LP. Csernai, NWE'2001, Bergen1 Part II Relativistic Hydrodynamics For Modeling Ultra-Relativistic Heavy Ion Reactions

LP. Csernai, NWE'2001, Bergen 1

Part II

Relativistic HydrodynamicsFor Modeling Ultra-Relativistic Heavy Ion Reactions


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


Global Flow Directed Transverse flow

Elliptic flow

3rd flow component(anti - flow)

Squeeze out


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]


More spherical flow at RHIC !

[N.Xu, QM’2001]


Global Flow Directed Transverse flow

Directed Transverse flow

Elliptic flow


Squeeze out


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]


Global FlowDirected

Transverse

flow

Elliptic flowElliptic flow


Squeeze out



Elliptic flow - SPS - NA49


pT dependence for ,p

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


Elliptic flow at RHIC

[Huovinen, QM’2001]


Elliptic flow in MPC

[ D. Molnar, QM’2001 ]



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]


Comparison of all v2 results

PHENIX (pT>500 MeV)

nch/nmax

v2

[P.Steinberg, QM’2001]



Global FlowDirected

Transverse

flow

Elliptic flow



Squeeze out


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


Third flow component

[SPS NA49]


Third flow component / SPS / NA49


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.


3rd flow component

Hydro

[Csernai, HIPAGS’93]


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


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


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





. .

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


NEXT

• Freeze-out

• Discontinuities in hydro --- Eq. => Eq.

• Freeze-out to non-eq.

• Kinetic freeze-out

Documents

LP. Csernai, NWE'2001, Bergen1 Part II Relativistic Hydrodynamics For Modeling Ultra-Relativistic Heavy Ion Reactions