Hydrodynamic Approaches to Relativistic Heavy Ion Collisions

1
Hydrodynamic Approaches to Relativistic Heavy Ion
Collisions

• Tetsufumi Hirano
• RIKEN BNL Research Center

2
Contents

• Introduction dynamics of heavy ion collisions
• Hydrodynamic Models
• Equation of State
• Initial Condition
• Freezeout
• Success and Failure of Hydrodynamic approaches at
  RHIC
• Elliptic Flow
• HBT puzzle
• Summary

3
Introduction 1 Space-Time Evolution of Heavy Ion
Collision
jets
photons leptons
t
hadrons
Hadron phase
Cross over?
z
x
QGP phase
Reaction plane
z (collision axis)
0
Time scale 10 fm/c
4
Introduction 2 Static to Dynamic
Matter produce in heavy ion collisions is
DYNAMIC.
STATIC QCD matter
Lattice QCD simulations

• Space-time evolution
• Expansion
• Cool down
• Phase transition

One possible description is HYDRODYNAMICS.
F.Karsch et al. (00)

• Powerful and reliable
• 1st principle calculations
• Currently, small size and
• no time evolution

Full 3D simulation by T.H. and Y.Nara (04)
5
Basics of Hydrodynamics
Hydrodynamic Equations
Energy-momentum conservation
Charge conservations (baryon, strangeness, etc)

• Need equation of state
• (EoS)
• P(e,nB)
• to close the system of eqs.
• ? Hydro can be connected
• directly with lattice QCD

For perfect fluids (neglecting viscosity),
Energy density
Pressure
4-velocity
Within ideal hydrodynamics, pressure gradient
dP/dx is the driving force of collective flow.
? Collective flow is believed to reflect
information about EoS! ? Phenomenon which
connects 1st principle with experiment
Caveat Thermalization, l ltlt (typical system size)
6
Inputs for Hydrodynamic Simulations
Final stage Free streaming particles ? Need
decoupling prescription
t
Intermediate stage Hydrodynamics can be valid if
thermalization is achieved. ? Need EoS
z

• Initial stage
• Particle production and
• pre-thermalization
• beyond hydrodynamics
• Instead, initial conditions
• for hydro simulations

Need modeling (1) EoS, (2) Initial cond., and (3)
Decoupling
7
Main Ingredient Equation of State
One can test many kinds of EoS in hydrodynamics.
Typical EoS in hydro model
Lattice QCD simulations
H resonance gas(RG)
Q QGPRG
F.Karsch et al. (00)
pe/3
From P.Kolb and U.Heinz(03)
Latent heat
Lattice QCD predicts cross over phase
transition. Nevertheless, energy density
explosively increases in the vicinity of Tc. ?
Looks like 1st order.
8
Interface 1 Initial Condition

• Need initial conditions (energy density, flow
  velocity,)

Initial time t0 thermalization time

• Take initial distribution
• from other calculations

• Parametrize initial
• hydrodynamic field

y
y
T.H.(02)
x
x
x
Energy density from NeXus. (Left) Average over 30
events (Right) Event-by-event basis
(Talk by Hama)
ex.) In transverse plane, energy density or
entropy density prop. to of participants, of
binary collisions, or etc.
9
Interface 2 Freezeout
Need translation from thermodynamic variables to
particle spectra to be observed.
Sudden freezeout (Cooper-Frye formula)
Continuous particle emission (Talk by Hama)
Hadronic afterburner via Boltzmann eq.
Hadronic Cascade (RQMD, UrQMD)
QGP Fluid
QGP Fluid
QGP Fluid
Escaping probability P
Hadron Fluid
l0
Tf.o.
Teaney, Lauret, Shuryak Bass, Dumitru
linfinity
ffree(x,p)Pf(x,p)
t
10
Hydrodynamic Models _at_ RHIC
There are many options

• In addition,
• Dimension
• Boost inv. (Bjorken, 83)
• 1D(r) boost inv.
• cylindrical sym.
• 2D(x,y) boost inv.
• Full 3D
• Cartesian (t,x,y,z)
• t-h coordinate

• Initial conditions
• Parametrization
• Taken from other model
• With/without fluctuation
• EoS
• Lattice inspired model
• With/without phase transition
• With/without chemical freeze out
• Decoupling
• Sudden freezeout
• Continuous emission
• Hadronic cascade

Each option reflects what one wants to study.
11
Success of Hydrodynamics--Elliptic Flow--
Ollitrault (92)
Talk by Voloshin
How the system respond to initial spatial
anisotropy?
Hydrodynamic expansion
y
f
x
INPUT
Initial spatial anisotropy
2v2
Rescattering
dN/df
OUTPUT
Final momentum anisotropy
f
0
2p
12
Boltzmann to Hydro !?
Molnar and Huovinen (04)
47mb inelastic cross section of pp at
RHIC energy!? Still 30 smaller than hydro
result!
elastic cross section
Hydro (l0) is expected to gain maximum v2 among
transport theories. ? hydrodynamic (maximum)
limit
13
Hydrodynamic Results of v2/e
STAR(02)
Kolb, Sollfrank, Heinz (00)

• Dimension
• 2Dboost inv.
• Initial condition
• Parametrization
• EoS
• QGP RG (chem. eq.)
• Decoupling
• Sudden freezeout

LHC?
(response)(output)/(input)

• Hydrodynamic response is
• const. v2/e 0.2 _at_ RHIC
• Exp. data reach hydrodynamic
• limit at RHIC for the first time.
• Exp. line is expected to bend
• at higher collision energy.

