2. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 1 Azimuthally Sensitive Buda-Lund Hydrodynamic Model and Fits to Spectra, Elliptic Flow and asHBT András Ster 1,, M.Csanád 2, T.Csörgő 1, B. Tomasik 3 MTA KFKI RMKI, Budapest, Hungary 1 MTA KFKI RMKI, Budapest, Hungary, ELTE University, Budapest, Hungary 2 ELTE University, Budapest, Hungary, Univ. Mat. Bela, Banska Bystrica, Slovakia 3 Univ. Mat. Bela, Banska Bystrica, Slovakia Buda-Lund hydro model Buda-Lund hydro model Observables Observables Review of old central hydro results Review of old central hydro results New non-central hydro results New non-central hydro results Conclusion Conclusion

3. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 2 The Buda-Lund hydro model General form of a particle emission function General form of a particle emission function With (Boltzmann) probability distribution for fluids With (Boltzmann) probability distribution for fluids

4. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 3 The Buda-Lund hydro model hypersurface hypersurface flow field flow field chemical potential chemical potential temperature temperature must comply with the 5 differential equations of fluid dynamics: must comply with the 5 differential equations of fluid dynamics: - continuity - continuity - momentum conservation - momentum conservation - energy conservation - energy conservation

5. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 4 The Buda-Lund hydro model Equations of non-relativistic inviscid fluid dynamics Equations of non-relativistic inviscid fluid dynamics Not closed, EoS needed, for example Not closed, EoS needed, for example

6. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 5 The Buda-Lund hydro model 3D expansion with axial or ellipsoidal symmetry 3D expansion with axial or ellipsoidal symmetry Local thermal equilibrium Local thermal equilibrium Analytic expressions for the observables Analytic expressions for the observables Reproduction known exact hydro solutions (nonrelativistic, hubble and bjorken limits) Reproduction known exact hydro solutions (nonrelativistic, hubble and bjorken limits) Core-halo picture (long lived resonances) Core-halo picture (long lived resonances) M. Csanád, T.Csörgő, B. Lörstad: Nucl.Phys.A742:80-94,2004; nucl-th/0310040 5 model principles 5 model principles

7. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 6 The Buda-Lund Hydro Model Buda-Lund form of hydro fields: in several cases parametric solutions of hydrodynamics see M. Csanád’s talk

8. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 7 The Buda-Lund Hydro Model (2) Where (in case of axial symmetry): Where (in case of axial symmetry): = H t r t H t :transverse Hubble constant

9. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 8 The Buda-Lund hydro model (3) Observables Observables

10. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 9 Buda-Lund Hydro: Observables Final form of the Invariant Momentum Distribution: Final form of the Invariant Momentum Distribution:

11. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 10 Buda-Lund Hydro Model: HBT radii Final form of the HBT radii: Final form of the HBT radii:

12. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 11 N. M. Agababyan et al, EHS/NA22, PLB 422 (1998) 395 T. Csörgő, hep-ph/001233, Heavy Ion Phys. 15 (2002) 1-80 Buda-Lund fits to NA22 h+p

13. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 12 Emission function from NA22 h+p

14. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 13 BudaLund fits to SPS Pb+Pb A. Ster, T.Csörgő, B. Lörstad, Nucl.Phys. A661 (1999) 419-422, nucl-th/9907338 NA49NA44

15. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 14 Emission function from SPS Pb+Pb

16. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 15 A. Ster, et al., Acta Phys.Polon. B35 (2004) 191-196, nucl-th/0311102 BudaLund fits to RHIC Au+Au

17. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 16 Emission function from RHIC Au+Au

18. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 17 M. Csanád, et al., J.Phys.G30: S1079-S1082, 2004, nucl-th/0403074 http://www.kfki.hu/~csorgo/budalund/budalund1.5.qm04.tar.gzudalund1.5.qm04.tar.gz BudaLund fits to RHIC Au+Au

19. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 18 Emission function from RHIC Au+Au

20. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 19 Buda-Lund fit results

21. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 20 BudaLund fits to RHIC preliminary p+p T. Csörgő, et al., Heavy Ion Physics, hep-ph/0406042

22. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 21 Emission function from RHIC p+p

23. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 22 BudaLund fit results

24. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 23 BudaLund fits to NA49 data (preliminary HBT, work in progress)

25. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 24 BudaLund fits to NA49 data (preliminary HBT, work in progress)

26. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 25 BudaLund fit results of NA49 data

27. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 26 source parameter excitation functions

28. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 27 Models with acceptable results: nucl-th/0207016 Buda-Lund / core-halo model. T.Csörgő. A. Ster, Heavy Ion Phys. 17 (2003) 295-312. nucl-th/0204054Multiphase Trasport model (AMPT). Z. Lin, C. M. Ko, S. Pal. nucl-ex/0307026Blast wave model. F. Retiére for STAR. nucl-th/0205053Hadron cascade model. T. Humanic. nucl-th/02080683D hydro model. T. Hirano, & T.Tsuda. hep-ph/0209054Hadron model. W.Broniowski, A. Baran W. Florkowski. Other interesting models: Some other hydro models

29. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 28 Femptoscopy of QGP BudaLund fits indicate: scaling of HBT radii BudaLund prediction (1995): each R 2 ~ 1 / m t

30. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 29 BudaLund model describes single particle distributions, rapidity distributions, HBT correlation function radii w/o puzzle in the following reactions: BudaLund model describes single particle distributions, rapidity distributions, HBT correlation function radii w/o puzzle in the following reactions: h+p @SPS, p+p @RHIC, Pb+Pb @SPS, h+p @SPS, p+p @RHIC, Pb+Pb @SPS, Au+Au @RHIC Au+Au @RHIC Rings of fire in h+p @SPS and p+p @RHIC Rings of fire in h+p @SPS and p+p @RHIC Fireballs in Pb+Pb @SPS and Au+Au @RHIC Fireballs in Pb+Pb @SPS and Au+Au @RHIC T < T c in h+p and Pb+Pb @SPS T < T c in h+p and Pb+Pb @SPS T > T c in p+p and Au+Au @RHIC ; T c (=172±3MeV) T > T c in p+p and Au+Au @RHIC ; T c (=172±3MeV) Conclusions on central collisions Conclusions on central collisions

31. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 30 asBuda-Lund fits to non-central RHIC data Model extensions to ellipsoidal symmetry for elliptic flow: calculate 2nd harmonic coefficient of anisotropy:

32. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 31 BudaLund fits to non-central RHIC data Exact non-relativistic result for elliptic flow: I n : modified Bessel functions I n : modified Bessel functions Effective temperatures in reaction plane and in perp. For detailed calculations see: M. Csanád et al., hep-ph/0801.4434v2

33. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 32 BudaLund fits to non-central RHIC data Model extensions to ellipsoidal symmetry for asHBT radii: for asHBT radii: X=R x,Y=R y We found that „a” is different in each direction

34. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 33 asBuda-Lund fits to non-central RHIC data Model extensions to ellipsoidal symmetry for azimuthally integrated spectra: Calculate the volume term for ellipsoids : replaced R 2 t by R x *R y

35. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 34 asBudaLund fits to non-central RHIC data

36. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 35 asBuda-Lund fit results of non-central RHIC data

37. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 36 BudaLund geometrical picture of non-central RHIC reactions RxRx RyRy R x > R y Schematic view 20-30% ~ b = 8-12 fm

38. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 37 Universal v2 scaling predicted by BudaLund model (2003)

39. Andras. Ster, RMKI, Hungary ZIMANYI-SCHOOL’09, Budapest, 01/12/2009 38 asBuda-Lund model describes single particle distributions, elliptic flow and asHBT correlation function radii of 20-30% centrality data of 200 GeV Au+Au reactions at RHIC. asBuda-Lund model describes single particle distributions, elliptic flow and asHBT correlation function radii of 20-30% centrality data of 200 GeV Au+Au reactions at RHIC. We find that T drops to 179 MeV from ~200 MeV of central collisions. We find that T drops to 179 MeV from ~200 MeV of central collisions. The source at freeze-out was found to be slightly extended in the reaction plane ( R x > R y ), in agreement with M. Csanád’s conclusion The source at freeze-out was found to be slightly extended in the reaction plane ( R x > R y ), in agreement with M. Csanád’s conclusion Conclusion Conclusion