Hydrodynamic Models of Heavy-Ion Collisions Tetsufumi Hirano RIKEN BNL Research Center.

Hydrodynamic Hydrodynamic Models of Heavy-Models of Heavy-

IIon Collisionson Collisions

Tetsufumi HiranoTetsufumi Hirano

RIKEN BNL Research RIKEN BNL Research CenterCenter

Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 22

Parallel Talks Based on Parallel Talks Based on HydroHydroJan. 13Jan. 13

•H. NiemiH. Niemi, , Photon production from non-equilibriumPhoton production from non-equilibrium QGP in heavy-ion collisionsQGP in heavy-ion collisions•M. CsanadM. Csanad, Indication for quark deconfinement and, Indication for quark deconfinement and evidence for a Hubble flow in Au+Au collisions at RHICevidence for a Hubble flow in Au+Au collisions at RHIC

Jan. 15Jan. 15•Y. NaraY. Nara, , CGC, hydrodynamics and the partonCGC, hydrodynamics and the parton energy lossenergy loss•E. ShuryakE. Shuryak, , Why does the QGP behaves liWhy does the QGP behaves likkee a perfect fluid?a perfect fluid?•U. HeinzU. Heinz, , Rapidity dependence of momentumRapidity dependence of momentum anisotropiesanisotropies in nuclear collisionsin nuclear collisions•D. TeaneyD. Teaney, , Viscosity and thermalizationViscosity and thermalization


OutlineOutline1.1. Why hydrodynamics?Why hydrodynamics?

2.2. How hydrodynamics works at RHICHow hydrodynamics works at RHIC

3.3. Hybrid models based on Hybrid models based on hydrodynamicshydrodynamics

– Information of the insideInformation of the inside (jet quenching , EM probe)(jet quenching , EM probe)– Improvement of initial stageImprovement of initial stage

4.4. Improvement of ideal hydro Improvement of ideal hydro (viscosity)(viscosity)

5.5. SummarySummary


1. Why Hydrodynamics?1. Why Hydrodynamics?Static•EoS from Lattice QCD•Finite T, field theory•Critical phenomena•Chiral property of hadron

Dynamic Phenomena in HIC•Expansion, Flow•Space-time evolution of thermodynamic variables

Once we accept localthermalization ansatz,life becomes very easy.

Caveat: Thermalization in HIC is a tough problem like building

the Golden Gate Bridge!

Energy-momentum:

Conserved number:


1. Why Hydrodynamics 1. Why Hydrodynamics (contd.)(contd.)

Transverse Longitudinal

e (G

eV

/fm3)

e (G

eV

/fm3)

A full 3D hydrodynamic simulation with a CGC initial conditionTalk by Y.Nara

Space-time evolution of energy density in sqrt(sNN)=200 GeV Au+Au collision at b=7.2fm

sp

ace-t

ime r

ap

idit

yHydrodynamics provides us a very intuitive

and simple description of relativistic heavy ion collisions.






4.4. Improvement of ideal hydro Improvement of ideal hydro (viscosity)(viscosity)

5.5. SummarySummary

Tetsufumi Hirano (RBRC)Tetsufumi Hirano (RBRC) 77:P.Kolb(’03), talk by A.Poskanzer

2. How Hydrodynamics 2. How Hydrodynamics Works at RHICWorks at RHIC

Elliptic flow (J.-Y.Ollitrault (’92))Elliptic flow (J.-Y.Ollitrault (’92))How does the system respond to initial spatial anisotropy?How does the system respond to initial spatial anisotropy?

A.Poskanzer & S.Voloshin (’98)

Dense or dilute?Dense or dilute?If dense, thermalization?If dense, thermalization?

If thermalized, EoS?If thermalized, EoS?


Elliptic Flow of Charged Elliptic Flow of Charged ParticlesParticles

T.H.(’01)

P.Huovinen(’03)Roughly speaking,ideal hydro gives a good description

For improvement of models, talk by U.Heinz

Roughly speaking,ideal hydro gives a good description

For improvement of models, talk by U.Heinz

P.Kolb et al.(’01)


More on Elliptic FlowMore on Elliptic Flow

See recent excellent reviews, P.Huovinen (QM2002) , nucl-th/0305064; P.Kolb and U.Heinz, nucl-th/0305084; E.Shuryak, hep-ph/0312227, today’s talk.

