hydrodynamics in high-density scenarios

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Hydrodynamics in High-Density Scenarios Assumes local thermal equilibrium (zero mean-free- Assumes local thermal equilibrium (zero mean-free- path limit) and solves equations of motion for path limit) and solves equations of motion for fluid elements (not particles) fluid elements (not particles) Equations given by continuity, conservation laws, Equations given by continuity, conservation laws, and and Equation of State (EOS) Equation of State (EOS) EOS relates quantities like pressure, temperature, EOS relates quantities like pressure, temperature, chemical potential, volume = chemical potential, volume = direct access to direct access to underlying physics underlying physics Kolb, Sollfrank & Heinz, hep-ph/0006129

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Hydrodynamics in High-Density Scenarios. Assumes local thermal equilibrium (zero mean-free-path limit) and solves equations of motion for fluid elements (not particles) Equations given by continuity, conservation laws, and Equation of State (EOS) - PowerPoint PPT Presentation

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Page 1: Hydrodynamics in High-Density Scenarios

Hydrodynamics in High-Density Scenarios Assumes local thermal equilibrium (zero mean-free-path limit) Assumes local thermal equilibrium (zero mean-free-path limit)

and solves equations of motion for fluid elements (not particles)and solves equations of motion for fluid elements (not particles) Equations given by continuity, conservation laws, and Equations given by continuity, conservation laws, and Equation of Equation of

State (EOS)State (EOS) EOS relates quantities like pressure, temperature, chemical EOS relates quantities like pressure, temperature, chemical

potential, volume = potential, volume = direct access to underlying physicsdirect access to underlying physics

Kolb, Sollfrank & Heinz,hep-ph/0006129

Page 2: Hydrodynamics in High-Density Scenarios

Hydromodels can describe mT (pT) spectra

• Good agreement with hydrodynamic prediction at RHIC & SPS (2d only)• RHIC: Tth~ 100 MeV, T ~ 0.55 c

Page 3: Hydrodynamics in High-Density Scenarios

Blastwave vs. Hydrodynamics

Tdec = 100 MeV

Kolb and Rapp,PRC 67 (2003)

044903.

Mike Lisa (QM04): Use it don’t abuse it ! Only use a static freeze-out parametrization when the dynamic model doesn’t work !!

Page 4: Hydrodynamics in High-Density Scenarios

Basics 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

Page 5: Hydrodynamics in High-Density Scenarios

TchemicalTchemical

Input for Hydrodynamic Simulations

Final stage:Hadronic interactions (cascade ?) Need decoupling prescription

Intermediate stage:Hydrodynamics can be appliedif thermalization is achieved. Need EoS (Lattice QCD ?)

Initial stage:Pre-equilibrium,Color Glass Condensate ?Instead parametrization () for hydro simulations

Page 6: Hydrodynamics in High-Density Scenarios

Caveats of the different stages

Initial stageInitial stage Recently a lot of interest (Hirano et al., Heinz et al.)Recently a lot of interest (Hirano et al., Heinz et al.) Presently parametrized through initial thermalization time Presently parametrized through initial thermalization time 00, ,

initial entropy density sinitial entropy density s00 and and parameter (pre-equilibrium parameter (pre-equilibrium

‘partonic wind’)‘partonic wind’) QGP stageQGP stage

Which EoS ? Maxwell construct with hadronic stage ?Which EoS ? Maxwell construct with hadronic stage ? Nobody uses Lattice QCD EoS. Why not ?Nobody uses Lattice QCD EoS. Why not ?

Hadronic stageHadronic stage Do we treat it as a separate entity with its own EoSDo we treat it as a separate entity with its own EoS Hadronic cascade allows to describe data without an Hadronic cascade allows to describe data without an

Page 7: Hydrodynamics in High-Density Scenarios

Interface 1: Initial ConditionInterface 1: Initial Condition

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

•Parametrize initialhydrodynamic field

Initial time 0 ~ thermalization time

Hira

no .

(’02)

•Take initial distributionfrom other calculations

e or s proportional to part, coll or apart + bcoll

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

x

x x

yy

Page 8: Hydrodynamics in High-Density Scenarios

Main Ingredient: Equation of State

Latent heat

One can test many kinds of EoS in hydrodynamics.

