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What do the scaling characteristics of elliptic flow reveal about the properties of the matter at RHIC ? Michael Issah Stony Brook University for the PHENIX Collaboration CIPANP 2006, Puerto Rico
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2 Outline Motivation Eccentricity scaling and thermalization Equation of state and speed of sound estimation Dependence of elliptic flow on kinetic energy and degrees of freedom Summary
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CIPANP 2006, Puerto Rico3 Elliptic Flow y x pypy pxpx coordinate-space-anisotropy momentum-space-anisotropy Initial/final conditions, dof, EOS Elliptic flow strength determined principally by initial conditions, initial eccentricity and EoS
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CIPANP 2006, Puerto Rico4 High energy densities are achieved, higher than required for phase transition to occur (~ 1 GeV/fm 3 ) Are energy densities high enough? PRL87, 052301 (2001) Central collisions peripheral collisions thermalization time ( 0 ~ 0.2 – 1 fm/c) Bj ~ 5 – 15 GeV/fm 3 Extrapolation From E T Distributions
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CIPANP 2006, Puerto Rico5 Elliptic flow at RHIC Elliptic flow at RHIC Large v 2 created at RHIC Indicates early thermalization Elliptic flow data agrees well with hydrodynamic predictions Can one exploit scaling properties of v 2 to get insight into the degree of thermalization and test for hydrodynamic behavior ? Hydro by Huovinen et al. hydro tuned to fit central spectra data. PRC 72 (05) 014904 200 GeV Au+Au min-bias PRL 91, 2003 (PHENIX)
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CIPANP 2006, Puerto Rico6 Eccentricity scaling as a test for the degree of thermalization Large v 2 indicative of high degree of thermalization of produced matter Are there other observables showing that the matter is thermalized ? Eccentricity scaled v 2 Ideal hydrodynamics is scale invariant. If the matter behaves hydrodynamically and is thermalized, v 2 should be independent of system size Do we observe such independence in the data? Data for different colliding systems (Au+Au, Cu+Cu) available to test this
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CIPANP 2006, Puerto Rico7 Determination of eccentricity Eccentricity usually obtained from a Glauber Model One can also use experimental quantity sensitive to initial eccentricity, like the integrated v 2 Integrated v 2 is proportional to the eccentricity STAR Collaboration
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CIPANP 2006, Puerto Rico8 Eccentricity scaling Eccentricity scaling observed in hydrodynamic model over a broad range of centralities Bhalerao, Blaizot, Borghini, Ollitrault, nucl-th/0508009 R: measure of size of system
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CIPANP 2006, Puerto Rico9 Eccentricity scaling and system size v 2 scales with eccentricity and across system size PHENIX Preliminary k ~ 3.1 (obtained from data )
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CIPANP 2006, Puerto Rico10 Energy dependence of elliptic flow Saturation of azimuthal anisotropy observed at RHIC energies Suggests the matter has a soft EoS
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CIPANP 2006, Puerto Rico11 Estimate of the speed of sound (I) Energy dependence at RHIC energies seem to indicate a soft equation of state. How soft ? Estimate of c s from elliptic flow measurements can be made from eccentricity scaled v 2 Bhalerao, Blaizot, Borghini, Ollitrault, nucl-th/0508009
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CIPANP 2006, Puerto Rico12 Estimation of the speed of sound (II) Assume simple EoS: relation between pressure and energy density c s ~ 0.35 ± 0.05 (c s 2 ~ 0.12), so ft EOS F. Karsch, hep-lat/0601013 v 2 /ε for ~ 0.45 GeV/c
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CIPANP 2006, Puerto Rico13 Scaling breaks Elliptic flow scales with KE T up to KE T ~1 GeV Indicates hydrodynamic behavior Possible hint of quark degrees of freedom become apparent at higher KE T Baryons scale together Mesons scale together PHENIX preliminary See H. Masui’s talk in this session Kinetic energy of a particle in a relativistic fluid: = m T – m Scaling v 2 with kinetic energy (I)
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CIPANP 2006, Puerto Rico14 PHENIX preliminary Transverse kinetic energy scaling works for a large selection of particles Scaling v 2 with kinetic energy (II)
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CIPANP 2006, Puerto Rico15 Constituent quark scaling works better with KE T as compared to p T Hadron mass (hydro) scaling at low KE T (KE T < 1 GeV) is not perturbed by constituent quark scaling at higher KE T ! Test for partonic degrees of freedom PHENIX preliminary STAR preliminary 200 GeV Au+Au
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CIPANP 2006, Puerto Rico16 KE T /n scaling and hydrodynamics Scaling works for a broad set of particles Supports the observation that all particles emerge from a common flow field Hydrodynamic calculation not incompatible with KET/n scaling PHENIX preliminary Chiho Nonaka: 3-D Hydro R. Fries, SQM2006
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CIPANP 2006, Puerto Rico17 KE T /n scaling across collision centralities KE T /n scaling observed across centralities
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CIPANP 2006, Puerto Rico18 Summary Scaling properties of elliptic flow provide a way to infer some properties of the matter formed in heavy- ion collisions at RHIC Eccentricity scaling shows that the medium is highly thermalized, with a soft EoS Transverse kinetic energy scaling indicates perfect fluid hydrodynamic behavior In addition, scaling with KE T /n leads to comprehensive scaling of elliptic flow data, which prevails over a broad range of centralities Taken together, these observations show that the matter is highly thermalized, has a soft equation of state and is made up of flowing constituent quarks
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