Hydrodynamic Approaches Hydrodynamic Approaches to Relativistic Heavy Ion to Relativistic Heavy Ion

CollisionsCollisions

Tetsufumi HiranoTetsufumi Hirano

RIKEN BNL Research CenterRIKEN BNL Research Center

ContentsContents

• 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 Introduction 1: Space-Time Evolution of Heavy Ion Evolution of Heavy Ion

Collision Collision

z(collision

axis)

t

QGP phase

Cross over?

0

hadrons

photonsleptons

Hadron phase

jets

z

x

Reaction plane

Time scale~10 fm/c

Introduction 2: Static to Introduction 2: Static to DynamicDynamic

Lattice QCD simulationsLattice QCD simulationsLattice QCD simulationsLattice QCD simulations

F.Karsch et al. (’00)

STATIC QCD matter Matter produce in heavy ion collisions is

DYNAMIC.

Full 3D simulation by T.H. and Y.Nara (’04)

•Powerful and reliable•1st principle calculations•Currently, small size andno time evolution

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

One possible description isHYDRODYNAMICS.

Basics of HydrodynamicsBasics of HydrodynamicsHydrodynamic Equations

Energy-momentum conservation

Charge conservations (baryon, strangeness, etc…)

For perfect fluids (neglecting viscosity),

Energy density Pressure 4-velocity

Within ideal hydrodynamics, pressure gradient dP/dx is the drivingforce of collective flow. Collective flow is believed to reflect information about EoS! Phenomenon which connects 1st principle with experiment

Need equation of state(EoS)

P(e,nB)

to close the system of eqs. Hydro can be connecteddirectly with lattice QCD

Caveat: Thermalization, << (typical system size)

Inputs for Hydrodynamic Inputs for Hydrodynamic SimulationsSimulations

Final stage:Free streaming particles Need decoupling prescription

Intermediate stage:Hydrodynamics can be validif thermalization is achieved. Need EoS

Initial stage:Particle production andpre-thermalizationbeyond hydrodynamicsInstead, initial conditions for hydro simulations

t

z

Need modeling(1) EoS, (2) Initial cond., and (3) Decoupling

Main Ingredient: Equation Main Ingredient: Equation of Stateof State

Latent heat

One can test many kinds of EoS in hydrodynamics.

Lattice QCD predicts cross over phase transition.Nevertheless, energy density explosively increases in the vicinity of Tc. Looks like 1st order.

Lattice QCD simulationsLattice QCD simulationsLattice QCD simulationsLattice QCD simulationsTypical EoS in hydro modelTypical EoS in hydro modelTypical EoS in hydro modelTypical EoS in hydro model

H: resonance gas(RG)

p=e/3

Q: QGP+RG

F.K

arsch et al. (’00)

From

P.K

olb and U.H

einz(’03)

Interface 1: Initial Interface 1: Initial ConditionCondition

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

•Parametrize initialhydrodynamic field

•Take initial distributionfrom other calculations

Initial time 0 ~ thermalization time

ex.) In transverse plane,energy density or entropy densityprop. to # of participants, # of binary collisions, or etc.

Energy density from NeXus.(Left) Average over 30 events(Right) Event-by-event basis (Talk by Hama)

T.H

.(’0

2)

xx x

yy

Interface 2: FreezeoutInterface 2: Freezeout

Need translation from thermodynamic variables to particle spectra to be observed.

Sudden freezeout(Cooper-Frye formula)

Continuous particleemission (Talk by Hama)

Hadronic afterburnervia Boltzmann eq.

HadronicCascade(RQMD,UrQMD)

QGP Fluid

Teaney,Lauret,ShuryakBass,Dumitru…

QGP FluidQGP Fluid

Hadron Fluid =0

=infinity

Tf.o.

Escaping

probability P

ffree(x,p)=Pf(x,p)

Hydrodynamic Models @ Hydrodynamic Models @ RHICRHIC

•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

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)• coordinate

Each option reflectswhat one wants to study.

Success of HydrodynamicsSuccess of Hydrodynamics--Elliptic Flow----Elliptic Flow--

How the system respond to initial spatial anisotropy?

Ollitrault (’92)

Hydrodynamic expansion

Initial spatial anisotropy

Final momentum anisotropy

INPUT

OUTPUT

Rescattering

dN/d

Free streaming

0 2

dN/d

0 2

2v2

x

y

Talk by Voloshin

Boltzmann to Hydro !?Boltzmann to Hydro !?Molnar and Huovinen (’04)

ela

stic cross se

ction

47mb ~ inelastic crosssection of pp at RHICenergy!?Still ~30% smaller thanhydro result!

