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Flow of Arguments in this Talk

Flow of Arguments in this Talk. * Evidence of strong transverse collectivity in HIC at RHIC. * Origin of this strong collectivity, rescattering and pressure early on. * Formulation of the hydrodynamic approach. * Applications of this approach to heavy ion collisions.

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Flow of Arguments in this Talk

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  1. Hydrodynamics of RHIC

  2. Flow of Arguments in this Talk * Evidence of strong transverse collectivity in HIC at RHIC * Origin of this strong collectivity, rescattering and pressure early on * Formulation of the hydrodynamic approach * Applications of this approach to heavy ion collisions - bulk observables at low transverse momenta - influence of the bulk dynamics on rare probes * Recent trends and future applications - role of details of phase transition - role of viscosity in heavy ion collisions * Summary Hydrodynamics of RHIC

  3. reaction plane reaction plane z z transverse plane y y no sin terms x x no odd cos terms (around z = 0) Characterize azimuthal dependence of the resulting observables by their Fourier expansion With the given symmetries and the chosen coordinate system: Momentum Spectra and Anisotropies Hydrodynamics of RHIC

  4. Evidence for Strong Transverse Collectivity ExperimentalInput: Massive amount of detailed data on spectra of identified particles, their slopes and their anisotropies Phenomenological Idea: If there is a common flow velocity shared by all particle species,heavier particles should receive a larger push in transverse momentum,i.e. their spectra will appear flatter in the low pT region Popular Realization: Parameterize a radial velocity field um (x,y,z,t), on a phenomenologically motivated freeze-out hypersurface s(x,y,z,t). Quantify the observed data in terms of a few physical fitting parameters to grasp the gross macroscopic features of the source Siemens and Rasmussen, Phys. Rev. Lett. 42 (1979) 880, Sollfrank, Schnedermann, Heinz, Phys. Rev. C 48 (1993) 2462. Hydrodynamics of RHIC

  5. A Popular Fit to Particle Spectra Broniowski, Florkowski, PRL 87(01)272302, Acta Phys. Pol 35(04)779 radial flow velocity convoluted with thermal distribution over a suitably parameterized emission surface Parameters for central collisionsat temperature ‘lifetime’ ‘radial extension’ ‘average radial rapidity’ Hydrodynamics of RHIC

  6. … with extension to non-central collisions Baran, Broniowski, Florkowski, Acta Phys. Pol 35(04)779Csanad, Csörgö, Lörstad, nucl-th/0310040Retiere, Lisa nucl-th/0312024 … and many more … New element:Azimuthal modulation on the transverse velocity (+ trans. geometry) Approach of Retiere and Lisa (fit includes geometry of HBT radii) ‘lifetime’ ‘radial extension’ ‘average radial rapidity’ Hydrodynamics of RHIC

  7. Common to These Schematic Fits: on the order of 0.5 c very large transverse velocities are achieved within on the order of 10 fm/c a short period of time What is at the Origin of this Development ? How are those Transverse Velocities Generated ? to answer these questions, turn away from parametrizations and investigate more fundamental DYNAMICAL Models Hydrodynamics of RHIC

  8. formalism: scattering of partons and hadrons kinetic transport equations collision terms continuity equations energy, momentum conservation equation of state timescales: scattering rate expansion rate dilution rate Modeling the Expansion Dynamics microscopic view vs macroscopic view um T t Hydrodynamics of RHIC

  9. 4 1 5equations for 6 fields close the system by supplying an equation of state, e.g. in the form of • - EOS I : ultrarelativistic, ideal gas, p = e/3 • EOS H: interacting resonance gas, p ~ 0.15 e • EOS Q: Maxwell construction of those two: • critical temperature Tcrit= 0.165 MeV • bag constant B1/4 = 0.23 GeV • latent heat elat=1.15 GeV/fm3 Relativistic (Ideal) Hydrodynamics conservation of energy and momentum and conserved currents (baryon-number) with energy momentum tensor and baryon current Hydrodynamics of RHIC

  10. Initialization of the Fields Central collisions: density of wounded nucleons: density of binary collisions: nuclear thickness function: Non-central collisions: wounded nucleons: binary collisions: PFK, Heinz, Huovinen, Eskola, Tuominen, Nucl. Phys. A 696 (2000) 197 Alternatively:use physical model (theory) for the initial state such as the Saturation Model or the Color Glass Condensate Hirano, Nara, nucl-th/0404039 Hydrodynamics of RHIC

  11. Hydrodynamic Evolution 1-dim expansion 3-d expansion Equations of Motion: + Equation of State: here a resonance gas EoS for Tcrit < 165 MeV with mixed phase and ideal gas EoS above + Initial Configuration: e.g. from an optical Glauber calculation t0 = 0.6 fm Hydrodynamics of RHIC

