1. Particle emission in hydrodynamic picture of ultra-relativistic heavy ion collisions Yu. Karpenko Bogolyubov Institute for Theoretical Physics and Kiev National Taras Shevchenko University M.S. Borysova, Yu.M.Sinyukov, S.V.Akkelin, B.Erazmus, Iu.A.Karpenko, nucl- th/0507057 (to be published in Phys. Rev. C), Yu.M. Sinyukov, Iu.A. Karpenko, nucl-th/0505041, nucl-th/0506002 (to be published in HIP)

2. Picture of evolution

3.  K  p  n  d, Hadronization Initial state Pre-equilibrated state QGP and hydro Freeze-out

4. Hydro model Sudden transition from local equilibrium to free streaming at some hypersurface  + EoS p=p( ε ) ideal fluid : (Ideal) hydrodynamics Cooper-Frye prescription : + initial conditions

5. Continuous emission Attempt to account nonzero emission time : (Blast-wave, Buda-Lund, …)  No x-t correlations : at early times – only surface emission!  Emission function is not proportional to the l.eq. distribution function (Sinyukov et.al. PRL 2002) Emission function “smeared” in  :

6. Freeze-out  Space-like sectors  Non-space-like sectors Continuous emission Enclosed freeze-out hypersurface, containing :

7. The idea of interferometry measurements CF=1+  cos q  x  |f(x,p) p 1 p 2 x1x1 x 2 q = p 1 - p 2,  x = x 1 - x 2  2 1 |q| 1/R 0 2R 0 f(x,p)

8. “General” parameterization at |q|  0 Podgoretsky’83, Bertsch-Pratt’95 Particles on mass shell & azimuthal symmetry  5 variables: q = {q x, q y, q z }  {q out, q side, q long }, pair velocity v = {v x,0,v z } q 0 = qp/p 0  qv = q x v x + q z v z y  side x  out  transverse pair velocity v t z  long  beam R i - Interferometry radii:  cos q  x  =1-½  (q  x) 2  …  exp(-R x 2 q x 2 –R y 2 q y 2 -R z 2 q z 2 )

9. R o /R s Using gaussian approximation of CFs (q  0), Long emission time results in positive contribution to R o /R s ratio Positive r out -t correlations give negative contribution to R o /R s ratio In the Bertsch-Pratt frame where Experimental data : Ro/Rs  1

10. To describe R o /R s ratio with protracted particle emission, one needs positive r out -t correlations

11. The model of continuous emission volume emission surface emission Induces space- time correlations for emission points (M.S.Borysova, Yu.M. Sinyukov, S.V.Akkelin, B.Erazmus, Iu.A.Karpenko, nucl-th/0507057, to be published in Phys. Rev. C)

12. Cooper-Frye prescription Simplest modification of CFp (for non-space-like f.o. hypersurface): (Sinyukov, Bugaev) Excludes particles that reenter the system crossing the outer side of surface in Cooper- Frye picture of emission.

13. Results : spectra

14. Results : interferometry radii

15. Results : R o /R s

16. Relativistic ideal hydrodynamics + EoS p=p( ε ) ideal fluid : + (additional equations depicting charge conservation)

17. New hydro solution The new class of analytic (3+1) hydro solutions (Yu.M.Sinyukov, Yu.A.Karpenko, nucl-th/0505041, nucl-th/0506002 - to be published in HIP) For “soft” EoS, p=p 0 =const Satisfies the condition of accelerationless : (quasi-inertial flows similar to Hwa/Bjorken and Hubble ones).

18. New hydro solution Is a generalization of known Hubble flow and Hwa/Bjorken solution with c s =0 :

19. Thermodynamical relations Chemically equilibrated evolution Chemically frozen case for particle number Density profile for energy and quantum number (particle number, if it conserves): with corresponding initial conditions.

20. Dynamical realization of freeze-out paramerization. Particular solution for energy density: System is a finite in the transverse direction and is an approximately boost-invariant in the long- direction at freeze-out.

21. Freeze-out conditions Impose a freeze-out at constant total energy density, and presume that this HS is confined in a space-time 4-volume which belongs to the region of applicability of our solution with constant pressure.

22. Dynamical realization of enclosed f.o. hypersurface Geometry : R t,max R t,0 decreases with rapidity increase. No exact boost invariance!

23. Thermodynamics Chemical potentials  (T) for each particle sort Smoothly decreases on t :

24. Observables from the latter calculations : spectra

25. Observables from the latter calculations : interferometry radii

26. Observables from the latter calculations : Ro/Rs ratio

27. Numerical hydro testing (T. Hirano, arXiv : nucl-th/0108004)

29. Conclusions The continuous hadronic emission in A+A collisions can be taken into account by the (generalized) Cooper-Frye prescription for enclosed freeze-out hypersurface. The phenomenological parameterization for enclosed hypersurface with positive (t-r) correlations can be reproduced by applying natural freeze-out criteria to the new exact solution of relativistic hydrodynamics. The proton, pion an kaon single particle momentum spectra and pion HBT radii in central RHIC  s=200 GeV Au+Au collisions are reproduced with physically reasonable set of the parameters that is similar in both approaches.

30. Conclusions Successful description of data needs protracted hadronic emission (  9 fm/c) from “surface” sector of the freeze-out hypersurface, and initial flows in transverse direction. The fitting temperature is about 110 MeV on the “volume” part of hypersurface and 130-150 MeV on the “surface” part.

31. Thank you for your attention

32. Extra slides

33. Known relativistic hydro solutions Hubble flow Hwa/Bjorken solution Biró solution spherical symmetry longitudinal boost invariance, cylindrical symmetry longitudinal boost invariance

34. Kinetic description & sudden freeze-out Duality in hydro-kinetic approach to A+A collisions (S.V. Akkelin, M.S. Borysova, Yu.M. Sinyukov, HIP, 2005) Evolution of observables in a numerical kinetic model (N.S. Amelin, R. Lednicky, L.I. Malinina, Yu.M. Sinyukov, Phys.Rev.C); Yu.M.Sinyukov, proc. ISMD2005 & WPCF 2005