Hydro: P.Kolb et al.(’99)(Note: Hydro+RQMD

gives a better description.D.Teaney et al.(’01))

STAR, PRC66(’02)034904

Hydro: P.Huovinen et al.(’01)

PHENIX, PRL91(’03)182301.


What’s next?What’s next?

Ideal hydro seems to give Ideal hydro seems to give aa

good description at RHICgood description at RHIC

1.1. Making the most use of hydroMaking the most use of hydromodels to study the RHIC physicsmodels to study the RHIC physics

2.2. Checking how robust theChecking how robust thecurrent results are whencurrent results are when

hydro models are improvedhydro models are improved





– Information inside fluidsInformation inside fluids (jet quenching , EM probe)(jet quenching , EM probe)– Improvement of initial stageImprovement of initial stage

4.4. Improvement of ideal hydro (viscosity)Improvement of ideal hydro (viscosity)

5.5. SummarySummary


3.1 Information inside 3.1 Information inside fluidsfluids

Jet quenching isJet quenching is a manifestationa manifestation

of interaction betweenof interaction betweenmattermatter and partons and partons

(Talks by G.Moore and I.Vitev)(Talks by G.Moore and I.Vitev)

For quantitative analysis,For quantitative analysis,the information aboutthe information about

the space-time evolutionthe space-time evolutionof matterof matter

is indispensable!is indispensable!


3.1.1 Hydro as a Tool to 3.1.1 Hydro as a Tool to Analyze Analyze Jet QuenchingJet Quenching

Color: parton densityPlot: mini-jets

Au+Au 200AGeV, b=8 fmtransverse plane@midrapidityFragmentation switched off

hydro+jet modelJet quenching analysis takingJet quenching analysis takingaccount of (2+1)D hydro resultsaccount of (2+1)D hydro results (M.Gyulassy et al.(’02))(M.Gyulassy et al.(’02))

Hydro+Jet modelHydro+Jet model (T.H. & Y.Nara (’02))(T.H. & Y.Nara (’02))

Parton density Parton density ((xx) taken) taken from full 3D hydro simulationsfrom full 3D hydro simulations

x

yGLV 1GLV 1stst order formula (M.Gyulassy et al.(’00)) order formula (M.Gyulassy et al.(’00))

Movie and data ofMovie and data of ((xx) ) are available atare available athttp://quark.phy.bnl.gov/~hirano/http://quark.phy.bnl.gov/~hirano/


Interplay between Soft Interplay between Soft and Hardand Hard

NSOFT~NHARD

ppTT

(1/

(1/ ppTT)

()(dNdN

// dpdpTT))

HydrodynamicHydrodynamicafterburnerafterburner

JetJetquenchingquenching

Interesting regionIntermediate pT

(2<pT<3.5 GeV/c)Pion hard, Proton soft

It’s the veryheavy ion physics!

T.H & Y.Nara(’03)

Crossing pCrossing pTT moves movestoward high ptoward high pTT

softhard

Au+Au at b=2 fm


Consequense from hadron Consequense from hadron species dependent pspecies dependent pT,crossT,cross

Hydro+Jet

Talk by R.FriesTalk by R.Fries

Recombination+Fragmentation

RAARAA Particle ratioParticle ratio

“Scaling v2”Interplay between soft and hard?

Recombination mechanism?


