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LP. Csernai, NWE'2001, Bergen 1
Part II
Relativistic HydrodynamicsFor Modeling Ultra-Relativistic Heavy Ion Reactions
LP. Csernai, NWE'2001, Bergen 2
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)
Experiment
LP. Csernai, NWE'2001, Bergen 3
Global Flow Directed Transverse flow
Elliptic flow
3rd flow component(anti - flow)
Squeeze out
LP. Csernai, NWE'2001, Bergen 4
Spherical Flow from Identified Particle Spectra
pT (GeV/c) pT (GeV/c)
Fit K, p spectra to obtain
<T> ~ 0.35Tfo ~ 180-200 MeV
Systematic errors:to be determined
[W.A. Zajc, QM’2001]
LP. Csernai, NWE'2001, Bergen 5
More spherical flow at RHIC !
[N.Xu, QM’2001]
LP. Csernai, NWE'2001, Bergen 6
Global Flow Directed Transverse flow
Directed Transverse flow
Elliptic flow
3rd flow component(anti - flow)
Squeeze out
LP. Csernai, NWE'2001, Bergen 7
Repulsion Driven by Gradients in Mean-Field
• Flow decreases as function of Ebeam
• Measured sideways flow cannot be reproduced by cascade calculations (RQMD 2.3)
– “thermal” pressure insufficient amount of deflection
• Additional repulsion caused by gradients in mean-field
E895, Phys. Rev. Lett 84, 5488 (2000) Mike Lisa E895 Talk[C.Ogilvie, QM’2001]
LP. Csernai, NWE'2001, Bergen 8
Global FlowDirected
Transverse
flow
Elliptic flowElliptic flow
3rd flow component(anti - flow)
Squeeze out
LP. Csernai, NWE'2001, Bergen 9
LP. Csernai, NWE'2001, Bergen 10
Elliptic flow - SPS - NA49
LP. Csernai, NWE'2001, Bergen 11
pT dependence for ,p
• Hydro calculations: P. Huovinen, P. Kolb and U. Heinz
LP. Csernai, NWE'2001, Bergen 12
Elliptic flow at RHIC
[Huovinen, QM’2001]
LP. Csernai, NWE'2001, Bergen 13
Elliptic flow in MPC
[ D. Molnar, QM’2001 ]
LP. Csernai, NWE'2001, Bergen 14
LP. Csernai, NWE'2001, Bergen 15
Elliptic flow vs. Squeeze out
• At LBL, GSI, AGS flow is orthogonal to the reaction plane: Squeeze out
• At SPS, RHIC central flow is in the reaction plane: Elliptic flow. This is due to the initial state and shadowing.
[R. Lacey, QM’2001]
LP. Csernai, NWE'2001, Bergen 16
Comparison of all v2 results
PHENIX (pT>500 MeV)
nch/nmax
v2
[P.Steinberg, QM’2001]
LP. Csernai, NWE'2001, Bergen 17
LP. Csernai, NWE'2001, Bergen 18
Global FlowDirected
Transverse
flow
Elliptic flow
3rd flow component(anti - flow)
3rd flow component(anti - flow)
Squeeze out
LP. Csernai, NWE'2001, Bergen 19
K0s Anti-Flow Au+Au 6 AGeV
• Striking opposite flow for K0s
• Reproduced using repulsive mean-field for K0
Chris Pinkenberg E895 Talk
proton Chung et al.,Phys. Rev Lett85, 940 (2000)
Pal et al.,Phys. Rev. C 62, 061903 (2000)
K0s
LP. Csernai, NWE'2001, Bergen 20
Third flow component
[SPS NA49]
LP. Csernai, NWE'2001, Bergen 21
Third flow component / SPS / NA49
LP. Csernai, NWE'2001, Bergen 22
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).
• The effect is attributed to a flat (Landau type) initial condition.
• Similarity to elliptic flow.
LP. Csernai, NWE'2001, Bergen 23
3rd flow component
Hydro
[Csernai, HIPAGS’93]
LP. Csernai, NWE'2001, Bergen 27
Multi 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)
1
2
3
LP. Csernai, NWE'2001, Bergen 28
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.]
LP. Csernai, NWE'2001, Bergen 29
Modified Initial State
LP. Csernai, NWE'2001, Bergen 30
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
LP. Csernai, NWE'2001, Bergen 31
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
LP. Csernai, NWE'2001, Bergen 32
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
LP. Csernai, NWE'2001, Bergen 33
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
LP. Csernai, NWE'2001, Bergen 34
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
LP. Csernai, NWE'2001, Bergen 35
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
LP. Csernai, NWE'2001, Bergen 36
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
LP. Csernai, NWE'2001, Bergen 37
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
LP. Csernai, NWE'2001, Bergen 38
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
LP. Csernai, NWE'2001, Bergen 39
NEXT
• Freeze-out
• Discontinuities in hydro --- Eq. => Eq.
• Freeze-out to non-eq.
• Kinetic freeze-out
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