Number density per unit transverse area
14
Hydrodynamic Results of v2(pT,m)
PHENIX(03)

• Correct pT dependence
• up to pT1-1.5 GeV/c
• Mass ordering
• Deviation in intermediate
• high pT regions
• ? Other physics
• Jet quenching
• (Talk by Vitev)
• Recombination
• (Talk by Hwa)
• Not compatible with particle ratio
• Need chem. freezeout
• mechanism

Huovinen et al.(01)

• Dimension
• 2Dboost inv.
• Initial condition
• Parametrization
• EoS
• QGP RG (chem. eq.)
• Decoupling
• Sudden freezeout

15
Hydrodynamic Results of v2(h)

• Hydrodynamics works
• only at midrapidity?
• Forward rapidity at RHIC
• Midrapidity at SPS?
• Heinz and Kolb (04)

T.H. and K.Tsuda(02)

• Dimension
• Full 3D (t-h coordinate)
• Initial condition
• Parametrization
• EoS
• QGP RG (chem. eq.)
• QGP RG (chem. frozen)
• Decoupling
• Sudden freezeout

16
Hydrodynamic Results of v2 (again)
Teaney, Lauret, Shuryak(01)

• Dimension
• 2Dboost inv.
• Initial condition
• Parametrization
• EoS
• Parametrized by latent heat
• (LH8, LH16, LH-infinity)
• RG
• QGPRG (chem. eq.)
• Decoupling
• Hadronic cascade (RQMD)

• Large gap (50 reduction) at SPS comes
• from finite l or viscosity.
• Latent heat 0.8 GeV/fm3 is favored.
• Hadronic afterburner explains forward rapidity?
• (T.H. and
  Y.Nara, in progress)

17
Summary for Success of Hydrodynamics

• Description of elliptic flow parameter v2
• v2(pT,m)
• Up to 1-1.5 GeV/c
• v2(h)
• Near midrapidity
• Multiplicity dependence
• Need cascade/viscosity for hadrons
• Phase transition with latent
• heat 0.8 GeV/fm3 is favored

• Future study
• Forward rapidity by hydrohadronic cascade
• Viscosity in QGP
• A lot of work should be done

18
Failure of Hydrodynamics--HBT puzzle--
Talks by Magestro, Csorgo and Hama
p1
Birds eye view
View from beam axis
q
Rside
Rlong
KT
y
p2
Rout
x
reaction plane
z
2
C2
Two particle corr. fn.
1/R
1
q
19
Source Function and Flow
Source fn.
Long wave length
Short wave length
Midrapidity cylindrical symmetry
x-y
x-t
KT Wave length to extract radii
Source fn. from hydro
From P.Kolb and U.Heinz(03)
20
Sensitivity to Chemical Composition
T.H. and K.Tsuda (02)

• Dimension
• Full 3D (t-h coordinate)
• Initial condition
• Parametrization
• EoS
• QGP RG (chem. eq.)
• QGP RG (chem. frozen)
• Decoupling
• Sudden freezeout

Rside
DASHED LINE
Rout
SOLID LINE
Rlong

• Rout/ Rside(hydro) gt Rout/ Rside(data)1
• HBT puzzle!!!
• HBT radii reflects last interaction points.
• ? Problem of sudden freezeout?

Rout/ Rside
Note that exp. data of Rout/Rside slightly
increase by considering core-halo picture
21
Sensitivity to Freezeout (contd.)
Soff, Bass, Dumitru (01)

• Dimension
• 1Dboost inv. cylindrical sym.
• Initial condition
• Parametrization
• EoS
• QGP RG (chem. eq.)
• Decoupling
• Hadronic afterburner by UrQMD

Hydrocascade 200
Hydro 160
Hydrocascade 160
Hydro 200
STAR
PHENIX

• Better in low pT region
• for Tc160 MeV case by
• smearing through cascade.
• Still something is missing
• to interpret the data. (Absolute
• value?)

Taken from D. Magestro, talk _at_ QM04
HBT radii from continuous particle emission
model ? Talk by Hama
22
x-t Correlation of Source Function
Why hydro doesnt work?
positive!
Positive? Negative?
RoutRside may require positive x-t corr.
t
t
Typical source fn. from hydro
Hubble like flow? Csorgo et al.
x
x
Positive x-t correlation
Negative x-t correlation
23
Summary and Outlook

• From elliptic flow point of view, a hydro
  cascade
• (RQMD) model with latent heat 0.8 GeV/fm3 gives
• a good description at both SPS and RHIC (in low
• pT and near midrapidity).
• Need full 3D hydro hadronic cascade
• (a possible model to describe all rapidity
  region
• at RHIC)
• However, a similar model (hydro UrQMD) fails
  to
• reproduce HBT radii.
• Need a thorough search for initial conditions
• Need more sophisticated description of the late
• stage (HBT is a quantum effects!)