1. 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 Department of Physics and Astronomy State University of New York Stony Brook, NY 11794 with support from the Alexander von Humboldt Foundation Peter F. Kolb

2. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro2 Modeling the Expansion Dynamics microscopic viewmacroscopic view vs uu T t scattering of partons and hadrons kinetic transport equations collision terms formalism: continuity equations energy, momentum conservation equation of state F. Karsch, Nucl. Phys. A 698 (2002) 1999 U. Heinz, Nucl. Phys. A 685 (2001) 414

3. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro3 Hydrodynamic Evolution (b=0) Equations of Motion: + Equation of State: + Initial Configuration: from an optical Glauber calculation  0 = 0.6 fm here a resonance gas EoS for T crit < 165 MeV with mixed phase and ideal gas EoS above

4. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro4 Evolution of Radial Flow radial flow at fixed r as a function of timeradial flow at fixed time as a function of r + mixed phase obstructs the generation of transverse flow + the transverse flow profile rapidly adopts a linear behavior v r =  r with  ~ 0.07 fm -1 PFK, nucl-th/0304036

5. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro5 Particle Spectra of Central Collisions: Au+Au @ 200 A GeV Hydro parameters:  0 = 0.6 fm/c s 0 = 110 fm -3 s 0 /n 0 = 250 T crit =T chem =165 MeV Data: PHENIX: NPA715(03)151; STAR: NPA715(03)458; PHOBOS: NPA715(03)510; BRAHMS: NPA715(03)478 Hydro-calculations including chemical potentials: PFK and R. Rapp, Phys. Rev. C 67 (03) 044903 T dec =100 MeV

6. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro6 Single Particle Spectra:  STAR collab., Nucl. Phys. A 715 (2003) 470c Hydro calculation as in PFK and R.Rapp, Phys. Rev. C 67 (2003) 044903 The Omega resonance shows as strong transverse flow as the lighter hadrons. It appears to fully participate in the collective expansion in the partonic as well as in the hadronic stage

7. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro7 Even Multistrange Particles Flow Javier Castillo for the STAR collaboration at SQM 2003 VERY PRELIMINARY ? The Omega picks up flow from both the partonic as well as the hadronic phase and falls right on the hydro-systematics! According to Batsouli, Kelly Gyulassy and Nagle (Phys. Lett. B 557 (2003) 26), even the D- meson spectrum is as flat as expected from hydro (however PYTHIA gives about the same result !) See also Zhangbu Xu’s talk for 200 GeV, Tuesday May 20

8. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro8 Still more exotic: Mesons with Heavy Quarks PHENIX collab: Phys. Rev. Lett. 88 (2002) 192303 S.Batsouli, S.Kelly, M.Gyulassy, J.L.Nagle, Phys. Lett. B 557 (2003) 26 Single electron spectra from charm decay can be described by PYTHIA, as well as by assuming transverse flow of D and B mesons. Elliptic flow will make a clear statement! (And such measurements are coming!)

9. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro9 Transverse Momentum and Trans. Energy PHENIX collab., Nucl. Phys. A 715 (2003) 151c Transverse momenta as function of centrality are well under control as long as the collisions are not too peripheral. Transverse energy agrees for all centralities.

10. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro10 Evolution of Non-Central Collisions spatial eccentricity momentum anisotropy evolution of the energy density initial energy density distribution PFK, J. Sollfrank and U.Heinz, PRC 62 (2000) 054909 (here b=7 fm) initial energy density distribution

11. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro11 Elliptic Flow at RHIC (130): Heinz, PFK, NPA 702(02)269; Huovinen et al. PLB 503(01)58; Teaney et al. PRL 68(01)4783; Hirano, PRC 65(01)011901 Mass, momentum and centrality dependence are well described up to p T ~ 2 GeV and b ~ 7 fm Over 99 % of the emitted particles follow hydro systematics STAR collab., PRL 87 (2001) 182301 STAR, J. Phys. G 28 (2002) 20

12. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro12 Elliptic flow requires Rapid Thermalization PFK, J. Sollfrank and U. Heinz, PRC 62 (2000) 054909 Free flow for an interval  t changes the initial distribution function. For massless particles in the transverse plane ( ):  Reduced spatial anisotropy  as, the elliptic flow is reduced accordingly. With typical dimensions of non-central collisions, one obtains a reduction of 30 % for  t = 2 fm/c.

13. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro13 Elliptic Flow requires Strong Rescattering PFK et al., PLB 500 (2001) 232; D. Molnar and M. Gyulassy, NPA 698 (2002) 379 Cross-sections and/or gluon densities of at some 10 to 80 times the perturbative estimates are required to deliver sufficient anisotropies. At larger p T the experimental results (as well as the parton cascade) saturate, indicating insufficient thermalization of the rapidly escaping particles to allow for a hydrodynamic description.

14. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro14 Sensitivity on the Equation of State Teaney, Lauret, Shuryak, nucl-th/0110037PFK and U. Heinz, nucl-ex/0204061 The data favor an equation of state with a soft phase and a latent heat  e between 0.8 and 1.6 GeV/fm 3

15. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro15 Elliptic Flow at Finite Rapidity T. Hirano and K. Tsuda, nucl-th/020868 Boost invariance and thermodynamic concepts seem to be justified over a pseudo-rapidity interval from -1.5 <  1.5 Observables at larger rapidities: hold pre-equilibrium information (  directed flow!) operate at higher  B (  close to the critical point!) -- - J.Bowers, K.Rajagopal, hep-ph/0209168

16. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro16 Hydrodynamics is THE TOOL to study the thermodynamic properties (i.e. the equation of state) of nuclear matter under extreme conditions Elliptic flow is THE OBSERVABLE to study the thermodynamic features of the equation of state from the earliest stages of the collision The data suggest rapid thermalization and favor an equation of state with a soft region of width e~ 1 GeV/fm 3 Summary 1: What Have we Learned

17. Peter Kolb, CIPANP03, May 22, 2003what we learn from hydro17 with the prerequisites for a hydrodynamic description given, and the many precise results on soft observables we can: Which particles flow? Multistrange? Charm? Summary 2: What Will we still Learn study the degree and breakdown of thermalization (in b, p T, s NN ), and quantify viscosity effects (i.e fundamentals of QCD and hadronic physics) get more quantitative to extract information on the equation of state (even at varying chemical potential) The bulk of the system follows hydrodynamics. Use this information as background for rarer observables and hard processes to answer: How does the dog wag its tail ? (see M. Gyulassy’s talk)