Scaling Characteristics of Azimuthal Anisotropy at RHIC

1. Scaling Characteristics ofAzimuthal Anisotropy at RHIC Michael Issah SUNY Stony Brook for the PHENIX Collaboration WWND, San Diego

2. Outline • Introduction • What can we learn from scaling characteristics of azimuthal anisotropy • Eccentricity scaling and thermalization • Speed of sound estimation • Scaling with transverse kinetic energy and implications • Summary WWND, San Diego

3. coordinate-space-anisotropy  momentum-space-anisotropy y py px x Initial/final conditions, dof, EOS Elliptic Flow Elliptic flow strength determined principally by EOS and initial eccentricity WWND, San Diego

4. PRL87, 052301 (2001) peripheral collisions Central collisions Energy density Extrapolation From ET Distributions • High energy densities are achieved, higher than required for phase transition to occur (~ 1 GeV/fm3) thermalization time (t0 ~ 0.2 – 1 fm/c) eBj~ 5 – 15 GeV/fm3 WWND, San Diego

5. PRC 72 (05) 014904 200 GeV Au+Au min-bias Hydro by Huovinen et al. hydro tuned to fit central spectra data. Hydrodynamic description of v2 PRL 91, 2003 (PHENIX) F. Wang, QM2005 Elliptic flow well described by hydrodynamic models up to pT ~ 1.5 GeV/c Perfect fluid WWND, San Diego

6. Important issues • Some important issues have been raised about: • The range of validity of perfect fluid hydrodynamics • The importance of viscosity effects and where they become important • Estimates of properties of the fluid : speed of sound, latent heat • Whether we can gain access to quark degrees of freedom WWND, San Diego

7. Exploring scaling properties • Scaling properties in science relate macroscopic observables to underlying system properties • In heavy-ion collisions, they can serve to find simple laws relating measured anisotropy to system properties and/or degrees of freedom • Eccentricity scaling • System size scaling • Mass scaling and constituent quark scaling • What can be learnt from these scaling properties ? WWND, San Diego

8. Is thermalization achieved ? • Large v2 indicative of high degree of thermalization of produced matter • Are there other observables showing that the matter is thermalized ? Eccentricity scaled v2 • Ideal hydrodynamics is scale invariant. If the matter behaves hydrodynamically and is thermalized, v2 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 WWND, San Diego

9. Determination of eccentricity • Eccentricity usually obtained from a Glauber Model • One can also use experimental quantity sensitive to initial eccentricity, like the integrated v2 • “Integrated v2 reflects momentum anisotropy of bulk matter and saturates within the first 3-4 fm/c just after collision” (Gyulassy,Hirano nucl-th/050604) • Integrated v2 is proportional to the eccentricity WWND, San Diego

10. 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 WWND, San Diego

11. Eccentricity scaling and system size PHENIX Preliminary PHENIX Preliminary v2 scales with eccentricity and across system size WWND, San Diego

12. Can we make an estimate of cs ? • Energy dependence at RHIC energies seem to indicate a soft equation of state. How soft ? • We can make an estimate of cs from elliptic flow measurements Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009 Definition of v2 in model typically 2 times larger than with usual definition WWND, San Diego

13. Estimation of cs Equation of state: relation between pressure and energy density v2/ecc for <pT> ~ 0.5 GeV/c cs ~ 0.35 ±0.5 (cs2 ~ 0.12), soft EOS F. Karsch, hep-lat/0601013 WWND, San Diego

14. Energy dependence of elliptic flow Kolb, Heinz, nucl-th/0305084 Saturation of azimuthal anisotropy observed at RHIC energies WWND, San Diego

15. PID scaling • Velocity of a particle in a non-relativistic perfect fluid Ollitrault, NPA638 Average kinetic energy of a particle: KE = KEcoll + KEth Pressure is a measure of average kinetic energy: Elliptic flow, being driven by pressure gradients, should be sensitive to the collective transverse kinetic energy Transverse kinetic energy of a particle in a relativistic fluid WWND, San Diego

16. Approximate scaling variable Buda-Lund Model nucl-th/0310040 R.Lacey, QM2005 • Equivalent to a transverse • kinetic energy • Non-relativistic expression Relativistic effects are important Use relativistic formula WWND, San Diego

17. Scaling v2 with transverse kinetic energy Scaling breaks PHENIX preliminary data Baryons scale together Mesons scale together Scaling holds up to 1 GeV Possible hint of quark degrees of freedom WWND, San Diego

18. Transverse kinetic energy scaling PHENIX preliminary data Transverse kinetic energy scaling works for a large selection of particles WWND, San Diego

19. STAR preliminary 200 GeV Au+Au Usual test for quark degrees of freedom Constituent quark scaling works above pT/n ~ 1 GeV/c M. Oldenburg, QM2005 WWND, San Diego

20. Test for partonic degrees of freedom Scaling works PHENIX preliminary data Scaling holds over the whole range of KET Quark mass matters ! WWND, San Diego

21. Universal scaling across centralities PHENIX preliminary data Scaling observed across centrality and particle species WWND, San Diego

22. Universal scaling : do phi mesons and dscale ? PHENIX preliminary data Scaling works for other particles too! WWND, San Diego

23. Summary • Eccentricity scaling holds over a broad range of centralities and is indicative of thermalization of matter produced at RHIC • Hydrodynamic model comparison leads to an estimate of the speed of sound. Data compatible with soft EOS • Transverse kinetic energy is an appropriate variable to scale elliptic flow; related to pressure gradients • Baryons and mesons scale together at low KET (<=1GeV) and separately at higher KET , showing the relevance of the quark degrees of freedom • Scaling with KET/n leads to universal scaling of elliptic flow over a broad range of centralties and particle species WWND, San Diego