lp. csernai, pasi'2002, brazil1 part i relativistic hydrodynamics for modeling...

LP. Csernai, PASI'2002, Brazil 1

Part I

Relativistic HydrodynamicsFor Modeling Ultra-Relativistic Heavy Ion Reactions

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Collaboration

• U of Bergen: C. Anderlik, L.P. Csernai, Ø Heggø-Hansen, Z. Lázár (U Cluj), V. Magas (U Lisbon), D. Molnár (Columbia U), A. Nyiri, K. Tamousiunas

• 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)

• U of Rio de Janeiro: Proceedings - G. Grise, L. LimaSilviaPortugal, B. MattosTavares, D. dePaula

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FLOW

Is fluid dynamics applicable in relativistic nuclear physics?

Collective Nuclear Flow: Greiner – Koonin [1973 Balaton]

Transverse Flow Exp. Proof : [1984 Plastic Ball LBL]

• By now: Mc increases – close to macro continuous matter

• Local equilibrium EoS / Phase Transition / QGP (during the middle part of the reaction, initial and final stages are out of equilibrium)

• Many flow-patterns are observed in nuclear collisions

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QGP: A new state of matter

“The combined data coming from the seven experiments on CERN's Heavy Ion programme have given a clear picture of a new state of matter. . . . We now have evidence of a new state of matter where quarks and gluons are not confined. There is still an entirely new territory to be explored concerning the physical properties of quark-gluon matter.” [ L. Maiani]

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Water –Vapor Phase Transition - Discovery

• HeronHeron of Alexandria: “Pneumatica” steam-engine fl. AD. 62– Roger Bacon: Heat, Kinetic theory 1220 – 1292

– Galileo Galilei: Temperature – Barothermoscope 1564 – 1642

– Anders Celsius: Temperature 1701 - 1744

– Joseph Black: Latent heat 1728 – 1799

– James Watt: Steam engine 1736 – 1819

– Sandi N.L. Carnot: Kinetic theory, Energy conservation 1796 – 1832

– Rudolf Clausius: 2nd law of thermodynamics, entropy 1822 – 1888

– Ludwig Boltzmann: Kinetic theory 1844 – 1906

– Josiah W. Gibbs: Phase equilibrium, kinetic theory 1839 –1903

– Johannes D. Van der Waals: molecular interactions/ph.t.1837 - 1923

– Max Planck: Black body radiation 1858 –1947

• Quantum Field Theory of phase transitions, mesoscopic dynamics Is there phase transition in a drop of water ?

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What did we see so far ?

• Phenomenology:– Strong stopping

– Decreasing pressure• Soft point ?

– Flow, spherical, directed, elliptic, 3rd component

– Increased entropy

– Chemical freeze-out at fixed T, fixed

– Strong strange baryon enhancement

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StoppingP+A: [Csernai, Kapusta, PRD31(1985)2795]:y=2.5

R. Stock [CERN (2000)]

[W.Busza PASI 2002]

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Stopping at SPS / NA49

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Stopping at RHIC

At RHIC y = 9.8 – 10.7 so

Y-gap = 4-5 !

At RHIC there is also more stopping than expected. No sign of gap.

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45-55% 35-45% 25-35%

15-25% 6-15% 0-6%

dNch

/d

dNch

/d

dNch/d vs. Centrality

Octagon Rings [Peter Steinberg, QM 2001]

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Peter Steinberg

Shapes of dNch/d for different Npart

dNch

/d

(dN

ch/d

)/(

½N

part)

dNch

/d

Data

HIJING

HIJING

(dN

ch/d

)/(

½N

part)

Systematic error ±(10%Systematic error ±(10%--20%)20%)

354

216

102

Mean Npart% 0-3

15-20

35-40

Data

[QM’2001]

Stopping - RHIC

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Local equilibrium Jüttner distr. (MB)

Stationary solution of the BTE , and generalization of the MB distribution

Lorentz

Transformation

Properties:

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Kinetic definition of density, energy, momentum

These definitions are applicable for any, equilibrium or non-eq. situation!

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Normalization of Jüttner distribution

From:

Similar expressions occur when we evaluate the EoS,energy density, e, pressure, P, and entropy density, s. [see also Takeshi Kodama PASI 2002]

15LP. Csernai, PASI'2002, Brazil

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Local equilibrium - Flow - LR frame

( Landau )

Def: Orthogonal proj. to flow

Then:These definitions are applicable for any, equilibrium or non-equilibrium situation!

