1. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20051 System size, energy and  dependence of directed and elliptic flow Steven Manly (Univ. of Rochester) For the PHOBOS Collaboration

2. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20052 Collaboration meeting, BNL October 2002 Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel, Wit Busza (Spokesperson), Zhengwei Chai, Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Kristjan Gulbrandsen, Clive Halliwell, Joshua Hamblen, Ian Harnarine, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Jay Kane,Piotr Kulinich, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Eric Richardson, Christof Roland, Gunther Roland, Joe Sagerer, Iouri Sedykh, Chadd Smith, Maciej Stankiewicz, Peter Steinberg, George Stephans, Andrei Sukhanov, Artur Szostak, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Donald Willhelm, Frank Wolfs, Barbara Wosiek, Krzysztof Woźniak, Shaun Wyngaardt, Bolek Wysłouch ARGONNE NATIONAL LABORATORYBROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOWMASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWANUNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLANDUNIVERSITY OF ROCHESTER Collaboration meeting in Maryland, 2003

3. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20053 Flow in PHOBOS Ring counter Octagon Spectrometer arm Paddle trigger Vertex detector

4. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20054 Correlate reaction plane determined from azimuthal pattern of hits in one part of detector Flow in PHOBOS Subevent A

5. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20055 with azimuthal pattern of hits in another part of the detector Flow in PHOBOS Subevent B

6. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20056 Or with tracks identified in the spectrometer arms Flow in PHOBOS Tracks

7. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20057 Separation of correlated subevents typically large in  Flow in PHOBOS

8. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20058 For directed flow we use subevents that are symmetric about  =0 Flow in PHOBOS Subevent B Subevent A

9. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20059 Differential flow has proven to be a useful probe of heavy ion collisions:  Centrality  p T  Pseudorapidity  Energy  System size  Species Probing collisions with flow

10. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200510 Au-Au – directed flow Au-Au 19.6 GeV h ± Au-Au 62.4 GeV h ± Au-Au 130 GeV h ± Au-Au 200 GeV h ± Update of directed flow result first shown at QM2004 Similar (2-subevent) technique Added 62.4 GeV data Confirmed with mixed harmonic analysis See poster by A. Mignerey in Poster 1, section 2, number 47 PHOBOS preliminary 0-40% centrality

11. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200511 PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303 PHOBOS Au-Au, h ± 0-40% centrality Au-Au – elliptic flow

12. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200512 PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303 PHOBOS Au-Au, h ± 0-40% centrality Au-Au – elliptic flow ó Recent theoretical progress in understanding v 2 (η). See, for example:  M.Csanád, T.Csörgó, B.Lörstad, Nucl. Phys. A742 (2004) 80 [nucl-th/0310040]  U.Heinz, P.F.Kolb, J.Phys. G30 (2004) S1229 [nucl-th/0403044]  T.Hirano, M.Isse, Y.Nara, AOhnishi, and K Yoshino, nucl-th/0506058

13. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200513 Directed flow exhibits extended longitudinal scaling, i.e., approximate rest frame of nucleus. Directed flow – extended longitudinal scaling Systematic errors only PHOBOS preliminary h ±, Au-Au 0-40% centrality  '=|  |-y beam v1v1

14. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200514 Au-Au data, h ± 0-40% centrality  '=|  |-y beam Elliptic flow exhibits striking extended longitudinal scaling PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303 v2v2 Elliptic flow – extended longitudinal scaling Systematic errors only

15. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200515  ’=|  |-y beam Elliptic flow exhibits striking extended longitudinal scaling PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303 If so, it is an unfortunate coincidence that we saturate v 2 right at the highest energy density we can achieve: no break in slope Mid-rapidity, 200 GeV, Au-Au Reached the hydro limit?  '=|  |-y beam v2v2 Elliptic flow – extended longitudinal scaling Au-Au data, h ± 0-40% centrality Systematic errors only

16. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200516 Differential flow has proven to be a useful probe of heavy ion collisions:  Centrality  p T  Pseudorapidity  Energy  System size  Species Elliptic flow – Cu-Cu results

17. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200517 Elliptic flow – Cu-Cu results  Cu flow is large  Track- and hit-based results agree (200 GeV)  ~20-30% rise in v 2 from 62.4 to 200 GeV PHOBOS preliminary Cu-Cu, h ± Hit based 62.4 GeV Hit based 200 GeV Track based 200 GeV

18. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200518 Elliptic flow – Cu-Cu results Cu-Cu v 2 (η) shape reminiscent of Au-Au PHOBOS preliminary Cu-Cu, 62.4 GeV, h± 0-40% centrality PHOBOS preliminary Cu-Cu, 200 GeV, h± 0-40% centrality

19. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200519 Elliptic flow – Cu-Cu results Longitudinal scaling reminiscent of Au-Au PHOBOS preliminary Cu-Cu, h ± v2v2  '=|  |-y beam Cu-Cu collisions also exhibit extended longitudinal scaling statistical errors only

20. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200520 Standard eccentricity (  standard ) x System size and eccentricity Expect the geometry, i.e., the eccentricity, of the collision to be important in comparing flow in the Au-Au and Cu-Cu systems Centrality measure  N part   Paddle signal, ZDC, etc. MC simulations What is the relevant eccentricity for driving the azimuthal asymmetry?

21. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200521 Fluctuations in eccentricity are important for small A. System size and eccentricity Participant eccentricity (  part ) x Standard eccentricity (  standard ) x Two possibilities

22. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200522 Fluctuations in eccentricity are important for the Cu-Cu system. System size and eccentricity Must use care in doing Au-Au to Cu-Cu flow comparisons. Eccentricity scaling depends on definition of eccentricity.

23. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200523 Elliptic flow – v 2 scaling  Expect / ~ constant for system at hydro limit.  Note the importance of the eccentricity choice. h ± 1  statistical and systematic errors added in quadrature h ±

24. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200524 Elliptic flow – v 2 scaling h ± 1  statistical and systematic errors added in quadrature h ± Given other similarities between Au-Au and Cu-Cu flow, perhaps this is evidence that  part is (close to) the relevant eccentricity for driving the azimuthal asymmetry

25. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200525 Elliptic flow – v 2 scaling Expectin “low density limit”.

26. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200526 Elliptic flow – v 2 scaling Approximate “LDL” scaling observed.  Caution: we used  part for PHOBOS data. Important for Cu-Cu, less critical for Au-Au.  Scale v 2 (  ) to ~v 2 (y) (10% lower)  Scale dN/d  to be ~dN/dy (15% higher)

27. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200527 Elliptic flow – v 2 scaling Approximate “LDL” scaling observed. Points for STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) 034904 with no adjustments  Caution: we used  part for PHOBOS data. Important for Cu-Cu, less critical for Au-Au.  Scale v 2 (  ) to ~v 2 (y) (10% lower)  Scale dN/d  to be ~dN/dy (15% higher)

28. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200528 Elliptic flow – system dependence Eccentricity difference is important for same centrality selection. V 2 (p T ) for Cu-Cu is similar v 2 (p T ) for Au-Au when scaled by  part PHOBOS preliminary h ± 0-50% centrality PHOBOS preliminary h ± 0-50% centrality PHOBOS preliminary h ± 0-50% centrality

29. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200529 v 2 for Cu-Cu is ~20% smaller than v 2 for Au-Au plotted 0-40% centrality. Drops another ~20% if scaled by ratio PHOBOS 62.4 GeV h ± 0-40% centrality Elliptic flow – system dependence preliminary PHOBOS 200 GeV h ± 0-40-% centrality Statistical errors only

30. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200530 This data shows v 2 does not scale linearly with A as expected by AMPT (factor of 3) AMPT multi-phase transport model (Chen and Ko, nucl-th/0505044) PHOBOS 62.4 GeV h ± 0-40% centrality Elliptic flow – system dependence preliminary PHOBOS 200 GeV h ± 0-40-% centrality Statistical errors only

31. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200531 Conclusions  Au-Au directed flow including the new 62.4 GeV data. PHOBOS preliminary Au-Au 19.6 GeV Au-Au 62.4 GeV Au-Au 130 GeVAu-Au 200 GeV

32. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200532 Conclusions  Cu-Cu elliptic flow large. Similar in shape to Au-Au. PHOBOS preliminary Cu-Cu, 62.4 GeV, h± 0-40% centrality PHOBOS preliminary Cu-Cu, 200 GeV, h± 0-40% centrality

33. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200533 Conclusions  Au-Au and Cu-Cu systems exhibit extended longitudinal scaling. No break in evolution as function of η due to reaching hydro limit. PHOBOS Au-Au, h ± PHOBOS preliminary Cu-Cu, h ± v2v2  '=|  |-y beam v2v2 statistical errors only

34. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200534 Conclusions  Eccentricity definition very important for small systems. h ± 1  statistical and systematic errors added in quadrature h ±

35. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200535 Conclusions  Similarity of Au-Au to Cu-Cu flow and the fact that scaling seems to work for  part may imply that  part (or something close to it) is the relevant geometric quantity for generating the azimuthal asymmetry.

36. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200536 Conclusions  Au-Au directed flow results updated.  Au-Au and Cu-Cu systems exhibit extended longitudinal scaling. No break in evolution as function of η due to reaching hydro limit.  Eccentricity definition very important for small systems.  Cu-Cu elliptic flow large. Similar in shape to Au-Au.  v 2 (p T ) is similar in Au-Au and Cu-Cu systems when  part is used.  Similarity of Au-Au to Cu-Cu flow and the fact that scaling seems to work for  part may imply that  part (or something close to it) is the relevant geometric quantity for generating the azimuthal asymmetry.

37. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200537 Backup Slides

38. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200538 Elliptic flow subevent regions Cu-Cu, 200 and 62.4 GeV and Au-Au, 19.6, 62.4, 130 and 200 GeV: 0.1<| η |<3.0 (use 0.5<|η|<3.0 and 1.0<|η|<3.0 for systematic studies) Regions used to determine reaction plane and resolution.

39. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200539 Directed flow subevent regions Regions used to determine reaction plane and resolution. v 1 baseline Au-Au, 19.6, 62.4, 130 and 200 GeV: 1.5<|η|<3.0 and 3.0<|η|<5.0 (use 1.5<|η|<2.5 and 3.5<|η|<5.0 for systematic studies) v 1 mixed harmonic Au-Au, 19.6, 62.4, 130 and 200 GeV: 1.5<|η|<3.0 and 3.0<|η|<5.0 for the first harmonic part and 0.1<|η|<3.0 for the second harmonic part

40. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200540 Baseline analysis overlaid with new PHOBOS mixed harmonic analysis Shows non-flow correlations small Mixed harmonic method: STAR collaboration, Phys. Rev. C 72 (2005) 014904 PHOBOS preliminary h ± Au-Au Au-Au update – directed flow PHOBOS preliminary h ± Au-Au

41. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200541 Au-Au update – directed flow 62.4 GeV results are particularly good due to:  large directed flow  large number of tracks/event  large elliptic flow (for mixed harmonic) STAR 62.4 GeV results from A.H. Tang (STAR Collaboration), nucl-ex/0409029 Preliminary PHOBOS and STAR results agree well at 62.4 GeV except at highest |  | 62.4 GeV Au-Au, h ±

42. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200542 Au-Au update – directed flow 62.4 GeV directed flow comparison STAR 62.4 GeV results from A.H. Tang (STAR Collaboration), nucl-ex/0409029

43. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200543 Au-Au update – directed flow Comparison of directed flow results at 62.4 GeV Estimated by PHOBOS from weighted average of STAR data in multiple centrality bins We used the centrality dependence of STAR’s results to estimate the STAR results in the 10-50% centrality bin 62.4 GeV Au-Au, h ± Discrepancy at high η possibly due to differences in low momentum cutoff?

44. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200544 Comparison of preliminary PHOBOS 200 GeV v 1 with published STAR results. Plots identical except for STAR centrality selection. Au-Au update – directed flow STAR 200 GeV results from Phys. Rev. C 72 (2005) 014904

45. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200545 Only statistical errors shown Au+Au data (0-40% central) Au-Au update – elliptic flow PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303

46. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200546 Elliptic flow – Cu-Cu results Models from Hirano et al., nucl-th/0506058, probably see more later this session Cu-Cu more like Hydro than JAM hadron string cascade model Here JAM uses a 1 fm/c formation time. Hydro (160) has kinetic freezeout temperature at 160 MeV preliminary 200 GeV Cu-Cu preliminary 200 GeV 15-25% Cu-Cu Statistical errors only

47. S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 200547 System size and eccentricity Au-Au Cu-Cu PHOBOS-Glauber MC preliminary Mean eccentricity shown in black