LP. Csernai, Montreal 26.6.03 1 Topics in Heavy Ion Collisions, 2003 Montreal, June 25-28, 2003 Flow effects and their measurable consequences in ultra-relativistic

LP. Csernai, Montreal 26.6.031

Topics in Heavy Ion Collisions, 2003Montreal, June 25-28, 2003

Flow effects and their measurable consequences in ultra-relativistic heavy-ion collisions


Collaboration

• U of Bergen: Cs. Anderlik, L.P. Csernai, Ø. Heggø-Hansen, V. Magas (U Lisbon), E. Molnár, A. Nyiri, D. Röhrich, and K. Tamousiunas (Trento)

• U of Oulu: A. Keranen, J. Manninen

• U of Sao Paulo: F. Grassi, Y. Hama

• U of Rio de Janeiro: T. Kodama

• U of Frankfurt: H. Stöcker, W. Greiner

• Los Alamos Nat. Lab.: D.D. Strottman

• 0.5 Tera-flop IBM e-series supercomputer, w/ 96 Power4 processors a’ 5.2 Giga-flop each (Bergen Computational Physics Lab. – EU Research Infrastructure)



Collective FLOW Patterns:

Lorentz contraction changes the GEOMETRY and Reaction Mechanism !

[ URQMD,

U. Frankfurt, 2000]


Local equilibrium

• Large no. of degrees of freedom• Strong stopping (AGS, SPS) / equilibration (RHIC)

• Local equilibration • Equation of State (EoS) characterizes the

equilibrium properties of matter [1]

• Dynamics is well approximated by fluid dynamics (perfect, viscous, …) at Mid Coll.!

• Multi Module Modeling [2]


Phase transition to QGP in small systems !

In macroscopic systems two phases of different densities (e) are in phase equilibrium. Negligible density fluctuations!

[Csernai, Kapusta, Osnes, PRD 67 (03) 045003 ]

STATIC


Small, Mesoscopic Systems

If N=100, fluctuations are getting strong (red). Close to the critical point, the two phases cannot be identified (green).

~~> Landau’s theory of fluctuations near the critical point.

Nuclear Liquid-Gas phase transition (first order)

[ Goodman, Kapusta, Mekjian, PRC 30 (1984) 851 ]

CRAY - 1

T/F eP

STATIC


Lattice Field Theory

[Farakos, Kajantie, et al. (1995) hep-lat/ ]

First order (EW) phase transition: statistical ensemble.

Fluctuations of density decrease with increasing Lattice volume !!

For macroscopic EoS extrapolation is needed!

For small systems, ~100-200 fermi3, fluctuations are REAL !!!

Supercomputers are needed !

[Csernai, Neda PL B337 (94) 25]

STATIC


Pressure – Soft Point?LBL, AGS, SPS:Collective flow –P-x vs. y Pressure sensitive

Directed transverseflow decreases with increasing energy:

[Holme, et al., 89][D. Rischke, 95][E. Shuryak, 95]

But, does it recoverat higher energies ?


Multi Module ModelingMulti Module Modeling• A: Initial state - Fitted to measured data (?)

• B: Initial state - Pre-equilibrium: Parton Cascade; Coherent Yang-Mills [Magas]

• Local Equilibrium Hydro, EoS

• Final Freeze-out: Kinetic models, measurables. - If QGP Sudden and simultaneous hadronization and freeze out (indicated by HBT, Strangeness, Entropy puzzle)

Landau (1953), Milekhin (1958), Cooper & Frye (1974)



Fire streak picture - Only in 3 dimensions!

Myers, Gosset, Kapusta, Westfall


String rope --- Flux tube --- Coherent YM field


Initial stage: Coherent Yang-Mills model

[Magas, Csernai, Strottman, Pys. Rev. C ‘2001]


Yo – Yo Dynamics wo/ dissipation


Modified Initial StateIn the previous model the fwd-bwd surface was too sharp two propagating peaks

Thus, after the formation of uniform streak, the expansion at its end is included in the model

This led to smoother energy density and velocity profiles

Z [fm]Z [fm]

ye [GeV/ fm3 ]

[Magas, Csernai, Strottman, in pr.]


Initial state

3rd flow component


Multi Module ModelingMulti Module Modeling

• Initial state - pre-equilibrium: Parton Cascade; Coherent Yang-Mills [Magas]


• Final Freeze-out: Kinetic models, measurables - If QGP Sudden and simultaneous hadronization and freeze out (indicated by HBT, Strangeness, Entropy puzzle)



Relativistic Fluid DynamicsRelativistic Fluid DynamicsEg.: from kinetic theory. BTE for the evolution of phase-space distribution:

Then using microscopic conservation laws in the collision integral C:

These conservation laws are valid for any, eq. or non-eq. distribution, f(x,p). These cannot be solved, more info is needed!

