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.

Slides:

Advertisements

Similar presentations

Mass, Quark-number, Energy Dependence of v 2 and v 4 in Relativistic Nucleus- Nucleus Collisions Yan Lu University of Science and Technology of China Many.

Advertisements

Elliptic flow of thermal photons in Au+Au collisions at 200GeV QNP2009 Beijing, Sep , 2009 F.M. Liu Central China Normal University, China T. Hirano.

Supported by DOE 11/22/2011 QGP viscosity at RHIC and LHC energies 1 Huichao Song 宋慧超 Seminar at the Interdisciplinary Center for Theoretical Study, USTC.

LP. Csernai, Sept. 4, 2001, Palaiseau FR 1 L.P. Csernai, C. Anderlik, V. Magas, D. Strottman.

Duke University Chiho NONAKA in Collaboration with Masayuki Asakawa (Kyoto University) Hydrodynamical Evolution near the QCD Critical End Point November,

Duke University Chiho NONAKA in Collaboration with Masayuki Asakawa (Kyoto University) Hydrodynamical Evolution near the QCD Critical End Point June 26,

Elliptic Flow Results From a Hybrid Model

LP. Csernai, Montreal Topics in Heavy Ion Collisions, 2003 Montreal, June 25-28, 2003 Flow effects and their measurable consequences in ultra-relativistic.

L.P. Csernai 1 Freeze-out and constituent quark formation in a space-time layer.

Phase transition of hadronic matter in a non-equilibrium approach Graduate Days, Frankfurt, , Hannah Petersen, Universität Frankfurt.

First Results From a Hydro + Boltzmann Hybrid Approach DPG-Tagung, Darmstadt, , Hannah Petersen, Universität Frankfurt.

Norway. 3-dim. QGP Fluid Dynamics and Flow Observables László Csernai (Bergen Computational Physics Lab., Univ. of Bergen)

The speed of sound in a magnetized hot Quark-Gluon-Plasma Based on: Neda Sadooghi Department of Physics Sharif University of Technology Tehran-Iran.

CERN May Heavy Ion Collisions at the LHC Last Call for Predictions Initial conditions and space-time scales in relativistic heavy ion collisions.

DNP03, Tucson, Oct 29, Kai Schweda Lawrence Berkeley National Laboratory for the STAR collaboration Hadron Yields, Hadrochemistry, and Hadronization.

Hydrodynamic Approaches to Relativistic Heavy Ion Collisions Tetsufumi Hirano RIKEN BNL Research Center.

Freeze-Out in a Hybrid Model Freeze-out Workshop, Goethe-Universität Frankfurt Hannah Petersen.

Marcus Bleicher, WWND 2008 A fully integrated (3+1) dimensional Hydro + Boltzmann Hybrid Approach Marcus Bleicher Institut für Theoretische Physik Goethe.

5-12 April 2008 Winter Workshop on Nuclear Dynamics STAR Particle production at RHIC Aneta Iordanova for the STAR collaboration.

Properties of the Quantum Fluid at RHIC Strangeness in Quark Matter March 26-31, 2006.

DPG spring meeting, Tübingen, March Kai Schweda Lawrence Berkeley National Laboratory for the STAR collaboration Recent results from STAR at RHIC.

WWND, San Diego1 Scaling Characteristics of Azimuthal Anisotropy at RHIC Michael Issah SUNY Stony Brook for the PHENIX Collaboration.

Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it? I. Radial flow fluctuations:

Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it? I. Transverse flow fluctuations:

Sept WPCF-2008 Initial conditions and space-time scales in relativistic heavy ion collisions Yu. Sinyukov, BITP, Kiev Based on: Yu.S., I. Karpenko,

Particle Spectra at AGS, SPS and RHIC Dieter Röhrich Fysisk institutt, Universitetet i Bergen Similarities and differences Rapidity distributions –net.

Flow Vorticity and Rotation in Peripheral HIC Dujuan Wang CBCOS, Wuhan, 11/05/2014 University of Bergen, Norway.

Collective Flow in Heavy-Ion Collisions Kirill Filimonov (LBNL)

Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it? I. Radial flow fluctuations:

Flow fluctuation and event plane correlation from E-by-E Hydrodynamics and Transport Model LongGang Pang 1, Victor Roy 1,, Guang-You Qin 1, & Xin-Nian.

The effects of viscosity on hydrodynamical evolution of QGP 苏中乾大连理工大学 Dalian University of Technology.

Two particle correlation method to Detect rotation in HIC Dujuan Wang University of Bergen Supervisor: Laszlo P. Csernai.

LP. Csernai, PASI'2002, Brazil1 Part I Relativistic Hydrodynamics For Modeling Ultra-Relativistic Heavy Ion Reactions.

