2. L.P. Csernai, BNL Nov 17-19 '03 1 L..P. Csernai Multi module modelling of heavy ion collisions Collective flow and QGP properties RIKEN-BNL workshop November 17-19, 2003

3. L.P. Csernai, BNL Nov 17-19 '03 2 Multi module modelling of heavy ion collisions L.P. Csernai, A. Anderlik, Cs. Anderlik, Ø. Heggø- Hansen, E. Molnár, A. Nyiri, D. Röhrich, and K. Tamousiunas U of Valencia: V.K. Magas U of Oulu: A. Keranen, J. Manninen Los Alamos National Lab.: D.D. Strottman, B. Schlei U of Sao Paulo: F. Grassi, Y. Hama U of Rio de Janeiro: T. Kodama U of Frankfurt: H. Stöcker, W. Greiner Bergen Computational Physics Lab. – EU Research Infrastructure, BCCS, Unifob AS, University of Bergen, Norway

4. L.P. Csernai, BNL Nov 17-19 '03 3 Multi Module Modeling Pre: Eq. of State (EoS) – Phases – Local eq.:BagM A: Initial state - Fitted to measured data (?) B: Initial state - Pre-equilibrium: Parton Cascade M.; Coherent Yang-Mills [Magas] Local Equilibrium  Hydro, EoS Final Freeze-out: Kinetic models, measurables. If QGP  Sudden and simultaneous hadronization and freeze out (indicated by HBT, Strangeness, Entropy puzzle)

5. L.P. Csernai, BNL Nov 17-19 '03 4 Phase transition to QGP in small systems ! In macroscopic systems two phases of different densities (e) are in phase equilibrium. Negligible density fluctuations! [Csernai, Kapusta, Osnes, PRD 67 (03) 045003 ] STATIC

6. L.P. Csernai, BNL Nov 17-19 '03 5 Small, Mesoscopic Systems If N=100, fluctuations are getting strong (red). Close to the critical point, the two phases cannot be identified (green). => Landau’s theory of fluctuations near the critical point. Nuclear Liquid-Gas phase transition (first order) [ Goodman, Kapusta, Mekjian, PRC 30 (1984) 851 ] CRAY - 1 STATIC

7. L.P. Csernai, BNL Nov 17-19 '03 6 Lattice Field Theory [Farakos, Kajantie, et al. (1995) hep-lat/ ] First order (EW) phase transition: statistical ensemble. Fluctuations of density decrease with increasing Lattice volume !! For macroscopic EoS extrapolation is needed! For small systems, ~100-200 fermi 3, fluctuations are REAL !!! Supercomputers are needed ! [Csernai, Neda PL B337 (94) 25] STATIC

8. L.P. Csernai, BNL Nov 17-19 '03 7 Pressure – Soft Point? LBL, AGS, SPS: Collective flow – P-x vs. y Pressure sensitive Directed transverse flow decreases with increasing energy: [Holme, et al., 89] [D. Rischke, 95] [E. Shuryak, 95] OBSERVED ! But, does it recover at higher energies ? WHAT HAPPENS?

9. L.P. Csernai, BNL Nov 17-19 '03 8 Phase transition dynamics – Out of thermal eq. Transition to QGP 0.1 – 0.3 fm/c (PCM) Structure functions - valence quarks - see quarks (~stopped) Flux-tube models - immediate eq. - Bjorken ’83 - Gyulassy & Cs. ‘86 Hadronization Nucleation ~30-100fm/c - local thermal equilibrium - Cs. & Kapusta ’92 Out of eq. ph.tr. possible: - supercooled QGP - Csorgo & Cs. ’94 - Cs. & Mishustin ’95 - ~1-2 fm/c  Hadronization and Freeze-out MUST be simultaneous ! / No T,p,.. - How can the Stat.Model work?

10. L.P. Csernai, BNL Nov 17-19 '03 9 Multi Module Modeling FO surface FO transfer

11. L.P. Csernai, BNL Nov 17-19 '03 10 Multi Module Modeling on GRID

12. L.P. Csernai, BNL Nov 17-19 '03 11

13. L.P. Csernai, BNL Nov 17-19 '03 12 Fire streak picture - Only in 3 dimensions! Myers, Gosset, Kapusta, Westfall

14. L.P. Csernai, BNL Nov 17-19 '03 13 String rope --- Flux tube --- Coherent YM field

15. L.P. Csernai, BNL Nov 17-19 '03 14 Initial stage: Coherent Yang-Mills model [Magas, Csernai, Strottman, Phys. Rev. C64 (01) 014901]

16. L.P. Csernai, BNL Nov 17-19 '03 15 Expanding string ropes – Full energy conservation

17. L.P. Csernai, BNL Nov 17-19 '03 16 Yo – Yo Dynamics wo/ dissipation

18. L.P. Csernai, BNL Nov 17-19 '03 17 wo/ dissipation

19. L.P. Csernai, BNL Nov 17-19 '03 18 Initial state 3 rd flow component

20. L.P. Csernai, BNL Nov 17-19 '03 19 Modified Initial State In the previous model the fwd-bwd surface was too sharp  two propagating peaks Thus, after the formation of uniform streak, the expansion at its end is included in the model  This led to smoother energy density and velocity profiles  Z [fm] y e [GeV/ fm 3 ] [Magas, Csernai, Strottman, in pr.]

