Particle emission in hydrodynamic picture of ultra-relativistic heavy ion collisions

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

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

5. Continuous emission Attempt to account nonzero emission time : (Blast-wave, Buda-Lund, …) Emission function “smeared” in  : • 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)

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

7. The idea of interferometry measurements p1 CF=1+cos qx|f(x,p) x1 f(x,p)  x2 2 p2 2R0 1/R0 q =p1- p2 , x = x1- x2 |q| 1

8. “General” parameterization at |q|  0 Podgoretsky’83, Bertsch-Pratt’95 Particles on mass shell & azimuthal symmetry  5 variables: q = {qx , qy , qz}  {qout , qside , qlong}, pair velocity v = {vx,0,vz} q0 = qp/p0 qv = qxvx+ qzvz y  side x  out transverse pair velocity vt z  long beam cos qx=1-½ (qx)2…exp(-Rx2qx2 –Ry2qy2-Rz2qz2) Ri - Interferometry radii:

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

10. To describe Ro/Rs ratio with protracted particle emission, one needs positive rout-t correlations

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

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 : Ro/Rs

16. Relativistic ideal hydrodynamics ideal fluid : + EoS p=p(ε) + (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=p0=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 cs=0 :

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

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, andpresume 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 : Rt,max Rt,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 spherical symmetry Hwa/Bjorken solution longitudinal boost invariance Biró solution longitudinal boost invariance, cylindrical symmetry

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