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

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Presentation on theme: "LP. Csernai, NWE'2001, Bergen1 Part II Relativistic Hydrodynamics For Modeling Ultra-Relativistic Heavy Ion Reactions."— Presentation transcript:

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

3 LP. Csernai, NWE'2001, Bergen2 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) Landau (1953), Milekhin (1958), Cooper & Frye (1974) Experiment

4 LP. Csernai, NWE'2001, Bergen3 Global Flow Directed Transverse flow Elliptic flow 3 rd flow component (anti - flow) Squeeze out

5 LP. Csernai, NWE'2001, Bergen4 Spherical Flow from Identified Particle Spectra p T (GeV/c) Fit  K, p spectra to obtain ~ 0.35 T fo ~ 180-200 MeV Systematic errors: to be determined [W.A. Zajc, QM’2001]

6 LP. Csernai, NWE'2001, Bergen5 More spherical flow at RHIC ! [N.Xu, QM’2001]

7 LP. Csernai, NWE'2001, Bergen6 Global Flow Directed Transverse flow Elliptic flow 3 rd flow component (anti - flow) Squeeze out

8 LP. Csernai, NWE'2001, Bergen7 Repulsion Driven by Gradients in Mean-Field Flow decreases as function of E beam Measured sideways flow cannot be reproduced by cascade calculations (RQMD 2.3) – “thermal” pressure insufficient amount of deflection Additional repulsion caused by gradients in mean-field E895, Phys. Rev. Lett 84, 5488 (2000) Mike Lisa E895 Talk [C.Ogilvie, QM’2001]

9 LP. Csernai, NWE'2001, Bergen8 Global Flow Directed Transverse flow Elliptic flow 3 rd flow component (anti - flow) Squeeze out

10 LP. Csernai, NWE'2001, Bergen9

11 10 Elliptic flow - SPS - NA49

12 LP. Csernai, NWE'2001, Bergen11 p T dependence for ,p Hydro calculations: P. Huovinen, P. Kolb and U. Heinz

13 LP. Csernai, NWE'2001, Bergen12 Elliptic flow at RHIC [Huovinen, QM’2001]

14 LP. Csernai, NWE'2001, Bergen13 Elliptic flow in MPC [ D. Molnar, QM’2001 ]

15 LP. Csernai, NWE'2001, Bergen14

16 LP. Csernai, NWE'2001, Bergen15 Elliptic flow vs. Squeeze out At LBL, GSI, AGS flow is orthogonal to the reaction plane: Squeeze out At SPS, RHIC central flow is in the reaction plane: Elliptic flow. This is due to the initial state and shadowing. [R. Lacey, QM’2001]

17 LP. Csernai, NWE'2001, Bergen16 Comparison of all v 2 results PHENIX (p T >500 MeV) n ch /n max v2v2 [P.Steinberg, QM’2001]

18 LP. Csernai, NWE'2001, Bergen17

19 LP. Csernai, NWE'2001, Bergen18 Global Flow Directed Transverse flow Elliptic flow 3 rd flow component (anti - flow) 3 rd flow component (anti - flow) Squeeze out

20 LP. Csernai, NWE'2001, Bergen19 K 0 s Anti-Flow Au+Au 6 AGeV Striking opposite flow for K 0 s Reproduced using repulsive mean-field for K 0 Chris Pinkenberg E895 Talk proton Chung et al., Phys. Rev Lett 85, 940 (2000) Pal et al., Phys. Rev. C 62, 061903 (2000) K0sK0s

21 LP. Csernai, NWE'2001, Bergen20 Third flow component [SPS NA49]

22 LP. Csernai, NWE'2001, Bergen21 Third flow component / SPS / NA49

23 LP. Csernai, NWE'2001, Bergen22 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). The effect is attributed to a flat (Landau type) initial condition. Similarity to elliptic flow.

24 LP. Csernai, NWE'2001, Bergen23 3 rd flow component Hydro [Csernai, HIPAGS’93]

25 LP. Csernai, NWE'2001, Bergen24 STRANGENESS and ENTROPY [N.Xu, QM’2001] Entropy Pion number T³ Strangeness Phase transition [Gazdiczki & Gorenstein]

26 LP. Csernai, NWE'2001, Bergen25 Strange baryon enhancement m Enhancement of  yield in central Pb+Pb compared to p+Be = 15

27 LP. Csernai, NWE'2001, Bergen26 Strange antibaryons In QGP s s-bar threshold is low Strangeness enhance. Hadronic and String models can reproduce this only if: Massive objects are formed – string ropes, quark clusters (QGP) [Quercigh, CERN 2000]

28 LP. Csernai, NWE'2001, Bergen27 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) 1 2 3

29 LP. Csernai, NWE'2001, Bergen28 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.]

30 LP. Csernai, NWE'2001, Bergen29 Modified Initial State

31 LP. Csernai, NWE'2001, Bergen30 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 8.7 x 4.4 fm

32 LP. Csernai, NWE'2001, Bergen31 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

33 LP. Csernai, NWE'2001, Bergen32 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

34 LP. Csernai, NWE'2001, Bergen33 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

35 LP. Csernai, NWE'2001, Bergen34 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

36 LP. Csernai, NWE'2001, Bergen35 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

37 LP. Csernai, NWE'2001, Bergen36 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

38 LP. Csernai, NWE'2001, Bergen37 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

39 LP. Csernai, NWE'2001, Bergen38 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

40 LP. Csernai, NWE'2001, Bergen39 NEXT Freeze-out Discontinuities in hydro --- Eq. => Eq. Freeze-out to non-eq. Kinetic freeze-out

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