Hydrodynamic Approaches to Relativistic Heavy Ion Collisions

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Transcript Hydrodynamic Approaches to Relativistic Heavy Ion Collisions

Hydrodynamic Approaches
to Relativistic Heavy Ion
Collisions
Tetsufumi Hirano
RIKEN BNL Research Center
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
Introduction 1: Space-Time Evolution
of Heavy Ion Collision
photons
leptons
Hadron phase
jets
t
hadrons
Cross over?
z
x
QGP phase
Reaction plane
Time scale
~10 fm/c
0
z
(collision
axis)
Introduction 2: Static to Dynamic
STATIC QCD matter
Lattice QCD simulations
Matter produce in heavy ion collisions is
DYNAMIC.
•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)
Basics of Hydrodynamics
Hydrodynamic Equations
Energy-momentum conservation
Charge conservations (baryon, strangeness, etc…)
For perfect fluids (neglecting viscosity),
Need equation of state
(EoS)
P(e,nB)
Energy density
Pressure
4-velocity
to close the system of eqs.
 Hydro can be connected
directly with lattice QCD
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 << (typical system size)
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
Need modeling
(1) EoS, (2) Initial cond.,
and (3) Decoupling
Initial stage:
Particle production and
pre-thermalization
beyond hydrodynamics
Instead, initial conditions
for hydro simulations
Main Ingredient: Equation of State
One can test many kinds of EoS in hydrodynamics.
Typical EoS in hydro model
Latent heat
Lattice QCD predicts cross over phase transition.
Nevertheless, energy density explosively increases
in the vicinity of Tc.  Looks like 1st order.
F.Karsch et al. (’00)
From P.Kolb and U.Heinz(’03)
H: resonance gas(RG)
Q: QGP+RG
Lattice QCD simulations
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
T.H.(’02)
y
y
x
x
ex.) In transverse plane,
energy density or entropy density
prop. to # of participants, # of
binary collisions, or etc.
x
Energy density from NeXus.
(Left) Average over 30 events
(Right) Event-by-event basis
(Talk by Hama)
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.
QGP Fluid
QGP Fluid
QGP Fluid Hadronic
Hadron Fluid
l=0
Escaping
probability P
Tf.o.
l=infinity
t
ffree(x,p)=Pf(x,p)
Cascade
(RQMD,
UrQMD)
Teaney,
Lauret,
Shuryak
Bass,
Dumitru
…
Hydrodynamic Models @ RHIC
There are many options:
In addition,
•Initial conditions
Dimension
•Parametrization
• Boost inv. (Bjorken, ’83)
•Taken from other model
• 1D(r) + boost inv.
•With/without fluctuation
+ cylindrical sym.
•EoS
• 2D(x,y) + boost inv.
•Lattice inspired model
• Full 3D
•With/without phase transition
• Cartesian (t,x,y,z)
•With/without chemical freeze out
• t-h coordinate
•Decoupling
•Sudden freezeout
•Continuous emission
Each option reflects
•Hadronic cascade
what one wants to study.
Success of Hydrodynamics
Ollitrault (’92)
--Elliptic Flow-- Talk by Voloshin
How the system respond to initial spatial anisotropy?
Free streaming
Hydrodynamic expansion
y
f
x
INPUT
Rescattering
OUTPUT
0
f
2p
Final momentum
anisotropy
2v2
dN/df
dN/df
Initial spatial
anisotropy
0
f
Boltzmann to Hydro !?
Molnar and Huovinen (’04)
elastic cross section
47mb ~ inelastic cross
section of pp at RHIC
energy!?
Still ~30% smaller than
hydro result!
Hydro (l~0) is expected to gain
maximum v2 among transport theories.
 “hydrodynamic (maximum) limit”
Hydrodynamic Results of v2/e
Kolb, Sollfrank, Heinz (’00)
LHC?
(response)=(output)/(input)
STAR(’02)
Number density per
unit transverse area
• Dimension
• 2D+boost inv.
• Initial condition
• Parametrization
• EoS
• QGP + RG (chem. eq.)
• Decoupling
• Sudden freezeout
•Hydrodynamic response is
const. v2/e ~ 0.2 @ RHIC
•Exp. data reach hydrodynamic
limit at RHIC for the first time.
•Exp. line is expected to bend
at higher collision energy.
Hydrodynamic Results of v2(pT,m)
PHENIX(’03)
Huovinen et al.(’01)
• Dimension
• 2D+boost inv.
• Initial condition
• Parametrization
• EoS
• QGP + RG (chem. eq.)
• Decoupling
• Sudden freezeout
• Correct pT dependence
up to pT=1-1.5 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
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
1. QGP + RG (chem. eq.)
2. QGP + RG (chem. frozen)
• Decoupling
• Sudden freezeout
Hydrodynamic Results of v2 (again)
Teaney, Lauret, Shuryak(’01)
• Dimension
• 2D+boost inv.
• Initial condition
• Parametrization
• EoS
• Parametrized by latent heat
(LH8, LH16, LH-infinity)
• RG
• QGP+RG (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)
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 hydro+hadronic cascade
• Viscosity in QGP
• A lot of work should be done…
Failure of Hydrodynamics
by Magestro,
--HBT puzzle-- Talks
Csorgo and Hama
Bird’s eye view
p1
View from beam axis
y Rside KT
q
Rlong
p2
Rout
x
z
C2
2
Two particle corr. fn.
1
1/R
q
Source Function and Flow
Long
wave
length
Short
wave
length
Source fn.
Midrapidity & cylindrical symmetry
x-y
x-t
Source fn. from hydro
From P.Kolb and U.Heinz(’03)
KT: “Wave length” to extract radii
Rout/ Rside
Rlong
Rout
Rside
Sensitivity to Chemical Composition
T.H. and K.Tsuda (’02)
• Dimension
• Full 3D (t-h coordinate)
• Initial condition
• Parametrization
• EoS
1. QGP + RG (chem. eq.)
2. QGP + RG (chem. frozen)
• Decoupling
• Sudden freezeout
DASHED
LINE
SOLID
LINE
•Rout/ Rside(hydro) > Rout/ Rside(data)~1
HBT puzzle!!!
•HBT radii reflects last interaction points.
 Problem of sudden freezeout?
Note that exp. data of Rout/Rside slightly
increase by considering core-halo picture
Sensitivity to Freezeout (contd.)
Soff, Bass, Dumitru (’01)
• Dimension
Hydro+cascade 200
1D+boost inv. + cylindrical sym.
Hydro 160
• Initial condition
Parametrization
• EoS
Hydro+cascade 160
QGP + RG (chem. eq.)
Hydro 200
• Decoupling
Hadronic afterburner by UrQMD
STAR
PHENIX
Taken from D. Magestro, talk @ QM04
HBT radii from continuous
particle emission model
 Talk by Hama
•Better in low pT region
for Tc=160 MeV case by
smearing through cascade.
Still something is missing
to interpret the data. (Absolute
value?)
x-t Correlation of Source
Function
Why
hydro doesn’t work?
positive!
Positive? Negative?
Rout~Rside may require positive x-t corr.
t
Typical source fn.
from hydro
x
Negative x-t correlation
t
Hubble like flow?
Csorgo et al.
x
Positive x-t correlation
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!)