l.p. csernai, bnl nov 17-19 '03 1 l..p. csernai multi module modelling of heavy ion collisions...
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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
L.P. Csernai, BNL Nov 17-19 '033
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)
L.P. Csernai, BNL Nov 17-19 '034
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
L.P. Csernai, BNL Nov 17-19 '035
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
L.P. Csernai, BNL Nov 17-19 '036
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
L.P. Csernai, BNL Nov 17-19 '037
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?
L.P. Csernai, BNL Nov 17-19 '038
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?
L.P. Csernai, BNL Nov 17-19 '039
Multi Module ModelingMulti Module Modeling
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
L.P. Csernai, BNL Nov 17-19 '0310
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
L.P. Csernai, BNL Nov 17-19 '0311
L.P. Csernai, BNL Nov 17-19 '0312
Fire streak picture - Only in 3 dimensions!
Myers, Gosset, Kapusta, Westfall
L.P. Csernai, BNL Nov 17-19 '0313
String rope --- Flux tube --- Coherent YM field
L.P. Csernai, BNL Nov 17-19 '0314
Initial stage: Coherent Yang-Mills model
[Magas, Csernai, Strottman, Phys. Rev. C64 (01) 014901]
L.P. Csernai, BNL Nov 17-19 '0315
Expanding string ropes – Full energy conservation
L.P. Csernai, BNL Nov 17-19 '0316
Yo – Yo Dynamics wo/ dissipation
L.P. Csernai, BNL Nov 17-19 '0317
wo/ dissipation
L.P. Csernai, BNL Nov 17-19 '0318
Initial state
3rd flow component
L.P. Csernai, BNL Nov 17-19 '0319
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.]
L.P. Csernai, BNL Nov 17-19 '0320
Modified Initial State
L.P. Csernai, BNL Nov 17-19 '0321
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.)
L.P. Csernai, BNL Nov 17-19 '0322
3-Dim Hydro for RHIC (PIC)3-Dim Hydro for RHIC (PIC)
L.P. Csernai, BNL Nov 17-19 '0323
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)
L.P. Csernai, BNL Nov 17-19 '0324
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!
L.P. Csernai, BNL Nov 17-19 '0325
Relativistic Fluid DynamicsRelativistic Fluid DynamicsFor any EoS, P=P(e,n), and any energy-momentum tensor in LE(!):
Not only for high v!
L.P. Csernai, BNL Nov 17-19 '0326
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 !!
L.P. Csernai, BNL Nov 17-19 '0327
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=2.3 fm/c, Tmax= 420 MeV, emax= 20.0 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
11.6 x 4.6 fm
L.P. Csernai, BNL Nov 17-19 '0328
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=4.6 fm/c, Tmax= 419 MeV, emax= 19.9 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
14.5 x 4.9 fm
L.P. Csernai, BNL Nov 17-19 '0329
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=6.9 fm/c, Tmax= 418 MeV, emax= 19.7 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
17.4 x 5.5 fm
L.P. Csernai, BNL Nov 17-19 '0330
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=9.1 fm/c, Tmax= 417 MeV, emax= 19.6 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
20.3 x 5.8 fm
L.P. Csernai, BNL Nov 17-19 '0331
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=11.4 fm/c, Tmax= 416 MeV, emax= 19.5 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
23.2 x 6.7 fm
L.P. Csernai, BNL Nov 17-19 '0332
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=13.7 fm/c, Tmax= 417 MeV, emax= 19.4 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
26.1 x 7.3 fm
L.P. Csernai, BNL Nov 17-19 '0333
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=16.0 fm/c, Tmax= 417 MeV, emax= 19.4 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
31.9 x 8.1 fm
L.P. Csernai, BNL Nov 17-19 '0334
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=18.2 fm/c, Tmax= 417 MeV, emax= 19.4 GeV/fm3, Lx,y= 1.45 fm, Lz=0.145 fm
. .