21. L.P. Csernai, BNL Nov 17-19 '03 20 Modified Initial State

22. L.P. Csernai, BNL Nov 17-19 '03 21 Matching Conditions  Conservation laws  Nondecreasing entropy Can be solved easily. Yields, via the “Taub adiabat” and “Rayleigh line”, the final state behind the hyper- surface. (See at freeze out.)

23. L.P. Csernai, BNL Nov 17-19 '03 22 3-Dim Hydro for RHIC (PIC)

24. L.P. Csernai, BNL Nov 17-19 '03 23 Multi Module Modeling Initial state - pre-equilibrium: Parton Cascade; Coherent Yang-Mills [Magas] Local Equilibrium  Hydro, EoS Final Freeze-out: Kinetic models, measurables - If QGP  Sudden and simultaneous hadronization and freeze out (indicated by HBT, Strangeness, Entropy puzzle)

25. L.P. Csernai, BNL Nov 17-19 '03 24 Relativistic Fluid Dynamics Eg.: from kinetic theory. BTE for the evolution of phase-space distribution: Then using microscopic conservation laws in the collision integral C: These conservation laws are valid for any, eq. or non-eq. distribution, f(x,p). These cannot be solved, more info is needed! Boltzmann H-theorem: (i) for arbitrary f, the entropy increases, (ii) for stationary, eq. solution the entropy is maximal,   EoS P = P (e,n) Solvable for local equilibrium!

26. L.P. Csernai, BNL Nov 17-19 '03 25 Relativistic Fluid Dynamics For any EoS, P=P(e,n), and any energy-momentum tensor in LE(!): Not only for high v!

27. L.P. Csernai, BNL Nov 17-19 '03 26 3-dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=0.0 fm/c, T max = 420 MeV, e max = 20.0 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. EoS: p= e/3 - 4B/3 B = 397 MeV/fm 3 ~ 4 times elongated !!

28. L.P. Csernai, BNL Nov 17-19 '03 27 3-dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=2.3 fm/c, T max = 420 MeV, e max = 20.0 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. 11.6 x 4.6 fm

29. L.P. Csernai, BNL Nov 17-19 '03 28 3-dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=4.6 fm/c, T max = 419 MeV, e max = 19.9 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. 14.5 x 4.9 fm

30. L.P. Csernai, BNL Nov 17-19 '03 29 3-dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=6.9 fm/c, T max = 418 MeV, e max = 19.7 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. 17.4 x 5.5 fm

31. L.P. Csernai, BNL Nov 17-19 '03 30 3-dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=9.1 fm/c, T max = 417 MeV, e max = 19.6 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. 20.3 x 5.8 fm

32. L.P. Csernai, BNL Nov 17-19 '03 31 3-dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=11.4 fm/c, T max = 416 MeV, e max = 19.5 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. 23.2 x 6.7 fm

33. L.P. Csernai, BNL Nov 17-19 '03 32 3-dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=13.7 fm/c, T max = 417 MeV, e max = 19.4 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. 26.1 x 7.3 fm

34. L.P. Csernai, BNL Nov 17-19 '03 33 3-dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=16.0 fm/c, T max = 417 MeV, e max = 19.4 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. 31.9 x 8.1 fm

35. L.P. Csernai, BNL Nov 17-19 '03 34 3-dim Hydro for RHIC Energies Au+Au E CM =65 GeV/nucl. b=0.5 b max A σ =0.08 => σ~10 GeV/fm e [ GeV / fm 3 ] T [ MeV] t=18.2 fm/c, T max = 417 MeV, e max = 19.4 GeV/fm 3, L x,y = 1.45 fm, L z =0.145 fm.. 34.8 x 8.7 fm

36. L.P. Csernai, BNL Nov 17-19 '03 35 Heavy Ion Coll. at RHIC - Transverse velocities - b=0.5 [ Strottman, Magas, Csernai, BCPL User Mtg. Trento, 2003 ] DYNAMIC z