Boltzmann H-theorem: (i) for arbitrary f, the entropy increases, (ii) for stationary, eq. solution the entropy is maximal, EoS

P = P (e,n)Solvable for local equilibrium!


Matching Conditions Conservation lawsConservation laws

Nondecreasing entropyNondecreasing entropy

Can be solved easily. Yields, via the “Taub adiabat” and “Rayleigh line”, the final state behind the hyper-surface. (See at freeze out.)


3-dim Hydro for RHIC EnergiesAu+Au ECM=65 GeV/nucl. b=0.5 bmax Aσ=0.08 => σ~10 GeV/fm

e [ GeV / fm3 ] T [ MeV]

t=0.0 fm/c, Tmax= 420 MeV, emax= 20.0 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm

. .

EoS: p= e/3 - 4B/3B = 397 MeV/fm3

8.7 x 4.4 fm





. .

11.6 x 4.6 fm





. .

14.5 x 4.9 fm





. .

17.4 x 5.5 fm





. .

20.3 x 5.8 fm





. .

23.2 x 6.7 fm





. .

26.1 x 7.3 fm





. .

31.9 x 8.1 fm





. .

34.8 x 8.7 fm


Global Flow Patterns: Directed Transverse flow

Elliptic flow

3rd flow component(anti - flow)

Squeeze out


Talk by S. Manly

Note: (1) There is no boost invariance !! . (2) Hydro [Hirano] yields less stopping


3rd flow component and QGP

• Csernai & Röhrich [Phys.Lett.B458(99)454]

observed a 3rd flow component at SPS energies, not discussed before.

• Also observed that in ALL earlier fluid dynamical calculations with QGP in the EoS there is 3rd flow comp.

• The effect was absent without QGP.

• In string and RQMD models only peripheral collision showed the effect (shadowing).


3rd flow component

Hydro

[Csernai, HIPAGS’93]


Heavy Ion Coll. at RHIC - Transverse velocities - b=0.5

120

100

80

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40

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0

5045403530252015

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.5

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50 cyclesb=0.5

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.3

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250 cyclesb=0.5

[ Strottman, Magas, Csernai, BCPL User Mtg. Trento, 2003 ]

DYNAMICz


Multi Module ModelingMulti Module Modeling

• Initial state - pre-equilibrium: Parton Cascade; Coherent Yang-Mills [Magas]


• Final Freeze-out: Kinetic models - If QGP Sudden and simultaneous hadronization and freeze out (indicated by HBT, Strangeness, Entropy puzzle)



Sudden Freeze-Out & Hadronization from Sc. QGP

Negative P

(Positive T)


A=A=0.0650.065

11.4 fm/c


“Wiggle”, Pb+Pb, Elab=40 and 158GeV [NA49-QM’02]Talk by A. WetzlerPreliminary

158 GeV/A

Note different scale for 40 and 158 GeV!The “wiggle” is there!

v1 < 0


v1(y) is not measured yet at RHIC!?

As v2 is measured, the reaction plane [x,z] is known, just the target/projectile side should be selected. This is not done due to the (Bjorken model) prejudice that the distribution of emitted particles is mirror-symmetric in CM:

f CM ( x, y, z, px, py, pz ) = f CM ( x, y, -z, px, py, -pz )

This is wrong (!) as the presented hydro calculations and SPS data show. At finite impact parameters, (2-15%) there is a fwd / bwd central symmetry.

Calculate event by event the Q-vector (a la [Danielewicz, Odyniecz,

PL (1985)] ): Qk = i

k

yCM px

For all particles, i, of type k. Only the sign is relevant, as the plane is known already. This Q-vector will select the same side (e.g. projectile) in each event. [Discussions with Art Poskanzer and Roy Lacey are gratefully acknowledged. ]

O.K.


Conclusions

• Hydro works amazingly well! Stronger and stronger hydro effects are observed!

Equilibrium and EoS exists ( in part of the reaction )

• We have a good possibility to learn more and more about the EoS, with improved experimental and theoretical accuracy!

• The determination of reaction plane is vital for flow, HBT, and for ALL observables influenced by the collective collision dynamics.

Documents

LP. Csernai, Montreal 26.6.03 1 Topics in Heavy Ion Collisions, 2003 Montreal, June 25-28, 2003 Flow effects and their measurable consequences in ultra-relativistic