Thermal photon is a penetrating probe of QGP (E.Shuryak(’78))

3.1.2 Hydro as a Tool to 3.1.2 Hydro as a Tool to Analyze Analyze Electromagnetic Electromagnetic RadiationRadiation

T, u

• Production rateProduction rate (Number per unit space-time volume)(Number per unit space-time volume)

• Invariant spectrum of photonsInvariant spectrum of photons

H.A.Weldon (’83), L.McLerran & T.Toimela (’84)C.Gale & J.Kapusta (’91)Talk by G.Moore

D.K.Srivastava & B.Sinha(’94), J.Sollfrank et al.(’97),J.Alam et al.(’01) and a lot of work

Importance of temperature profileImportance of temperature profile


Chemical Non-Chemical Non-EquilibriumEquilibriumQGP phaseQGP phase ““Gluon Plasma (GP)” Gluon Plasma (GP)”

QGPQGP

Hadron Hadron phasephase

Chemical freezeoutChemical freezeout

Talk by H.Niemi

Hydro + rate eq.Hydro + rate eq.Smaller d.o.f. Smaller d.o.f. Larger Larger

initial initial TT

T.H. & K.Tsuda(’02)

Hydro( )Hydro( )Overpopulation of Overpopulation of resonance resonance Rapid Rapid

cooling cooling

T.S.Biro et al.(’93), D.K.Srivastava et al.(’97),A.K.Chaudhuri(’00), D.M.Elliott & D.Rischke(’00)

N.Arbex et al.(’01), T.H. & K.Tsuda(’02),D.Teaney(’02), P.Kolb & R.Rapp(’03)

Talk by H.Niemi

QGP phaseQGP phase Hadron phaseHadron phase

100

200

300

400

500

600

700

800

Tem

pera

ture

(M

eV

)

0


Novel Temperature Novel Temperature EvolutionEvolution

Caveat: one has to take account offugacity in calculating EMspectra.

•QGP phase: <1•Hadron phase: >1

Compensation betweenT and ? Talk by H.Niemiproper time

Tc

tem

pera

ture

chemical non-eq.

chemical eq.


3.2 Improvement of Initial 3.2 Improvement of Initial ConditionCondition -Toward an unified model -Toward an unified model in HIC-in HIC-

GroupGroup HydroHydro Initial conditionInitial conditionM.Gyulassy et M.Gyulassy et al.al.

SHASTA (2+1D, SHASTA (2+1D, Bjorken)Bjorken)

HIJING, event-by-eventHIJING, event-by-event

C.Nonaka et C.Nonaka et al.al.

Lagrangian hydro (full Lagrangian hydro (full 3D)3D)

URASiMA, event averageURASiMA, event average

B.Schlei et al.B.Schlei et al. HYLANDER (2+1D)HYLANDER (2+1D) VNI, event averageVNI, event average

C.E.Aguiar et C.E.Aguiar et al.al.

SPheRIO (full 3D)SPheRIO (full 3D) NeXus, event-by-eventNeXus, event-by-event

L.P.Csernai et L.P.Csernai et al.al.

Particle-in-cell (full Particle-in-cell (full 3D)3D)

String ropes, flux tubes, String ropes, flux tubes, classical YMclassical YM

K.Eskola et al.K.Eskola et al. SHASTA (2+1D, SHASTA (2+1D, Bjorken)Bjorken)

pQCD + final state pQCD + final state saturationsaturation

T.H. & Y.NaraT.H. & Y.Nara coordinate (full coordinate (full 3D)3D)

CGC, CGC, ((kkTT22,,xx) a la Kharzeev ) a la Kharzeev

& Levin& Levin

…… …… ……


3.2.1 SPheRIO*3.2.1 SPheRIO*Main features:Main features:• ““Particle” method (a kind of Lagrangian hydro)Particle” method (a kind of Lagrangian hydro)• Numerical cost cheaper than conventional finite Numerical cost cheaper than conventional finite

grids method (Even in 3+1 D, any geometry)grids method (Even in 3+1 D, any geometry)• Event-by-event physicsEvent-by-event physics ( (NeXusNeXus + +

SPheRIO=NeXSPheRIO) SPheRIO=NeXSPheRIO) (NeXus: parton based Gribov-Regge theory)(NeXus: parton based Gribov-Regge theory)

*Smoothed Particle hydrodynamical evolution of Relativistic heavy IOn collisions (Sao Paulo & Rio de Janeiro)

C.E.Aguiar, R.Andrade, F.Grassi, Y.Hama,T.Kodama, T.Osada, O.Socolowski Jr….Poster by F.Grassi

Energy Energy densitydensityof single of single

eventeventSpectrafrom

Energy Energy densitydensityof single of single

eventevent Spectrafrom

Conventional approachSPheRIO

Similar approach based on HIJING: M.Gyulassy et al.(’97)


Initial Conditions in Initial Conditions in NeXSPheRIONeXSPheRIO

Single event (b=0fm)Single event (b=0fm) Average over 30 events (b=0fm)Average over 30 events (b=0fm)

Energy density in the transverse plane (z=0)Energy density in the transverse plane (z=0)

Bumpy!


