Relativistic Hydrodynamics

1
Part II
Relativistic Hydrodynamics For Modeling
Ultra-Relativistic Heavy Ion Reactions
2
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)

Experiment
Landau (1953), Milekhin (1958), Cooper Frye
(1974)
3
Global Flow
Directed Transverse flow
3rd flow component (anti - flow)
X
b
Z
Squeeze out
Spherical flow
Elliptic flow
4
Spherical Flow from Identified Particle Spectra

• Fit p, K, p
• spectra to obtain
• ltbTgt 0.35
• Tfo 180-200 MeV
• Systematic errorsto be determined

W.A. Zajc, QM2001
5
More spherical flow at RHIC !
N.Xu, QM2001
6
Global Flow
Directed Transverse flow
3rd flow component (anti - flow)
X
b
Z
Squeeze out
Elliptic flow
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, QM2001
8
Global Flow
Directed Transverse flow
3rd flow component (anti - flow)
X
b
Z
Squeeze out
Elliptic flow
9
(No Transcript)
10
Elliptic flow - SPS - NA49
11
pT dependence for p,p

• Hydro calculations P. Huovinen, P. Kolb and U.
  Heinz

12
Elliptic flow at RHIC
Huovinen, QM2001
13
Elliptic flow in MPC
D. Molnar, QM2001
14
(No Transcript)
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, QM2001
16
Comparison of all v2 results
v2
PHENIX (pTgt500 MeV)
nch/nmax
P.Steinberg, QM2001
17
(No Transcript)
18
Global Flow
Directed Transverse flow
3rd flow component (anti - flow)
X
b
Z
Squeeze out
Elliptic flow
19
K0s Anti-Flow AuAu 6 AGeV
proton
Chung et al., Phys. Rev Lett 85, 940 (2000) Pal
et al., Phys. Rev. C 62, 061903 (2000)

• Striking opposite flow for K0s
• Reproduced using repulsive mean-field for K0

Chris Pinkenberg E895 Talk
20
Third flow component
SPS NA49
21
Third flow component / SPS / NA49
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.

23
3rd flow component
Hydro Csernai, HIPAGS93
24
STRANGENESS and ENTROPY
N.Xu, QM2001
Entropy Pion number
T³
Strangeness Phase
transition
Gazdiczki Gorenstein
25
Strange baryon enhancement
Enhancement of ? yield in central PbPb compared
to pBe 15
m
26
Strange antibaryons

• In QGP s s-bar threshold is low
• Strangeness enhance.
• Hadronic and String models can reproduce this
  only if
• Massive objects are formed string ropes, quark
  clusters (QGP)

Quercigh, CERN 2000
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
28
Modified Initial State
In 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 ?
e GeV/ fm3
y
Z fm
Z fm
Magas, Csernai, Strottman, in pr.
29
Modified Initial State
30
3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t0.0 fm/c, Tmax 420 MeV, emax 20.0 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
EoS p e/3 - 4B/3
B 397 MeV/fm3
8.7 x 4.4 fm
31
3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t2.3 fm/c, Tmax 420 MeV, emax 20.0 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
11.6 x 4.6 fm
32
3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t4.6 fm/c, Tmax 419 MeV, emax 19.9 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
14.5 x 4.9 fm
33
3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t6.9 fm/c, Tmax 418 MeV, emax 19.7 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
17.4 x 5.5 fm
34
3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t9.1 fm/c, Tmax 417 MeV, emax 19.6 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
20.3 x 5.8 fm
35
3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t11.4 fm/c, Tmax 416 MeV, emax 19.5 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
23.2 x 6.7 fm
36
3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t13.7 fm/c, Tmax 417 MeV, emax 19.4 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
26.1 x 7.3 fm
37
3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t16.0 fm/c, Tmax 417 MeV, emax 19.4 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
31.9 x 8.1 fm
38
3-dim Hydro for RHIC Energies
AuAu ECM65 GeV/nucl. b0.5 bmax As0.08
gt s10 GeV/fm
e GeV / fm3 T MeV
.
.
t18.2 fm/c, Tmax 417 MeV, emax 19.4 GeV/fm3,
Lx,y 1.45 fm, Lz0.145 fm
34.8 x 8.7 fm
39
NEXT

• Freeze-out
• Discontinuities in hydro --- Eq. gt Eq.
• Freeze-out to non-eq.
• Kinetic freeze-out