1 Roy Lacey ( for the PHENIX Collaboration ) Nuclear Chemistry Group Stony Brook University PHENIX Measurements of 3D Emission Source Functions in Au+Au.

Workshop for Particle Correlations and Femtoscopy 2011

Jaipur February 2008 Quark Matter 2008 Initial conditions and space-time scales in relativistic heavy ion collisions Yu. Sinyukov, BITP, Kiev (with participation.

Relativistic Hydrodynamics T. Csörgő (KFKI RMKI Budapest) new solutions with ellipsoidal symmetry Fireball hydrodynamics: Simple models work well at SPS.

Zagreb, Croatia, 2015/04/20 Csörgő, T. 1 New exact solutions of hydrodynamcs and search for the QCD Critical Point T. Csörgő 1,2 with I.Barna 1 and M.

Joint CATHIE/TECHQM Workshop, BNL, Dec 14-18, 2009 Huichao Song The Ohio State University Supported by DOE 12/14/2009 Lawrence Berkeley National Lab QGP.

Norway Relativistic Hydrodynamics and Freeze-out László Csernai (Bergen Computational Physics Lab., Univ. of Bergen)

Anisotropic flow, Azimuthal Balance Function, and Two-charged-particle Azimuthal Correlations in RQMD and AMPT We are very grateful to Zhixu Liu and Jiaxin.

LP. Csernai, NWE'2001, Bergen1 Part II Relativistic Hydrodynamics For Modeling Ultra-Relativistic Heavy Ion Reactions.

Flow fluctuation and event plane correlation from E-by-E Hydrodynamics and Transport Model Victor Roy Central China Normal University, Wuhan, China Collaborators.

Dynamical equilibration of strongly- interacting ‘infinite’ parton matter Vitalii Ozvenchuk, in collaboration with E.Bratkovskaya, O.Linnyk, M.Gorenstein,

Presentation for NFR - October 19, Trine S.Tveter Recent results from RHIC Systems studied so far at RHIC: - s NN 1/2 = 

Masashi Kaneta, First joint Meeting of the Nuclear Physics Divisions of APS and JPS 1 / Masashi Kaneta LBNL

Peter Kolb, November 18, 2003Momentum Anisotropies1 Momentum Anisotropies -- Probing the detailed Dynamics Department of Physics and Astronomy State University.

Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro1 What did we learn, and what will we learn from Hydro CIPANP 2003 New York City, May 22, 2003.

LP. Csernai, NWE'2001, Bergen1 Part III Relativistic Hydrodynamics For Modeling Ultra-Relativistic Heavy Ion Reactions.

11/18/2003Tetsufumi Hirano (RBRC)1 Rapidity Dependence of Elliptic Flow from Hydrodynamics Tetsufumi Hirano RIKEN BNL Research Center (Collaboration with.

T. Csörgő 1,2 Scaling properties of elliptic flow in nearly perfect fluids 1 MTA KFKI RMKI, Budapest, Hungary 2 Department of.

WPCF-2005, Kromirez A. Ster Hungary 1 Comparison of emission functions in h+p, p+p, d+A, A+B reactions A. Ster 1,2, T. Csörgő 2 1 KFKI-RMKI, 2 KFKI-MFA,

Results from an Integrated Boltzmann+Hydrodynamics Approach WPCF 2008, Krakau, Jan Steinheimer-Froschauer, Universität Frankfurt.

Heavy-Ion Physics - Hydrodynamic Approach Introduction Hydrodynamic aspect Observables explained Recombination model Summary 전남대 이강석 HIM

R. Lednicky: Joint Institute for Nuclear Research, Dubna, Russia I.P. Lokhtin, A.M. Snigirev, L.V. Malinina: Moscow State University, Institute of Nuclear.

Roy A. Lacey, Stony Brook, ISMD, Kromĕříž, Roy A. Lacey What do we learn from Correlation measurements at RHIC.

Budapest, 4-9 August 2005Quark Matter 2005 HBT search for new states of matter in A+A collisions Yu. Sinyukov, BITP, Kiev Based on the paper S.V. Akkelin,

PhD student at the International PhD Studies Institute of Nuclear Physics PAN Institute of Nuclear Physics PAN Department of Theory of Structure of Matter.

Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/ Azimuthally Sensitive Buda-Lund Hydrodynamic Model and Fits to Spectra, Elliptic.

Particle emission in hydrodynamic picture of ultra-relativistic heavy ion collisions Yu. Karpenko Bogolyubov Institute for Theoretical Physics and Kiev.

