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Elliptic flow and Thermalization at RHIC

Elliptic flow and Thermalization at RHIC. J-Y Ollitrault 1st International Workshop on Soft Physics in ultrarelativistic Heavy Ion Collisions (SPHIC’06), Catania, Sept. 28, 2006. Outline.

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Elliptic flow and Thermalization at RHIC

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  1. Elliptic flow and Thermalization at RHIC J-Y Ollitrault 1st International Workshop on Soft Physics in ultrarelativistic Heavy Ion Collisions (SPHIC’06), Catania, Sept. 28, 2006

  2. Outline • Which are the robust observables for thermalisation? (Bhalerao Blaizot Borghini & JYO, nucl-th/0508009) • The centrality dependence of elliptic flow and the magnitude of v4 show deviations from ideal hydro • Can we model deviations from ideal hydro? Preliminary results from a new transport calculation (C. Gombeaud & JYO, work in progress)

  3. Good probe of thermalisation:Elliptic flow v2 Interactions among the produced particles: Pressure gradients generate positive elliptic flow v2 (v4 smaller, but also measured)

  4. When does elliptic flow build up? In hydro, at a time of order R/cs where R = transverse size cs= sound velocity For a given equation of state, v2 scales roughly like the initial eccentricity ε

  5. What is the density then? Assuming particle number conservation, the density at t=R/cs is (this is particle density, not energy density) It varies little with centrality and system size !!

  6. How can we probe hydro behaviour?(= thermalisation) • We want to measure the equation of state so that we should not assume any value of cs a priori, but rather obtain it from the data The robust method is to compare systems with the same density, hence the same cs , and check that they have the same v2/ε • Au-Au collisions and Cu-Cu collisions at midrapidity, and moderate centralities do a good job • The rapidity dependence of v2 is interesting, but interpretation is more difficult since the density varies significantly with rapidityv • v4 /(v2)2 is another robust observable (=1/2 in ideal hydro) Bhalerao Blaizot Borghini & JYO, nucl-th/0508009 Borghini & JYO, nucl-th/0506045

  7. Why does this really probe thermalisation? Notation: mean free path/system size =Kn: Knudsen number. The hydro limit is Kn«1. If not satisfied, one expects smaller v2 than in hydro. Varying centrality and system size, one does not change the density, but one varies Kn-1~σ/S (dN/dy)~Number of collisions per particle

  8. v2/ε: Data from SPS and RHIC Continuous increase with Kn-1, no saturation seen in data SPS and RHIC fall on the same curve although ≠ densities: Suggests similar values of cs at both densities (?)

  9. Modelling deviations from ideal hydro • Need a theory that goes to ideal hydro in some limit. • First method: viscous hydrodynamics (papers by Teaney, Muronga, Baier Romatschke & Wiedemann, Heinz & Chaudhuri, Pratt) : this is a general approach to small deviations from ideal hydro, but quantitative results are not yet available • Second method: Boltzmann equation. Limitation : applies only to a dilute system (not to the liquid produced at RHIC).Advantage: directly involves microscopic physics through collisional cross-sections

  10. Previous transport calculations Boltzmann ≠hydro although Kn«1?? Molnar, Huovinen, nucl-th/0404065, Phys. Rev. Lett.

  11. A new transport calculation (C. Gombeaud & JYO, in preparation) • Two-dimensions (three later) • Massless particles (mass later) • Billiard-ball calculation, but with Lorentz contraction taken into account: this ensures Lorentz invariance of the number of collisions (≠Molnar-Gyulassy) • N particles of size r in a box of size R: dilute system if r«R/√N

  12. pT dependence of elliptic flow v2/ε pT The transport calculation coincides with the hydro calculation in the limit of small Knudsen number, as it should!

  13. Time dependence of elliptic flow The transport calculation again coincides with the hydro calculation in the limit of small Kn, as it should!

  14. Variation of v2 with Kn-1~Nb collisions/particle Best fit: v2=v2hydro/(1+1.76 Kn): goes to hydro for Kn→0

  15. Hexadecupole flow : v4 Ideal hydro : universal prediction v4=0.5 (v2)2 at large pt . Confirmed by the transport calculation. v4/(v2)2 pT Data ~1.2 suggest Kn~1:No thermalisation at RHIC!

  16. Model inputs Exp. constraints Revisiting the perfect liquid scenario • Initial density profiles: participant scaling • The color glass condensate gives much larger values of ε! • Global observables: multiplicity • Equation of state • Pt-spectra • Thermalization assumed: Kn«1 • Elliptic flow « saturates the hydro limit » • Elliptic flow no longer saturates the hydro limit! • Thermalization not seen!! What is wrong with this scenario? Drescher Dumitru Hayashigaki Nara nucl-th/0605012

  17. Qualitative predictions for LHC • Higher multiplicity : smaller Kn: closer to hydro. • There is room for significant increase of v2 • v4/(v2)2 somewhat smaller than at RHIC

  18. Work in progress • Obtain the value of Kn by comparing the shape of the curve with exp. data • Generalize to massive particles • Generalize to three dimensions with longitudinal expansion

  19. Test of the algorithm: thermalisation in a static system Initial conditions: monoenergetic particles. Relaxation time = mean free path= tau=S/(Nr) # particles with energy <E in the gas versus # particles with energy <E in thermal equilibrium

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