L.P. Csernai, BNL Nov 17-19 '03 1 L..P. Csernai Multi module modelling of heavy ion collisions...

L.P. Csernai, BNL Nov 17-19 '031L..P.

Csernai

Multi module modelling of heavy ion collisions

Collective flow and QGP properties

RIKEN-BNL workshop

November 17-19, 2003

L.P. Csernai, BNL Nov 17-19 '032

Multi module modelling of heavy ion collisions

• L.P. Csernai, A. Anderlik, Cs. Anderlik, Ø. Heggø-Hansen, E. Molnár, A. Nyiri, D. Röhrich, and K. Tamousiunas

• U of Valencia: V.K. Magas • U of Oulu: A. Keranen, J. Manninen• Los Alamos National Lab.: D.D. Strottman, B.

Schlei• U of Sao Paulo: F. Grassi, Y. Hama• U of Rio de Janeiro: T. Kodama• U of Frankfurt: H. Stöcker, W. Greiner• Bergen Computational Physics Lab. – EU Research

Infrastructure,BCCS, Unifob AS, University of Bergen, Norway


Multi Module ModelingMulti Module Modeling

• Pre: Eq. of State (EoS) – Phases – Local eq.:BagM

• A: Initial state - Fitted to measured data (?)• B: Initial state - Pre-equilibrium: Parton

Cascade M.; 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)


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]OBSERVED !

But, does it recoverat higher energies ?WHAT HAPPENS?


Phase transition dynamics – Out of thermal eq.

Transition to QGP• 0.1 – 0.3 fm/c (PCM)• Structure functions

- valence quarks- see quarks (~stopped)

• Flux-tube models- immediate eq.- Bjorken ’83- Gyulassy & Cs. ‘86

Hadronization• Nucleation ~30-100fm/c

- local thermal equilibrium- Cs. & Kapusta ’92

• Out of eq. ph.tr. possible:- supercooled QGP- Csorgo & Cs. ’94- Cs. & Mishustin ’95- ~1-2 fm/c

Hadronization and Freeze-out MUST be simultaneous ! / No T,p,..- How can the Stat.Model work?



Breakdown of a complex task into modules

Input 1

InitialTransportModule

1Fluid

DynamicalModule

2

Freeze OutModule

3Hadroni-

zationModule

Calculationof

ObservablesResult 1

4 5

Time

Standard interfaces

FO surface FO transfer


Multi Module Modeling on GRIDMulti Module Modeling on GRIDExecution of complex modular tasks on GRID

time

Machine A Machine B Machine C Machine D Machine E

Input 11

1

1

1

1

Input 2

Input 3

2

2

2

2

3

3

3

4

4

4

5

5

5

Result 3

Result 2

Result 1



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, Phys. Rev. C64 (01) 014901]


Expanding string ropes – Full energy conservation


Yo – Yo Dynamics wo/ dissipation


wo/ dissipation


Initial state

3rd flow component


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.]


Modified Initial State


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



• 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)


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!


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

~ 4 times elongated !!





. .

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


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

120

100

80

60

40

20

0

5045403530252015

0.6

0

.5

0.5

0.4

0.4

0.3

0.3

0.3

0.3

0.2

0.2

0.1

0.1

50 cyclesb=0.5

120

100

80

60

40

20

0

5045403530252015

0.2

0.2

0.1

5

0.1

5

0.1

0.1

0.1

0.1

0.0

5

0.0

5

20 cyclesb=0.5

120

100

80

60

40

20

0

5045403530252015

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.3

0.3

0.2

0.2

0.1

0.1

0.1

150 cyclesb=0.5

120

100

80

60

40

20

0

5045403530252015

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3 0

.3

0.2

0.2

0.1

0.1

0.1

0

.1

0.1

250 cyclesb=0.5

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

DYNAMICz



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

• Local Equilibrium Hydro, EoS• Final Freeze-out: F.O. Surface • Final Freeze-out: Kinetic models

- If QGP Sudden and simultaneous hadronization and freeze out (indicated by HBT, Strangeness, Entropy puzzle)Landau (1953), Milekhin (1958), Cooper & Frye (1974)


[ Bernd R. Schlei (T-1) - LA-UR-03-3410 ]

Freeze-Out Hyper-Surface Extraction with Digital Image Processing Techniques

VESTA and Projections of FOHS (e.g., “Firestreaks” for Au + Au @ RHIC)

x

yz

xyz - Projection

t fixed

Impact Parameter b = 0.5

3+1 D Hydrodynamic Density Data are based on “Firestreak” Initial Conditions;V. K. Magas, L. P. Csernai, D. Strottman, Nucl. Phys. A712 (2002) 167.

