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Article
Report number	arXiv:0805.1756 ; CERN-PH-TH-2008-100 ; CERN-PH-TH-2008-100
Title	Multiplicity scaling in ideal and viscous hydrodynamics
Author(s)	Song, Huichao (Ohio State U.) ; Heinz, Ulrich W. (Ohio State U. ; CERN)
Publication	2008
Imprint	14 May 2008
Number of pages	15
In:	Phys. Rev. C 78 (2008) 024902
DOI	10.1103/PhysRevC.78.024902
Subject category	Nuclear Physics - Theory
Abstract	Using numerical results from ideal and viscous relativistic hydrodynamic simulations with three different equations of state, for Au+Au and Cu+Cu collisions at different centralities and initial energy densities, we explore the dependence of the eccentricity-scaled elliptic flow, v_2/epsilon, and the produced entropy fraction, Delta S/S_0, on the final charged hadron multiplicity density dN_ch/dy per unit transverse overlap area S, (1/S)(dN_ch/dy). The viscous hydrodynamic simulations are performed with two different versions of the Israel-Stewart kinetic evolution equations, and in each case we investigate the dependence of the physical observables on the kinetic relaxation time. We find approximate scaling of v_2/epsilon and Delta S/S_0 with (1/S)(dN_ch/dy), with scaling functions that depend on the EOS and, in particular, on the value of the specific shear viscosity eta/s. Small scaling violations are seen even in ideal hydrodynamics, caused by a breaking of the scale invariance of ideal fluid dynamics by the freeze-out condition. Viscous hydrodynamics shows somewhat larger scale-breaking effects that increase with increasing eta/s and decreasing system size and initial energy density. We propose to use precision studies of these scaling violations to help constrain the shear viscosity eta/s of the quark-gluon plasma created in relativistic heavy ion collisions.

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