JET Collaboration Meeting June 17-18, 2014, UC-Davis1/25 Flow and “Temperature” of the Parton Phase from AMPT Zi-Wei Lin Department of Physics East Carolina.

“ Critical Point and Onset of Deconfinement ” Florence, July 2nd-9th 2006.

Japanese Physics Society meeting, Hokkaido Univ. 23/Sep/2007, JPS meeting, Sapporo, JapanShinIchi Esumi, Inst. of Physics, Univ. of Tsukuba1 Collective.

Helen Caines Yale University Strasbourg - May 2006 Strangeness and entropy.

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.

Duke University 野中千穂 Hadron production in heavy ion collision: Fragmentation and recombination in Collaboration with R. J. Fries (Duke), B. Muller (Duke),

Chiho Nonaka QM2009 Nagoya University Chiho NONAKA March 31, Matter 2009, Knoxville, TN In collaboration with Asakawa, Bass, and Mueller.

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 1 Observables and initial conditions for rotating and expanding fireballs T. Csörgő 1,2, I.Barna 1.

Hydro + Cascade Model at RHIC

Norwegian High-Energy Heavy Ion Theory

Presentation transcript:

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

L.P. Csernai, BNL Nov '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

L.P. Csernai, BNL Nov '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)

L.P. Csernai, BNL Nov '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) ] STATIC

L.P. Csernai, BNL Nov '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

L.P. Csernai, BNL Nov '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, ~ fermi 3, fluctuations are REAL !!! Supercomputers are needed ! [Csernai, Neda PL B337 (94) 25] STATIC

L.P. Csernai, BNL Nov '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?

L.P. Csernai, BNL Nov '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?

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

L.P. Csernai, BNL Nov '03 10 Multi Module Modeling on GRID

L.P. Csernai, BNL Nov '03 11

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

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

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

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

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

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

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

L.P. Csernai, BNL Nov '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.]

L.P. Csernai, BNL Nov '03 20 Modified Initial State

L.P. Csernai, BNL Nov '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 hypersurface. (See at freeze out.)

L.P. Csernai, BNL Nov ' Dim Hydro for RHIC (PIC)

L.P. Csernai, BNL Nov '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)

L.P. Csernai, BNL Nov '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!

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

L.P. Csernai, BNL Nov ' 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 !!

L.P. Csernai, BNL Nov ' 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 x 4.6 fm

L.P. Csernai, BNL Nov ' 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 x 4.9 fm

L.P. Csernai, BNL Nov ' 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 x 5.5 fm

L.P. Csernai, BNL Nov ' 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 x 5.8 fm

L.P. Csernai, BNL Nov ' 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 x 6.7 fm

L.P. Csernai, BNL Nov ' 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 x 7.3 fm

L.P. Csernai, BNL Nov ' 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 x 8.1 fm

L.P. Csernai, BNL Nov ' 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 x 8.7 fm

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

L.P. Csernai, BNL Nov '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)

L.P. Csernai, BNL Nov '03 37 [ Bernd R. Schlei (T-1) - LA-UR ] Freeze-Out Hyper-Surface Extraction with Digital Image Processing Techniques VESTA and Projections of FOHS (e.g., “Firestreaks” for Au + RHIC) x y z xyz - Projection t fixed Impact Parameter b = 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

L.P. Csernai, BNL Nov '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 ] 10 times elongated !!

L.P. Csernai, BNL Nov '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 ] Y X Z 10 times elongated in z- direction, to compensate for L. contraction ! b=0.

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

L.P. Csernai, BNL Nov '03 41

L.P. Csernai, BNL Nov '03 42

L.P. Csernai, BNL Nov '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

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

L.P. Csernai, BNL Nov '03 45

L.P. Csernai, BNL Nov '03 46

L.P. Csernai, BNL Nov '03 47

L.P. Csernai, BNL Nov '03 48

L.P. Csernai, BNL Nov '03 49

L.P. Csernai, BNL Nov '03 50

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

L.P. Csernai, BNL Nov '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!

L.P. Csernai, BNL Nov '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 hypersurface. (See at freeze out.)

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

L.P. Csernai, BNL Nov '03 55 Hypersurface

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

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

L.P. Csernai, BNL Nov '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) !

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

L.P. Csernai, BNL Nov '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.]

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

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

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

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

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

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

L.P. Csernai, BNL Nov ' 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).

L.P. Csernai, BNL Nov ' rd flow component Hydro [Csernai, HIPAGS’93]

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

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

L.P. Csernai, BNL Nov '03 71 A= fm/c

L.P. Csernai, BNL Nov '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

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

L.P. Csernai, BNL Nov '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

L.P. Csernai, BNL Nov '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]

L.P. Csernai, BNL Nov '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.