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Local equilibrium

• Large no. of degrees of freedom• Strong Stopping• Local equilibration • Equation of State (EoS) characterizes the

equilibrium properties of matter• Dynamics is well approximated by fluid

dynamics (perfect, viscous, …)• Model predictions become similar• Multi Module Modeling

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EoS from the local eq. phase space distribution

Eg.: From Jüttner Ideal gas EoS & 2nd law of thermodyn. (!) [see T.Kodama PASI’2002]

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Pressure – Soft Point?

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

Directed transverseflow decreases with increasing energy.

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

But, does it recoverat higher energies ?

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[F. Karsch, PASI 2002]

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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!

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Relativistic Fluid DynamicsRelativistic Fluid DynamicsFor any EoS, P=P(e,n), and any energy-momentum tensor in LE(!):

Not only for high v!

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Multi Module ModelingMulti Module Modeling

• 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)

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Initial State

• At low energies stopping in SHOCK or DETONATION waves (supersonic!) of width of 1-3fm (possible in Pb+Pb) [BEVALAC, GSI, AGS]

• Idealized: as discontinuity across a hyper-surface (or layer) in space time.

• Simple solutions of Rel. Fluid dynamics

• Generalized to other stationary processes: freeze-out, initial equilibration, phase trans.

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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.)

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Fire streak picture - Only in 3 dimensions!

Myers, Gosset, Kapusta, Westfall

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

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Initial stage: Coherent Yang-Mills model

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

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Expanding string ropes – Full energy conservation

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Yo – Yo Dynamics

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Initial state

3rd flow component

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Multi Module ModelingMulti Module Modeling

• 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)

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3-Dim Hydro for RHIC (PIC)3-Dim Hydro for RHIC (PIC)

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3-dim Hydro for RHIC EnergiesAu+Au ECM=65 GeV/nucl. b=0.1 bmax Aσ=0.08 => σ~10 GeV/fm

n / n0 [ 1 ] e [ GeV / fm3 ]

T= 0.0 fm/c nmax = 8.67 emax=32.46 GeV / fm3 Lx,y= 1.45 fm Lz=0.145 fm

. .

4.4 x 1.3 fm

EoS: P = e/3

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3-dim Hydro for RHIC EnergiesAu+Au ECM=65 GeV/nucl. b=0.1 bmax Aσ=0.08 => σ~10 GeV/fm

n / n0 [ 1 ] e [ GeV / fm3 ]

T=1.9 fm/c nmax = 8.66 emax= 31.82 GeV / fm3 Lx,y= 1.45 fm Lz=0.145 fm

. .

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3-dim Hydro for RHIC EnergiesAu+Au ECM=65 GeV/nucl. b=0.1 bmax Aσ=0.08 => σ~10 GeV/fm

n / n0 [ 1 ] e [ GeV / fm3 ]

T= 3.8 fm/c nmax = 7.77 emax= 27.22 GeV / fm3 Lx,y= 1.45 fm Lz=0.145 fm

.

.

.

4.4 x 1.3 fm

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3-dim Hydro for RHIC EnergiesAu+Au ECM=65 GeV/nucl. b=0.1 bmax Aσ=0.08 => σ~10 GeV/fm

n / n0 [ 1 ] e [ GeV / fm3 ]

T= 5.7 fm/c nmax = 6.36 emax= 26.31 GeV / fm3 Lx,y= 1.45 fm Lz=0.145 fm

. .

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3-dim Hydro for RHIC EnergiesAu+Au ECM=65 GeV/nucl. b=0.1 bmax Aσ=0.08 => σ~10 GeV/fm

n / n0 [ 1 ] e [ GeV / fm3 ]

T= 7.6 fm/c nmax = 5.22 emax= 37.16 GeV / fm3 Lx,y= 1.45 fm Lz=0.145 fm

. .

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3-dim Hydro for RHIC EnergiesAu+Au ECM=65 GeV/nucl. b=0.1 bmax Aσ=0.08 => σ~10 GeV/fm

n / n0 [ 1 ] e [ GeV / fm3 ]

T= 9.5 fm/c nmax = 4.45 emax= 32.86 GeV / fm3 Lx,y= 1.45 fm Lz=0.145 fm

. .

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Global FlowDirected

Transverse

flow

Elliptic flow

3rd flow component(anti - flow)

3rd flow component(anti - flow)

Squeeze out

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A=A=0.0650.065

11.4 fm/c

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Aside: v1 is not measured yet at RHIC!? (neither STAR nor PHENIX)

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 prejudice that the distribution of emitted particles is mirror-symmetric in CM:

f CM ( px, py, pz ) = f CM ( px, py, -pz )

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

Calculate event by event the Q-vector (a la [Danielevicz, 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. ]

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NEXT:

• Flow experiments

• Modified Rel. Hydro with supercooling

• Freeze-out

• Discontinuities in hydro – Eq. => Eq.

• Freeze-out to non-eq.

• Kinetic freeze-out