  12. Freeze-Out: Scattering rate meets expansion rate PFK, nucl-th/0304036 Macroscopic timescale: Local exponent of dilution alpha Hubble-like Expansion rate: Bjorken-like Microscopic timescale: Scattering rate Hung and Shuryak PRC 57 (1998) 1891 for a hydrodynamic description scattering rate > expansion rate Hydrodynamics of RHIC

  13. Evolution of Radial Flow radial flow at fixed R as a function of time radial 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 vr =  r with  ~ 0.07 fm-1 Hydrodynamics of RHIC

  14. equilibration time central entropy density (net) baryon density Particle Spectra of Central Collisions Translation of the hydrodynamic information into particle contents(thermal source with blue-shift according to radial velocity) with PFK and R. Rapp, Phys. Rev. C 67 (2003) 044903 Parameters of the calculation: Hydrodynamics of RHIC

  15. Particle Spectra of Non-Central Collisions PHENIX collab., PRL 88 (2002) 242301; STAR collab., PRL 87 (2001) 262302, nucl-ex/0111004 Hydro calc.: U.Heinz, PFK, NPA 702(02)269 negative pions antiprotons Having the parameters fixed in central collisions, particle spectra at non-zero impact parameter are well reproduced up to b ~ 9 fm Hydrodynamics of RHIC

  16. PFK, J. Sollfrank, U. Heinz, PRC 62 (2000) 054909 Time evolution of anisotropies Coordinate space Momentum space Geometry converts to Momentum Space Hydrodynamics of RHIC

  17. PFK, J. Sollfrank and U.Heinz, PRC 62 (2000) 054909 SPS 17 GeV * strong rescattering required * transition of spatial to momentum anisotropy has to occur early Which was not yet the case at the SPS the hydrodynamic limit appears to be exhausted can’t allow a delay larger than 1 fm/c Momentum Anisotropy and Strong rescattering D. Molnar and M. Gyulassy, NPA 698 (2002) 379 PFK et al. PLB, 500 (2001) 232 Hydrodynamics of RHIC

  18. Sensitivity on the Nuclear Equation of State PFK und U. Heinz, nucl-ex/0204061 D.Teaney, J.Lauret, E.Shuryak, nucl-th/0110037 peripheral central Centrality the experimental data carry clear indications for a strong push from the plasma phase with a sensitivity on the transition region Hydrodynamics of RHIC

  19. Systematic Mass Effects Huovinen, PFK, Heinz, Ruuskanen, Voloshin, PLB 503 (2001) 58 J. Castillo for the STAR collaboration at Quark Matter 2004 * elliptic flow shows a strong hydrodynamic mass effect all quark flavors share a common flow field Hydrodynamics of RHIC

  20. Not Many Particles are Beyond 2 GeV … Au+Au at 200 GeV G. Roland for the Phobos Collaboration, CIPANP May 2003 Phobos Preliminary Systematic Errors not shown G. Roland for the Phobos Collaboration, CIPANP May 2003 but these few are an important probe of the matter they traverse! Hydrodynamics of RHIC

  21. The Dynamics of the Bulk influences Other Probes dynamical evolution of the thermalized background influences the evolution of various other (non-thermal) probes of the medium use the information gained for hydrodynamics for the systematic investigation of the bulk medium on rare probes. e.g. quenching of fast partons Hirano, Nara, PRC66 (2002) 041901, PRC69 (2004) 034908 use GLV 1st order formula for parton energy loss (Gyulassy et al. ’00) Hirano, Nara, PRC66 (2002) 041901 Other examples for this technique: generation of dileptons in the medium Huovinen, Ruuskanen, Räsänen Phys. Lett. B 535 (2002) 109 calculation of thermal photons from the fireball Hydrodynamics of RHIC

  22. Recent and Future Developments improve the parameterization of the equation of state and investigate the allowed parameter space of the transition region include and study the influence of viscous effectsin the plasma as well as in the hadronic phase drop the assumption of boost invarianceand exploit the full phase space Hydrodynamics of RHIC

  23. at finite baryon density a critical point acts as an attractor Chiho Nonaka at ‘Collective Flow and QGP properties’workshop, BNL November 2003 Lines of constant nB/s for an EOS with critical endpoint 0.04 Lines of constant nB/s for Bag Model withexcluded volume EOS 0.02 Improvements on the Equation of state phase transition at RHIC is not expected to be first orderbut more gradual G.Boyd et al., Nucl. Phys. B 469 (1996) 419 See also Paech, Stoecker, Dumitru, nucl-th/0302013 Hydrodynamics of RHIC