Results from Results from NeXSPheRIONeXSPheRIOPb+Pb 17.3A GeV

Multiplicity is reduced by ~10%!

:(event average)

Effect of initial energy densityfluctuation (simple EoS case):

Negative!

pT slope is not affected largely. v2(pT) and its fluctuation?

Now the hydro simulation becomes

close to experimental situations

like event-generators!


3.2.2 CGC+Hydro+Jet 3.2.2 CGC+Hydro+Jet ModelModel T.H. & Y.Nara

Talk by Y.Nara

Dense MediumDense Medium

These three physics closely related with each other!

Talk by J.Jalilian-Marian

Talk by I.Vitev


CGC+Hydro+Jet Model CGC+Hydro+Jet Model (contd.)(contd.)

Full 3Dhydro evolution

pQCDpQCDpartonpartondilutedilute

timetimemom

en

tum

scale

mom

en

tum

scale

ggg

22

CGCCGCsmall xsmall xdensedense

collinearfactorization

kT factorization

Partonenergy loss

Initial condition of

energy density from

CGCAu+Au

200AGeVb=7.2fm, =0.6fm

transversetransverse longitudinallongitudinal


Results from Results from CGC+hydro+jetCGC+hydro+jet

Au+Au sqrt(sNN) = 200 GeV

For details, talk by Y.Nara

CGC initial conditionworks very well!

(Energy, rapidity, centralitydependences)






4.4. Improvement of ideal hydro (viscosity)Improvement of ideal hydro (viscosity)

5.5. SummarySummary


4. Viscosity4. ViscosityChange not only the equations of motionbut the local thermal distribution function A.Dumitru(’02), D.Teaney(’03)

• Blast wave model + dist. fn. with viscous correction

Talks by E.Shuryak and D.Teaney

1st order correction to dist. fn.:

:Sound attenuation length

:Tensor part of thermodynamic force

Reynolds number in Bjorken flow

Nearly ideal hydro !? D.Teaney(’03)


Break Down of Naive Break Down of Naive Navier-Stokes Eq. and a Navier-Stokes Eq. and a Relaxation MethodRelaxation Method•Non-relativistic case (Based on discussion by Cattaneo (1948))

0: Fourier’s law

: “relaxation time”

Parabolic equation (heat equation)ACAUSAL!!

Finite Hyperbolic equation (telegraph equation)

Balance eq.:

Constitutive eq.:

Talk by D.TeaneySee also, A.Muronga (’02)


5. Summary5. Summary

• Open our mind Open our mind !! Hydrodynamics Hydrodynamics can be used even can be used even for “high pfor “high pTT physics in HIC”.physics in HIC”.– Jet tomographyJet tomography– EM probeEM probe– (J/(J/ suppression) suppression)– ……

• Keep in mind Keep in mind !! How robust is the How robust is the

current agreement current agreement of hydro?:of hydro?:– Chemical non-eq.?Chemical non-eq.?– Initial fluctuation?Initial fluctuation?– Viscosity?Viscosity?– Thermalization?Thermalization?– EoS?EoS?– (Freeze-out?)(Freeze-out?)

Hydrodynamics is one of the valuable tools at RHIC energies


Thank you!Thank you!

Special thanks goes to: H.Niemi, D.Teaney,

Y.Hama, T.Kodama(SPheRIO collaboration),

Y.Nara,and

L.McLerranSpace-time evolution of energy density in

sqrt(sNN)=200 GeV Au+Au collision at b=7.2fm


Spare SlidesSpare Slides


No Boost Invariant Region No Boost Invariant Region at RHIC?at RHIC?