In 3+1 D Hydrodynamical Calculations,VESTA is useful for the Graphical Rendering of Projections of FOHS.A Construction of a 4D FOHS requires a Generalization of VESTA into 4D.

x

z

t

xtz - Projection

y fixed

Impact Parameter b = 0.5



Time-Sequence of FOHS Projections

t1

t8

t2 t3 t4 t5 t6 t7

t14t13t12t11t10t9

3+1 D Hydrodynamic Density Data, courtesy D. Strottman, Theoretical Division, Los Alamos National Laboratory.

VESTA Rendering of FOHS in 3+1 D Hydrodynamics at fixed Times (t1 < … < t14).

x

y z Impact Parameter b = 0.0

[ Bernd R. Schlei (T-1) - LA-UR-03-3410 ]

10 times elongated !!


Bernd R. Schlei (T-1)

3+1 D Hydrodynamic Density Data, D. Strottman, Theoretical Division, Los Alamos National Laboratory.


Movie: Time-Sequence of F.O. H-S Projections

[ Bernd R. Schlei (T-1)LA-UR-03-3410 ]

Y

X

Z10 times elongated in z-direction, to compensate for L. contraction !

b=0.


Y

X

Z

b=0.5 bmax

Modified Initial State




Quick Time Movie - External

[Due to MS’s competitive business practices]

Axonometric view

Heavy Ion reaction - Surface visualization T = 139 MeV

Hy-mov-004.mov


Reaction Plane - [ X , Z ]X

Z








Quick Time - Movie - External

[Due to MS’s competitive business practices]

Reaction Plane

Surface at T = 139 MeV

Hy-mov-00.mov


Multi Module ModelingMulti Module Modeling• Initial state - pre-equilibrium: Parton

Cascade; Coherent Yang-Mills [Magas]• Local Equilibrium Hydro, EoS• Final Freeze-out: F.O. Surface • Final Freeze-out: Kinetic models

QGP Sudden and simultaneous hadronization and freeze out – CF formula

Problem 1: Conservation laws to non-eq!Problem 2: Post FO, non-eq. distribution!


Matching Conditions Again 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.)


Freeze outFreeze out

[L Bravina et al.]


Hypersurface


Space-like hypersurface - Problem II


Space-like hypersurface II


Post F.O. - Cut-Jüttner distribution

[Bugaev, Nucl.Phys.A606(96)559] No Eq., T, p, …, EoS !!![Anderlik et al., Phys.Rev.C59(99)3309]

Proposed by:

Solved:p

p

x

y

Post F.O. distribution:

pf(p)

V-parameter

V-flowMatching conditions determine 5 parameters only . Ansatz in needed for final f(x,p) !


Phase-Space FO probability


Phase-Space FO probability

A B C

D E F

Uniform =1

Time-like

F.O.

Space-like

F.O.

d3 = u

[A. Anderlik, E. Molnar, et al.]


Freeze out distribution with rescattering from kinetic model across

a layer

V=0V=0

[V. Magas, et al.,] Heavy Ion Phys.9:193-216,1999


Analytic fit to Kinetic Model Solution:

.

.[Karolis Tamosiunas et al.]


Cancelling Juttner Distribution [Karolis Tamosiunas et al.]


Sudden Freeze-Out & Hadronization from Sc. QGP

Negative P

(Positive T)

[O. Heggo-Hansen, MSc. Thesis, ‘03 ]


Global FlowDirected

Transverse

flow

Elliptic flow

3rd flow component(anti - flow)

3rd flow component(anti - flow)

Squeeze out


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]


Third flow component

[SPS NA49]


Anti-flow from shadowing :

[ L. Bravina, et al., PL B470 (99) 27.]

Only for b > 8 fm !

N


A=A=0.0650.065

11.4 fm/c


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

158 GeV/A

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

v1 0


V-1 flow at RHIC/STAR


Consequences

If v1 0 , earlier v2 results have to be modified (re-analyzed)

3-dim models and 3-dim initial conditions are needed to fit data

Impact parameter / multiplicity dependence is essential (more data)

Detailed models including equilibrium and non-equilibrium features will be required to describe the data


Flow & Azimuthal effects in HBT• HBT is biased by theor. Assumptions, eq. C(q,K) R=2fm /Gauss | R=8fm/u.Sphr.

• Flow changes C(q,K) essentially ! Use of analysis based on static sphr. Gauss. S is ?

[STAR ’01, Phenix ’02, Hydro: P Kolb et al ’03]


Conclusions

• Hydro works well! 3-dim. hydro, initial & final state models are important!

Local 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 detailed determination of flow patterns is vital for HBT, and for ALL observables influenced by the collective collision dynamics.

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L.P. Csernai, BNL Nov 17-19 '03 1 L..P. Csernai Multi module modelling of heavy ion collisions...

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