Hydro (~0) is expected to gainmaximum v2 among transport theories. “hydrodynamic (maximum) limit”

Hydrodynamic Results of Hydrodynamic Results of vv22//

•Hydrodynamic response isconst. v2/ ~ 0.2 @ RHIC•Exp. data reach hydrodynamiclimit at RHIC for the first time.•Exp. line is expected to bendat higher collision energy.

(re

spo

nse

)=(o

utp

ut)/

(inp

ut)

Number density per unit transverse area

• Dimension• 2D+boost inv.

• Initial condition• Parametrization

• EoS• QGP + RG (chem. eq.)

• Decoupling• Sudden freezeout

STAR(’02)

LHC

?

Kolb, Sollfrank, Heinz (’00)

Hydrodynamic Results of Hydrodynamic Results of vv22((ppTT,,mm) )

• Dimension• 2D+boost inv.

• Initial condition• Parametrization

• EoS• QGP + RG (chem. eq.)

• Decoupling• Sudden freezeout

PHENIX(’03)

• 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

Huovinen et al.(’01)

Hydrodynamic Results of Hydrodynamic Results of vv22(())

• Dimension• Full 3D ( coordinate)

• Initial condition• Parametrization

• EoS1. QGP + RG (chem. eq.)2. QGP + RG (chem. frozen)

• Decoupling• Sudden freezeout

•Hydrodynamics worksonly at midrapidity?•Forward rapidity at RHIC~ Midrapidity at SPS? Heinz and Kolb (’04)

T.H. and K.Tsuda(’02)

Hydrodynamic Results of Hydrodynamic Results of vv22 (again)(again)

• 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)

Teaney, Lauret, Shuryak(’01)

• Large gap (~50% reduction) at SPS comesfrom finite 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 Summary for Success of HydrodynamicsHydrodynamics

• Description of elliptic flow parameter v2

• v2(pT,m)• Up to 1-1.5 GeV/c

• v2()• 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 HydrodynamicsFailure of Hydrodynamics--HBT puzzle----HBT puzzle-- Talks by Magestro,

Csorgo and Hama

p1

p2

reaction planez

Rlong KT

Rout

Rside

x

y

Two particle corr. fn.

Bird’s eye view View from beam axisq

1

2

C2

q

1/R

Source Function and Source Function and FlowFlow

Longwavelength

Shortwavelength

Source fn. from hydro

x-y

x-t

Midrapidity & cylindrical symmetry

From P.Kolb and U.Heinz(’03)

KT: “Wave length” to extract radii

Source fn.

Sensitivity to Chemical Sensitivity to Chemical CompositionComposition

• Dimension• Full 3D ( coordinate)

• Initial condition• Parametrization

• EoS1. QGP + RG (chem. eq.)2. QGP + RG (chem. frozen)

• Decoupling• Sudden freezeout

T.H. and K.Tsuda (’02)

SOLIDLINE

DASHEDLINE

Rsi

de

Ro

ut

Rlo

ng

Ro

ut/

Rsi

de

Note that exp. data of Rout/Rside slightly increase by considering core-halo picture

•Rout/ Rside(hydro) > Rout/ Rside(data)~1HBT puzzle!!!HBT puzzle!!!

•HBT radii reflects last interaction points. Problem of sudden freezeout?

Sensitivity to Freezeout Sensitivity to Freezeout (contd.)(contd.)

HBT radii from continuousparticle emission model Talk by Hama

• Dimension1D+boost inv. + cylindrical sym.

• Initial conditionParametrization

• EoSQGP + RG (chem. eq.)

• DecouplingHadronic afterburner by UrQMD

•Better in low pT region for Tc=160 MeV case by smearing through cascade.Still something is missingto interpret the data. (Absolutevalue?)

STARPHENIX

Taken from D. Magestro, talk @ QM04

Hydro 200

Hydro 160

Hydro+cascade 200

Hydro+cascade 160

Soff, Bass, Dumitru (’01)

x-tx-t Correlation of Source Correlation of Source FunctionFunctionWhy hydro doesn’t work?

positive!

x

t

Negative x-t correlation

Positive? Negative?

Typical source fn.from hydro

x

t

Positive x-t correlation

Hubble like flow?Csorgo et al.

Rout~Rside may require positive x-t corr.

Summary and OutlookSummary 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!)