collaborators: G.S. Denicol 1 , P. Huovinen 1 , E. Molnár 2,3 , H. Niemi 2,4 , D.H. Rischke 1,2
1 Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, 2 Frankfurt Institute for Advanced Studies, 3 MTA
Wigner Research Centre for Physics, Budapest, Hungary, 4 Department of Physics, University of Jyväskylä, Finland
Presently, most hydrodynamical models of ultrarelativistic heavy-ion collisions assume a constant, temperatureindependent
shear viscosity to entropy ratio η/s. In several works it has been claimed that in order to describe
elliptic flow data, this constant value cannot be significantly larger than the lower bound η/s = 1/4π conjectured
in the framework of the AdS/CFT correspondence. A constant η/s is, however, in contrast to the typical
behavior observed in common fluids, where η/s has a strong temperature dependence and, typically, a minimum
near phase transitions. A similar behavior of η/s is expected for finite-temperature matter described
by quantum chromodynamics (QCD) near the transition from hadronic matter to the QGP (the QCD phase
transition). We have investigated a question, whether the temperature dependence of η/s has an effect on the
collective flow of hadrons in heavy-ion collisions.
In Au+Au collisions at RHIC, we find almost no difference in elliptic flow whether η/s is constant in the QGP
phase or strongly increasing with temperature. In contrast, the elliptic flow is highly sensitive to the values of
η/s in the low-temperature hadronic phase. On the other hand, we found that the sensitivity of the elliptic flow
to the values of η/s in the high-temperature QGP increases with increasing collision energy, while the effect
of the hadronic viscosity decreases. At the highest LHC energy, the above conclusion for RHIC energies is
reversed: suppression of the elliptic flow is dominated by the viscosity of the QGP and insensitive to that of the
hadronic phase.
The insensitivity of the elliptic flow to the high-temperature shear viscosity in Au+Au collisions at RHIC is
illustrated in the Figure below, where our result from the hydrodynamical simulations are compared with the
data from the STAR Collaboration.
η/s
1.2
1.0
0.8
0.6
0.4
0.2
LH-LQ
LH-HQ
HH-LQ
HH-HQ
0.0
0.10 0.20 0.30 0.40
T [GeV]
v 2 (p T )
0.2
0.1
STAR v 2 {4}
20-30 %
0.0
charged hadrons
RHIC 200 AGeV
0 1 2
pT [GeV]
3
Left: The parametrizations of η/s as a function of temperature Right: Elliptic flow of charged hadrons in 20-30 %
centrality class in Au+Au collisions at RHIC. The data is 4-particle cumulant data from the STAR Collaboration
Related publications in 2011:
1) H. Niemi, G. S. Denicol, P. Huovinen, E. Molnar and D. H. Rischke, Influence of the shear viscosity of
the quark-gluon plasma on elliptic flow in ultrarelativistic heavy-ion collisions, Phys. Rev. Lett. 106 (2011)
212302.
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