34.8 x 8.7 fm
L.P. Csernai, BNL Nov 17-19 '0335
Heavy Ion Coll. at RHIC - Transverse velocities - b=0.5
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5045403530252015
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50 cyclesb=0.5
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5045403530252015
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[ Strottman, Magas, Csernai, BCPL User Mtg. Trento, 2003 ]
DYNAMICz
L.P. Csernai, BNL Nov 17-19 '0336
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
- If QGP Sudden and simultaneous hadronization and freeze out (indicated by HBT, Strangeness, Entropy puzzle)Landau (1953), Milekhin (1958), Cooper & Frye (1974)
L.P. Csernai, BNL Nov 17-19 '0337
[ 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
L.P. Csernai, BNL Nov 17-19 '0338
Freeze-Out Hyper-Surface Extraction with Digital Image Processing Techniques
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 !!
L.P. Csernai, BNL Nov 17-19 '0339
Bernd R. Schlei (T-1)
3+1 D Hydrodynamic Density Data, D. Strottman, Theoretical Division, Los Alamos National Laboratory.
Freeze-Out Hyper-Surface Extraction with Digital Image Processing Techniques
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.
L.P. Csernai, BNL Nov 17-19 '0340
Y
X
Z
b=0.5 bmax
Modified Initial State
L.P. Csernai, BNL Nov 17-19 '0341
L.P. Csernai, BNL Nov 17-19 '0342
L.P. Csernai, BNL Nov 17-19 '0343
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
L.P. Csernai, BNL Nov 17-19 '0344
Reaction Plane - [ X , Z ]X
Z
L.P. Csernai, BNL Nov 17-19 '0345
L.P. Csernai, BNL Nov 17-19 '0346
L.P. Csernai, BNL Nov 17-19 '0347
L.P. Csernai, BNL Nov 17-19 '0348
L.P. Csernai, BNL Nov 17-19 '0349
L.P. Csernai, BNL Nov 17-19 '0350
L.P. Csernai, BNL Nov 17-19 '0351
Quick Time - Movie - External
[Due to MS’s competitive business practices]
Reaction Plane
Surface at T = 139 MeV
Hy-mov-00.mov
L.P. Csernai, BNL Nov 17-19 '0352
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!
L.P. Csernai, BNL Nov 17-19 '0353
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.)
L.P. Csernai, BNL Nov 17-19 '0354
Freeze outFreeze out
[L Bravina et al.]
L.P. Csernai, BNL Nov 17-19 '0355
Hypersurface
L.P. Csernai, BNL Nov 17-19 '0356
Space-like hypersurface - Problem II
L.P. Csernai, BNL Nov 17-19 '0357
Space-like hypersurface II
L.P. Csernai, BNL Nov 17-19 '0358
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) !
L.P. Csernai, BNL Nov 17-19 '0359
Phase-Space FO probability
L.P. Csernai, BNL Nov 17-19 '0360
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.]
L.P. Csernai, BNL Nov 17-19 '0361
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
L.P. Csernai, BNL Nov 17-19 '0362
Analytic fit to Kinetic Model Solution:
.
.[Karolis Tamosiunas et al.]
L.P. Csernai, BNL Nov 17-19 '0363
Cancelling Juttner Distribution [Karolis Tamosiunas et al.]
L.P. Csernai, BNL Nov 17-19 '0364
Sudden Freeze-Out & Hadronization from Sc. QGP
Negative P
(Positive T)
[O. Heggo-Hansen, MSc. Thesis, ‘03 ]
L.P. Csernai, BNL Nov 17-19 '0365
Global FlowDirected
Transverse
flow
Elliptic flow
3rd flow component(anti - flow)
3rd flow component(anti - flow)
Squeeze out
L.P. Csernai, BNL Nov 17-19 '0367
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).
L.P. Csernai, BNL Nov 17-19 '0368
3rd flow component
Hydro
[Csernai, HIPAGS’93]
L.P. Csernai, BNL Nov 17-19 '0369
Third flow component
[SPS NA49]
L.P. Csernai, BNL Nov 17-19 '0370
Anti-flow from shadowing :
[ L. Bravina, et al., PL B470 (99) 27.]
Only for b > 8 fm !
N
L.P. Csernai, BNL Nov 17-19 '0371
A=A=0.0650.065
11.4 fm/c
L.P. Csernai, BNL Nov 17-19 '0372
“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
L.P. Csernai, BNL Nov 17-19 '0373
V-1 flow at RHIC/STAR
L.P. Csernai, BNL Nov 17-19 '0374
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
L.P. Csernai, BNL Nov 17-19 '0375
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]
L.P. Csernai, BNL Nov 17-19 '0376
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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