elliptic flow and thermalization at rhic
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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. - PowerPoint PPT PresentationTRANSCRIPT
Elliptic flow and Thermalization at RHIC
J-Y Ollitrault1st International Workshop on Soft Physics in
ultrarelativistic Heavy Ion Collisions
(SPHIC’06), Catania, Sept. 28, 2006
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)
Good probe of thermalisation:Elliptic flow v2
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Interactions among the produced particles: Pressure gradients generate positive elliptic flow v2
(v4 smaller, but also measured)
...)2cos2cos21(2
121
vv
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dN
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In hydro, at a time of order R/cs where R = transverse size cs= sound velocity
When does elliptic flow build up?
For a given equation of state, v2 scales roughly like the initial eccentricity ε
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 !!
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/0508009Borghini & JYO, nucl-th/0506045
Why does this really probe thermalisation?
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
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.
v2/ε: Data from SPS and RHIC
Continuous increase with Kn-1, no saturation seen in dataSPS and RHIC fall on the same curve although ≠ densities:Suggests similar values of cs at both densities (?)
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
Previous transport calculations
Molnar, Huovinen, nucl-th/0404065, Phys. Rev. Lett.
Boltzmann ≠hydro although Kn«1??
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
pT dependence of elliptic flow
The transport calculation coincides with the hydro calculation in the limit of small Knudsen number, as it should!
v2/ε
pT
Time dependence of elliptic flow
The transport calculation again coincides with the hydro calculation in the limit of small Kn, as it should!
Variation of v2 with Kn-1
~Nb collisions/particle
Best fit: v2=v2hydro/(1+1.76 Kn): goes to hydro for Kn→0
Hexadecupole flow : v4
Ideal hydro : universal prediction v4=0.5 (v2)2 at large pt . Confirmed by the transport calculation.
Data ~1.2 suggest Kn~1:No thermalisation at RHIC!
v4/(v2)2
pT
Revisiting the perfect liquid scenario
Model inputs Exp. constraints
What is wrong with this scenario?
• Initial density profiles: participant scaling
• Global observables: multiplicity
• Equation of state • Pt-spectra
• Thermalization assumed: Kn«1
• Elliptic flow « saturates the hydro limit »
•The color glass condensate gives much larger values of ε!
Drescher Dumitru Hayashigaki Nara nucl-th/0605012
• Elliptic flow no longer saturates the hydro limit!
• Thermalization not seen!!
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
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
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