  24. Relax Assumption of Full Thermalization U.Heinz and S.M.H.Wong, Phys. Rev. C 66 (2002) 014907 in an extreme scenario assume vanishing longitudinal pressure, but thermalized behavior transversally energy-momentum tensor in a local restframe: which is traceless: -> EOS larger transverse pressure, less longitudinal work flatter spectra (too flat) larger anisotropies Hydrodynamics of RHIC

  25. Include Viscous Terms both Longitudinally And Transversally A. Muronga, Phys. Rev. C 69 (2003) 034903 D. Teaney, nucl-th/0403053 viscous contribution to energy momentum tensor: stress term: in the local rest-frameand long. boost invariance: D. Teaney, nucl-th/0403053 first calculations show how viscous matter ‘sticks around longer’ but then develops larger transverse velocities Hydrodynamics of RHIC

  26. Consider Corrections to thermal distribution D. Teaney, Phys. Rev. C 68 (2003) 034913 first order correction to thermal distribution with sound attenuation length exemplified by elliptic anisotropy the data do not allow for large distortions of the equilibrium distributionOverall, throughout the significant stages of the expansion, the system behaves like an ideal liquid Hydrodynamics of RHIC

  27. Z.Fodor and S. Katz, JHEP 0203 (2002) 014 Relax Assumption of Boost invarianceFor Physics at . T. Hirano, Phys. Rev. C 65 (2002) 011901 U. Heinz und P. Kolb, J. Phys. G (2004) Physics phenomena at finite rapidity: Less energy deposition - delayed thermalization (if at all) - viscosity effects of larger influence Larger net-baryon density - probe different regions of the phase diagram - can we get close to the critical point ? Unknown longitudinal evolution - how good is the longitudinal Bjorken scaling ? - where does it break down ? - what is the longitudinal flow profile that establishes ? Hydrodynamics of RHIC

  28. Summary: The Significance of HydrodynamicsIn Relativistic Heavy Ion Collisions Spectra and their anisotropies at pT < 1.5 - 2 GeV can only be well described under the assumption of very strong rescattering at very early times. G. Roland for the Phobos Collaboration, CIPANP May 2003 Many observables in momentum space can be qualitatively and quantitatively described through a single set of initial conditions followed by a hydrodynamic evolution. PHOBOSAu+Au 200 GeV At RHIC we are dealing with a system, which exhibits the thermo-dynamic features of the bulk matter. Ultimatively we can study the thermodynamic properties of strongly interacting matter beyond Tc. Hydrodynamics of RHIC

  29. Physics Possibilities in Anisotropies dynamical evolution source geometry thermalization flow properties of the medium energy density of initial state suppressionmechanism Equation of State viscous effects hadronizationmechanism Hydrodynamics of RHIC

  30. Supplements Hydrodynamics of RHIC

  31. for small expansion coefficients: v1 : shift of the entire system directed flow v2 : elliptic deformation elliptic flow v3 : triangular deformation etc… Characteristic Shapes of the Series Beware: for large coefficients this terminology is unappropriate ! Hydrodynamics of RHIC

  32. PHENIX Collaboration, nucl-ex/0305013 Elliptic Flow at Large Pt is HUGE ! PHENIX Collaboration, nucl-ex/0305013 v2 = 0.25 means that there are 3 times as many particles emitted into the reaction plane than out of the reaction plane!Furthermore the distribution is not elliptic any longer! Hydrodynamics of RHIC

  33. Simplifications: Partonic part factorizes into one particle phase space distributions Extent of hadron wave function much smaller than system size Energy momentum conservation ensured by surrounding medium Meson - distribution Baryon - distribution Coalescence: Some Quick Basics Fries, Müller, Nonaka, Bass, PRC 68(03)044902; Greco, Ko, Levai, PRC 68(03)034902; Hwa, Yang, PRC 67 (03) 034902. Wigner functions Meson distribution Quark-Soup Meson Hydrodynamics of RHIC

  34. 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 well described up to pT ~ 2 GeV and b ~ 7 fm Over 99 % of the emitted particles follow hydro systematics Data: STAR collab., J. Phys. G 28 (2002) 20; PRL 87 (2001) 182301 Hydrodynamics of RHIC

  35. Schematic Models for 3 Dimensionen Characterize the final state of the expansion for 3 dimensionswithin a few parameters that capture the essence i.e. ‘blast wave spectra’ (originally developped for central collisions) Lee, Heinz Schnedermann, Z. Phys. C 48 (1990) 525 Generalize to non-central collisions Azimuthal modulation of the radial flow profile Huovinen, PFK, Heinz, Ruuskanen, Voloshin, PLB 503 (01) 58 Tdec = 140 MeV r0= 0.58 f2= 7.7 % Folded with the thermal decoupling temperature Tdec Further generalization to 3 Dimensionen to characterize and classify the data and as a cross check for the full 3d-calculation Hydrodynamics of RHIC

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