Basic assumption1.Finite Bjorken rod (-0<s<0)2.Massless pions3.Thermalization and Boltzmann approximation

20

Spac

e-tim

e ra

pidi

ty

Not free streaming,but thermal fluctuation!


Thermalization?Thermalization?Hydro people often usedHydro people often used

00 =0.2-1.0 fm/c =0.2-1.0 fm/cat RHIC energies to get large vat RHIC energies to get large v22..

pQCD +Boltzmann eq. analyses :pQCD +Boltzmann eq. analyses :•Elastic (ggElastic (gggg) collisions:gg) collisions:eqeq>6-10 fm/c>6-10 fm/c•Inelastic (ggInelastic (ggggg) collisions:ggg) collisions:eqeq=2-3fm/c=2-3fm/c

A.H.Mueller, R.Baier et al., J.Serreau et al., A.Dumitru et al.,J.Bjoraker et al. …

Thermalization controlled byThermalization controlled bynon-perturbative physics?non-perturbative physics?


Protons with pProtons with pTT=4 GeV/c in =4 GeV/c in hydro?hydro?

Proton: Proton: ppTT=4 GeV/=4 GeV/cc in lab. frame in lab. frame

ppTT~2.4GeV/~2.4GeV/cc in local rest frame with in local rest frame with vvTT=0.5=0.5cc

No!No!

Lorentz tr.Lorentz tr.Suppose momentum parallel to flowSuppose momentum parallel to flow


RecombinatioRecombinationn + +

FragmentatioFragmentation?n?

•Work in intermediate and high pT•Parameterized flow•How do we obtain such a large flow(vT~0.55c) at T=Tc?•What happens for high pT v2 if a realistic density profile is used instead of hard sphere?

•Work in low and high pT•Flow is dynamically obtained.•Radial flow in hadron phase is also important. At T=Tc, <vT>~0.25c T=100 MeV, <vT>~0.55c

Talk by R.FriesTalk by R.FriesT.H. & Y.NaraT.H. & Y.Nara

Hydro + Jet ?Hydro + Jet ?


Hydro + Rate Eq. in QGP Hydro + Rate Eq. in QGP phasephase

Including ggqqbar and ggggg

Collision term:

T.S.Biro et al.,Phys.Rev.C48(’93)1275.

Assuming “multiplicative” fugacity, EoS is unchanged.


Hydro+Jet ModelHydro+Jet Model

N

N

3

4

Fragmentation:IndependentFragmentationModel

PYTHIA

3D Hydro PYTHIAhadrons

hadronsPDF:Collinear: CTEQ5LOkT: Gaussian

Parton energy loss

pQCD LO:pQCD LO:

*Initial and final state radiation are included.


Initial energy density Initial energy density fluctuationfluctuation

Suppose massless free EoS,

Multiplicity is proportional to the entropy.

The 1st order term vanishes.

In the conventional approach,one uses average

initial energy density

Multiplicity WITH fluctuation < Multiplicity WITHOUT fluctuation


dN/ddN/d from a Saturation from a Saturation ModelModel

Qs2

kT20

gggggg

D. Kharzeev and E. Levin, Phys.Lett.B523,79(2001)

Parton-hadron dualityParton-hadron duality

s


Initial Condition from CGCInitial Condition from CGC

““CGC +CGC + Hydro + Jet model” Hydro + Jet model”

Saturation scale at a transverse position: Saturation scale at a transverse position:

Momentum rapidity Momentum rapidity yy space time rapidity space time rapidity ss

Input for hydrodynamicsInput for hydrodynamics

wherewhere

Unintegrated gluon distribution can be writtenUnintegrated gluon distribution can be written


vv22(() from CGC+Hydro) from CGC+Hydro


22ndnd order formula… order formula…

14 equations…

1st order 2nd order

How obtain additional equations?

In order to ensure the second law of thermodynamics , one can choose

Balance eqs.

Constitutive eqs.

Hydrodynamic Models of Heavy-Ion Collisions Tetsufumi Hirano RIKEN BNL Research Center.

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