37. L.P. Csernai, BNL Nov 17-19 '03 36 Multi Module Modeling Initial state - pre-equilibrium: Parton Cascade; Coherent Yang-Mills [Magas] Local Equilibrium  Hydro, EoS Final Freeze-out: F.O. Surface Final Freeze-out: Kinetic models - If QGP  Sudden and simultaneous hadronization and freeze out (indicated by HBT, Strangeness, Entropy puzzle ) Landau (1953), Milekhin (1958), Cooper & Frye (1974)

38. L.P. Csernai, BNL Nov 17-19 '03 37 [ Bernd R. Schlei (T-1) - LA-UR-03-3410 ] Freeze-Out Hyper-Surface Extraction with Digital Image Processing Techniques VESTA and Projections of FOHS (e.g., “Firestreaks” for Au + Au @ RHIC) x y z xyz - Projection t fixed Impact Parameter b = 0.5 3+1 D Hydrodynamic Density Data are based on “Firestreak” Initial Conditions; V. K. Magas, L. P. Csernai, D. Strottman, Nucl. Phys. A712 (2002) 167. In 3+1 D Hydrodynamical Calculations, VESTA is useful for the Graphical Rendering of Projections of FOHS. A Construction of a 4D FOHS requires a Generalization of VESTA into 4D. x z t xtz - Projection y fixed Impact Parameter b = 0.5

39. L.P. Csernai, BNL Nov 17-19 '03 38 Freeze-Out Hyper-Surface Extraction with Digital Image Processing Techniques Time-Sequence of FOHS Projections t1t1 t8t8 t2t2 t3t3 t4t4 t5t5 t6t6 t7t7 t 14 t 13 t 12 t 11 t 10 t9t9 3+1 D Hydrodynamic Density Data, courtesy D. Strottman, Theoretical Division, Los Alamos National Laboratory. VESTA Rendering of FOHS in 3+1 D Hydrodynamics at fixed Times (t 1 < … < t 14 ). x y z Impact Parameter b = 0.0 [ Bernd R. Schlei (T-1) - LA-UR-03-3410 ] 10 times elongated !!

40. L.P. Csernai, BNL Nov 17-19 '03 39 Bernd R. Schlei (T-1) 3+1 D Hydrodynamic Density Data, D. Strottman, Theoretical Division, Los Alamos National Laboratory. Freeze-Out Hyper-Surface Extraction with Digital Image Processing Techniques Movie: Time-Sequence of F.O. H-S Projections [ Bernd R. Schlei (T-1) LA-UR-03-3410 ] Y X Z 10 times elongated in z- direction, to compensate for L. contraction ! b=0.

41. L.P. Csernai, BNL Nov 17-19 '03 40 Y X Z b=0.5 b max Modified Initial State

42. L.P. Csernai, BNL Nov 17-19 '03 41

43. L.P. Csernai, BNL Nov 17-19 '03 42

44. L.P. Csernai, BNL Nov 17-19 '03 43 Quick Time Movie - External [Due to MS’s competitive business practices] Axonometric view Heavy Ion reaction - Surface visualization T = 139 MeV Hy-mov-004.mov

45. L.P. Csernai, BNL Nov 17-19 '03 44 Reaction Plane - [ X, Z ] X Z

46. L.P. Csernai, BNL Nov 17-19 '03 45

47. L.P. Csernai, BNL Nov 17-19 '03 46

48. L.P. Csernai, BNL Nov 17-19 '03 47

49. L.P. Csernai, BNL Nov 17-19 '03 48

50. L.P. Csernai, BNL Nov 17-19 '03 49

51. L.P. Csernai, BNL Nov 17-19 '03 50

52. L.P. Csernai, BNL Nov 17-19 '03 51 Quick Time - Movie - External [Due to MS’s competitive business practices] Reaction Plane Surface at T = 139 MeV Hy-mov-00.mov

53. L.P. Csernai, BNL Nov 17-19 '03 52 Multi Module Modeling Initial state - pre-equilibrium: Parton Cascade; Coherent Yang-Mills [Magas] Local Equilibrium  Hydro, EoS Final Freeze-out: F.O. Surface Final Freeze-out: Kinetic models QGP  Sudden and simultaneous hadronization and freeze out – CF formula  Problem 1: Conservation laws to non-eq!  Problem 2: Post FO, non-eq. distribution!

54. L.P. Csernai, BNL Nov 17-19 '03 53 Matching Conditions Again  Conservation laws  Nondecreasing entropy Can be solved easily. Yields, via the “Taub adiabat” and “Rayleigh line”, the final state behind the hyper- surface. (See at freeze out.)

