Hydrodynamics: Overview

1
Hydrodynamics Overview
Agnes NyiriEtele MolnarKorolis Tamosiunas
SQM 2004 - Cape Town, Sept. 14-20, 2004
L.P. Csernai
2
Topics

• Importance and success of Fluid-Dynamics (FD)
• Initial conditions
• Final Freeze Out (FO)
• Viscosity and numerics
• Outlook

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Importance
HeinzSQM2004
4
Importance
Gyulassy - QGP stands on 3 legs,
1st is the flow
EoS and Phase Transition are properties of
locally equilibrated and thermalized
matter, so we need some proof that
the matter reached this stage.

5
Success
Radial and Elliptic flow at central rapidity
strong dominant.
Simple, 21 dim. FD models can fit data.
String hadron cascade models usually do not.
ZabrodinSQM2004
v2(pt) data are well fitted,
however, v2(y) data (PHOBOS) are not!!!
6
Success
NEW ! Phenix v2 scaling data. Strong proof of
FD behaviour quark recombination. Analyzed and
reproduced in more FDmodels.
HeinzSQM2004
D.MolnarSQM2004
7
Success
RohrichSQM2004
Yp

• Landau hydrodynamics
• Gaussian rapidity distribution
• Width ? depends only on c.m. energy

Difficult to imagine a joint initial state !
Finite boost-invariant region ? lt 2
L.D. Landau, Izv. Akad. Nauk SSSR 17 (1953)
52 P.Carruthers, M.Duong-van, PRD 8 (1973) 859
8
Success
NEW ! PHOBOS v1 data are described by
QGSM. Caused by shadowing central softening
inthe model.
ZabrodinSQM2004
9
Success
GSI - FOPI
AGS
?0 Directed flow AGS finds difference
between ?0 and p flow.
MerschmeyerSQM2004
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Hints from elliptic flow
UrQMD

• Data shows saturation of scaled v2
• High mass resonances like in UrQMD 2.1 can not
  explain v2 above 40 AGeV
• Strong hint for initial QGP pressure from
  30 AGeV on !

30 AGeV
Data for h-
BleicherSQM2004
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Flow excitation functions Summary

• Standard transport models can not describe
  radial flow
• Inclusion of high mass resonances leads to
  additional flow (maybe necessary at low
  energies)
• Inclusion of Cronin effect leads to additional
  flow (maybe necessary at high energies)
• Assumption of an early QGP phase might create
  additional flow

BleicherSQM2004
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QGSM
BravinaSQM2004
13
Initial condition
FD is applicable at the middle stages of a heavy
ion reaction. The Initial State and final Freeze
Out must be described in another way.
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Initial condition
Simple, 21 dim. FD models can fit data quite
well ! This is not too surprising as most FD
model calculations
HeinzSQM2004
These parameters are fitted to the measured
data! Not to the initial parameters of the
collision. (except the EoS)
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Initial condition

• Alternative (more demanding) approach all (or
  part) of parameters are calculated from the
  principal collisionparameters in an INITIAL
  STATE MODEL
• Nexus in NexSpherio
• Parton Cascade
• Yang Mills FT model Color Glas Condensate
• Yang Mills FT model - Color Flux tube streaks

3rd Flow Component (Anti-flow)
GrassiSQM2004
Magas, Csernai, Strottman, Phys. Rev. C64 (01)
014901
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Freeze Out
FD is applicable at the middle stages of a heavy
ion reaction. The Initial State and final Freeze
Out must be described in another way.
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QGSM
BravinaSQM2004
FO layer
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Freeze Out
FO from Fluid Dynamics (Frankfurt) At a FO
hyper-surface UrQMD is attached to Fluid
Dynamics. Hadronization happens usually before
the FO hyper-surface, in the FD regime(Maxwell
construction in the EoS).
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Freeze Out
Alternative FO possibility Rapid, simultaneous
FO and hadronization from super-cooled QGP in a
thin layer (2-3 fm).
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Freeze Out
Modified Boltzmann Transport Equation FO prob.
TamosiunasSQM2004
Grassi, Sinyukov, Hama,Kodama, Bugaev,
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Fluid Dynamics

• A standard, known, old theory.
• However, there are many delicacies
• Relativity
• Viscosity
• Numerics
• ? Strong feedbacks, instabilities,

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Viscosity
Related to the cross section. In class. kinetic
theory
D.MolnarSQM2004
At low energies, lt 1AGeV,from A E scaling?
5-70 MeV/fm2 c Lsf 1-4 fm
Schurmann, Bonasera,Danielevicz, L.P. Cs 80s
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Viscosity
HeinzSQM2004
DANGER
Is this really small ??Depends on other
conditions!
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Viscosity
Second order, extended viscous FD solves the
acausality and stability problems of rel.
NS-FD. Improved Bjorken model solutions !!! How
is this connected to numerical methods ?
MurongaSQM2004
25
Viscosity
Reynolds number
DANGER

• ? is sufficiently LARGE the flow in a heavy ion
  collision is laminar! It can be calculated
  withfluid dynamics!
• If

the flow is unstable, turbulent.
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Viscosity
High resolution Small numerical viscosity Low
resolution Large numerical viscosity Small
viscosity leads to instabilities, fluctuations
turbulence ! (Re gtgt 100) Numerical and parametric
viscosities add up to give the physical viscosity
in the model. Movies with low and high resolution
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Viscosity
Relativistic, 31 dim., viscous FD modelis very
delicate (no free copies!) www Parametric,
extended numerical visco-sities should be
added up. wwwwww Euler eq. can be used with
well chosennumerical viscosity and method.
www Very special approach - Spherio -soft
Lagrangian particles smooth high fq.-entropy
conservation is enforced-dissipated high fq.
energy is returned to low fq. kinetic
excitations.
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Outlook
Full Experimental detection of flow is alsovery
delicate many complex flow patternse.g.
v2, dN/dy, are notpublished yet in thisy range.
No modelsfit these data !!!
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Outlook
Several experimental methods exist, and it takes
time and effort to analyse the data in a best
way.
NyiriSQM2004
v1,v2 vs. pt,y dN/dy, dN/dpt simultaneous
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Outlook
Very complex and delicate theoretical analysis
is needed 31 dim. FD, with goodinitial state
and FO description. Concepts like non-flow
should be clarified.
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Good Hope gt
that these experiments with more detailed
theoretical analysis will provide a large
amount of valuable information, more than up to
now EoS, transport coeff., string tension,
initial dynamics, hadronization dynamics,