1. System size and beam energy dependence of azimuthal anisotropy from PHENIX Michael Issah Vanderbilt University for the PHENIX Collaboration QM2008, Jaipur, India

2. 2 Origin of azimuthal anisotropy Interactions among the produced particles lead to pressure gradients which generate an azimuthal anisotropy in particle emission or elliptic flow, measured by v 2, from which can be obtained valuable information about the early dynamics after the collision Spatial anisotropyMomentum anisotropy

3. QM 2008, Jaipur, India3 Azimuthal anisotropy at different beam energies in Au+Au collisions  Comparison between v 2 for different p T and centralities show that the measured v 2 is very similar at different beam energies  Suggests that v 2 does not change much with beam energy over the range √s=62.4-200 GeV 0-10%10-20%20-30%30-40%

4. QM 2008, Jaipur, India4 Centrality and p T dependence of elliptic flow at different beam energies  Detailed differential centrality and p T dependence of v 2 show similar magnitudes at √s = 62.4, 130 and 200 GeV  Increase in measured v 2 between SPS energies and RHIC energies PRL 94, 232302 (2005)

5. QM 2008, Jaipur, India5 Beam energy dependence of elliptic flow  v 2 saturates in the energy range √s=62.4-200 GeV suggesting a softening of the equation of state of matter at RHIC  Extracted value for ≈ 0.35 ± 0.05 or ≈ 0.12 (PRL 98, 162301)  This value lies between the ideal gas limit (c s 2 =1/3) and mixed phase value (c s 2 =0) PRL 94, 232302 (2005) F. Karsch, hep-lat/0601013

6. QM 2008, Jaipur, India6 Beam energy comparison in Cu+Cu  Measured v 2 in Cu+Cu at √s = 62.4 GeV is observed to be of comparable magnitude or somewhat lower than v 2 √s = 200 GeV.  Systematic errors are big.  The smaller size of the system and smaller energy densities created in Cu+Cu may be factors in explaining the difference observed in Cu+Cu compared Au+Au system 0-10%10-20%20-30%30-40%

7. QM 2008, Jaipur, India7 PRL. 98, 162301 (2007 )  Hydrodynamic behavior tested by transverse kinetic energy scaling for low transverse kinetic energy KE T = m T – m  Baryon and mesons scale separately after KE T ≥ 1 GeV  Partonic recombination manifest by scaling by the number of constituent quarks n q (NCQ scaling)  NCQ scaling is observed to break at around KE T /n q ~1 GeV – see S. Huang’s talk later in the sesssion Test of hydrodynamic behavior and partonic degrees of freedom in Au+Au collisions at √s = 200 GeV Test of hydrodynamic behavior and partonic degrees of freedom in Au+Au collisions at √s = 200 GeV

8. QM 2008, Jaipur, India8  Similar picture in Au+Au at 200 GeV and 62.4 GeV  Partonic degrees of freedom are manifest in Au+Au collisions at √s=62.4 GeV Au + Au at √s = 62.4 GeV

9. QM 2008, Jaipur, India9 NCQ scaling NCQ scaling across systems and beam energies Au+Au 200 GeVCu+Cu 200 GeVAu+Au 62.4 GeV PRL. 98, 162301 (2007)  Number of constituent quark scaling holds in Au+Au and Cu+Cu colliding systems at 200 GeV at low KE T  Suggests that coalescence of particles with the quantum numbers of quarks occurs over the energy range 62.4 – 200 GeV for colliding systems of different sizes Centrality 10-40% min bias

10. QM 2008, Jaipur, India10 KE T + Number of constituent Quarks (NCQ) scaling  Scaling seems to hold well for different centralities up to 60% centrality  The goodness of the scaling can be tested by fitting the scaled curves with a polynomial and taking ratio of data/fit

11. QM 2008, Jaipur, India11  Ratio of measured v 2 to a fit to the data confirms that there is good NCQ scaling in the region where such scaling is expected to hold  Scaling fails at low KE T /n q (<0.2). Could be due to feed down from resonances  More in-depth study of systematic errors needed at low KE T as well as comparison to hydrodynamic models NCQ scaling and fit to data

12. QM 2008, Jaipur, India12  Reaction plane v 2 less affected by non-flow than cumulant v 2 because of large rapidity gap between PHENIX central arms and BBCs  Non-flow mainly due to jet correlations  Differences between reaction plane and cumulant v 2 measurements show that jet correlations become influential as from p T ~3.5 GeV/c at all centralities Non-flow contributions in Au+Au at √s=200 GeV PHENIX Preliminary

13. QM 2008, Jaipur, India13  High statistics Run7 data enable detailed study of different flow harmonics  v 4 of unidentified hadrons scale with integral flow between centrality 10-40%  v 4 /(ε ’ ) 2 is well described by (v 2 /ε ’ ) 2 up to p T ≈ 2 GeV/c  Ratio v 4 /v 2 2 probes degree of thermalization  Results for different particle species reported in S. Huang’s talk later in this session v 4 of unidentified charged hadrons A.Taranenko Poster 212 ε’ :

14. QM 2008, Jaipur, India14 Summary  Differential azimuthal anisotropy measurements in Au+Au and Cu+Cu at different beam energies and centralities indicate saturation of v 2 with beam energy at RHIC  Transverse kinetic energy (KE T ) scaling, as well as number of constituent quark scaling, is observed in both systems at different beam energies and for KE T /n q < 1 GeV and for centrality up to 60%  More in depth study needed to look into the goodness of the KE T /n q scaling at low KE T  Comparison between reaction plane and cumulant v 2 shows that non-flow correlations due to jet correlations exist for different centralities as from p T ~3.0 – 4.0 GeV/c. May explain the break of the NCQ scaling at KE T > 1 GeV  Detailed study of different flow harmonics carried out in Run7. It is observed that v 4 scales with eccentricity and with v 2 2

15. QM 2008, Jaipur, India15 Thanks to: M. Shimomoura, H. Masui and A. Taranenko Acknowledgements

16. QM 2008, Jaipur, India16 BACK UP

17. QM 2008, Jaipur, India17 Eccentricity scaling across colliding systems k ~ 3.1 (from data )  Eccentricity scaling observed in hydrodynamic model over a broad range of centralities  v 2 is observed to scale with eccentricity and across system size Hydrodynamic model simulations (Bhalerao, Blaizot, Borghini, Ollitrault, nucl-th/0508009 )

18. QM 2008, Jaipur, India18 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

19. QM 2008, Jaipur, India19 Eccentricity scaling from PHOBOS