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


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


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


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]


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 ?


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


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

R. Stock [CERN (2000)]

[W.Busza PASI 2002]


Stopping at SPS / NA49


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.


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]


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


Local equilibrium Jüttner distr. (MB)

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

Lorentz

Transformation

Properties:


Kinetic definition of density, energy, momentum

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


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


Local equilibrium - Flow - LR frame

( Landau )

Def: Orthogonal proj. to flow

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


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


EoS from the local eq. phase space distribution

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


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 ?


[F. Karsch, PASI 2002]


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!


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

Not only for high v!


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)


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.


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.)


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]


Expanding string ropes – Full energy conservation


Yo – Yo Dynamics


Initial state

3rd flow component


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)


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


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



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

. .



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



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


. .


Global FlowDirected

Transverse

flow

Elliptic flow

3rd flow component(anti - flow)

3rd flow component(anti - flow)

Squeeze out


A=A=0.0650.065

11.4 fm/c


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. ]


NEXT:

• Flow experiments

• Modified Rel. Hydro with supercooling

• Freeze-out

• Discontinuities in hydro – Eq. => Eq.

• Freeze-out to non-eq.

• Kinetic freeze-out

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

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