55. L.P. Csernai, BNL Nov 17-19 '03 54 Freeze out [L Bravina et al.]

56. L.P. Csernai, BNL Nov 17-19 '03 55 Hypersurface

57. L.P. Csernai, BNL Nov 17-19 '03 56 Space-like hypersurface - Problem II

58. L.P. Csernai, BNL Nov 17-19 '03 57 Space-like hypersurface II

59. L.P. Csernai, BNL Nov 17-19 '03 58 Post F.O. - Cut-Jüttner distribution [Bugaev, Nucl.Phys.A606(96)559] No Eq., T, p, …, EoS !!! [Anderlik et al., Phys.Rev.C59(99)3309] Proposed by: Solved: p p x y Post F.O. distribution:  p m L m   f(p) V-parameter V-flow Matching conditions determine 5 parameters only. Ansatz in needed for final f(x,p) !

60. L.P. Csernai, BNL Nov 17-19 '03 59 Phase-Space FO probability

61. L.P. Csernai, BNL Nov 17-19 '03 60 Phase-Space FO probability AB C DEF Uniform =1 Time-like F.O. Space- like F.O. d 3   = u  [A. Anderlik, E. Molnar, et al.]

62. L.P. Csernai, BNL Nov 17-19 '03 61 Freeze out distribution with rescattering from kinetic model across a layer V=0 [V. Magas, et al.,] Heavy Ion Phys.9:193-216,1999

63. L.P. Csernai, BNL Nov 17-19 '03 62 Analytic fit to Kinetic Model Solution :.. [Karolis Tamosiunas et al.]

64. L.P. Csernai, BNL Nov 17-19 '03 63 Cancelling Juttner Distribution [Karolis Tamosiunas et al.]

65. L.P. Csernai, BNL Nov 17-19 '03 64 Sudden Freeze-Out & Hadronization from Sc. QGP Negative P (Positive T) [O. Heggo-Hansen, MSc. Thesis, ‘03 ]

66. L.P. Csernai, BNL Nov 17-19 '03 65 Global Flow Directed Transverse flow Elliptic flow 3 rd flow component (anti - flow) 3 rd flow component (anti - flow) Squeeze out

67. L.P. Csernai, BNL Nov 17-19 '03 66 Talk by S. Manly Note: (1) There is no boost invariance !!. (2) Hydro [Hirano] yields less stopping

68. L.P. Csernai, BNL Nov 17-19 '03 67 3 rd flow component and QGP Csernai & Röhrich [Phys.Lett.B458(99)454] observed a 3 rd flow component at SPS energies, not discussed before. Also observed that in ALL earlier fluid dynamical calculations with QGP in the EoS there is 3 rd flow comp. The effect was absent without QGP. In string and RQMD models only peripheral collision showed the effect (shadowing).

69. L.P. Csernai, BNL Nov 17-19 '03 68 3 rd flow component Hydro [Csernai, HIPAGS’93]

70. L.P. Csernai, BNL Nov 17-19 '03 69 Third flow component [SPS NA49]

71. L.P. Csernai, BNL Nov 17-19 '03 70 Anti-flow from shadowing : [ L. Bravina, et al., PL B470 (99) 27.] Only for b > 8 fm ! N 

72. L.P. Csernai, BNL Nov 17-19 '03 71 A=0.065 11.4 fm/c

73. L.P. Csernai, BNL Nov 17-19 '03 72 “Wiggle”, Pb+Pb, E lab =40 and 158GeV [NA49] Talk by A. Wetzler Preliminary 158 GeV/A Different scale for 40 and 158 GeV! The “wiggle” is there! v 1  0

74. L.P. Csernai, BNL Nov 17-19 '03 73 V-1 flow at RHIC/STAR

75. L.P. Csernai, BNL Nov 17-19 '03 74 Consequences  If v 1  0, earlier v 2 results have to be modified (re-analyzed)  3-dim models and 3-dim initial conditions are needed to fit data  Impact parameter / multiplicity dependence is essential (more data)  Detailed models including equilibrium and non-equilibrium features will be required to describe the data

76. L.P. Csernai, BNL Nov 17-19 '03 75 Flow & Azimuthal effects in HBT HBT is biased by theor. Assumptions, eq. C(q,K)  R=2fm /Gauss | R=8fm/u.Sphr. Flow changes C(q,K) essentially ! Use of analysis based on static sphr. Gauss. S is ? [STAR ’01, Phenix ’02, Hydro: P Kolb et al ’03]

77. L.P. Csernai, BNL Nov 17-19 '03 76 Conclusions Hydro works well! 3-dim. hydro, initial & final state models are important!  Local Equilibrium and EoS exists ( in part of the reaction ) We have a good possibility to learn more and more about the EoS, with improved experimental and theoretical accuracy! The detailed determination of flow patterns is vital for HBT, and for ALL observables influenced by the collective collision dynamics.