Typical 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

EoS with chemical freezeoutEoS with chemical freezeoutEoS with chemical freezeoutEoS with chemical freezeout

Kol

b an

d H

einz

(’0

3)

Hira

no a

nd T

suda

(’02)

PCE:partial chemical equilibliumCFO:chemical freeze outCE: chemical equilibrium

Page 9: Hydrodynamics in High-Density Scenarios

Interface 2: HadronizationInterface 2: Hadronization

Tc

QG

P p

has

eH

ad

r on

ph a

s e

PartialChemical

EquilibriumEOS

Hirano & Tsuda;Teaney;

Kolb & Rapp

Teaney, Lauret & Shuryak;

Bass & Dumitru

Tch

Tth

HadronicCascade

ChemicalEquilibrium

EOS

Tth

Kolb, Sollfrank,Huovinen & Heinz;

Hirano;…

Ideal hydrodynamics

Page 10: Hydrodynamics in High-Density Scenarios

The Three Pillars of Experimental Tests to Hydrodynamics Identified SpectraIdentified Spectra

Radial Flow in partonic and hadronic phaseRadial Flow in partonic and hadronic phase

Identified Elliptic Flow (v2)Identified Elliptic Flow (v2) Spatial to Momentum anisotropy, mostly in partonic phaseSpatial to Momentum anisotropy, mostly in partonic phase

HBT resultsHBT results Kinetic Freezeout SurfaceKinetic Freezeout Surface Lifetime of SourceLifetime of Source

Conclusions from hydroConclusions from hydro Early local thermalizationEarly local thermalization Viscosity, mean free pathViscosity, mean free path Coupling, CollectivityCoupling, Collectivity

Page 11: Hydrodynamics in High-Density Scenarios

π-, K-, p : reasonable agreement

BestBest agreement for : agreement for : TTdecdec= 100 MeV= 100 MeV

αα = 0.02 fm = 0.02 fm-1-1 αα ≠≠ 0 : importance of 0 : importance of

inital conditionsinital conditions Only at Only at low plow pTT

(p(pTT < 1.5 – 2 GeV/c) < 1.5 – 2 GeV/c)

FailingFailing at at higherhigher p pTT (> (>

2 GeV/c) expected:2 GeV/c) expected: Less rescatteringLess rescattering

NNAu+Au, s = 200 GeV

Tdec = 165 MeVTdec = 100 MeV

α : initial (at τ0) transverse velocity : vT(r)=tanh(αr)

Central Data

Thermalization validity limitP.F. Kolb and R. Rapp, Phys. Rev. C 67 (2003) 044903

Page 12: Hydrodynamics in High-Density Scenarios

π-, K-, p : apparent disagreement?

Predictions Predictions normalizednormalized to data to data LimitedLimited range of agreement range of agreement Hydro starts failing at 62 GeV?Hydro starts failing at 62 GeV? different feed-down treatment in different feed-down treatment in

data and hydro?data and hydro? DifferentDifferent initial / final initial / final

conditionsconditions than at 200 GeV ? than at 200 GeV ? Lower TLower Tdecdec at 62 GeV ? at 62 GeV ?

Larger Larger ττ00 at 62 GeV ? at 62 GeV ?

Increasing Increasing ττ00 gives much gives much betterbetter

agreement!agreement! TTdecdec = 100 MeV = 100 MeV

STAR preliminary data

NNAu+Au, s = 62.4 GeV

Page 13: Hydrodynamics in High-Density Scenarios

PHENIX proton and pion spectra vs. hydro

Page 14: Hydrodynamics in High-Density Scenarios

Conclusions from spectra

Central spectra well described either by including a pre-Central spectra well described either by including a pre-equilibrium transverse flow or by using a hadron cascade for equilibrium transverse flow or by using a hadron cascade for the hadronic phase.the hadronic phase.

Multistrange Baryons can be described with common Multistrange Baryons can be described with common decoupling temperature. Different result than blast wave fit. decoupling temperature. Different result than blast wave fit. Blast wave fit is always better.Blast wave fit is always better.

Centrality dependence poorly described by hydroCentrality dependence poorly described by hydro Energy dependence (62 to 200 GeV) indicates lower Energy dependence (62 to 200 GeV) indicates lower

decoupling temperature and longer initial thermalization decoupling temperature and longer initial thermalization time at lower energy. System thermalizes slower and stays time at lower energy. System thermalizes slower and stays together longer. together longer.

Page 15: Hydrodynamics in High-Density Scenarios

Collective anisotropic flow

x

yz

Page 16: Hydrodynamics in High-Density Scenarios

Elliptic Flow (in the transverse plane)

for a mid-peripheral collision

Dashed lines: hard sphere radii of nuclei

Reactionplane

In-planeOu

t-o

f-p

lan

e

Y

X

Re-interactions FLOW Re-interactions among what? Hadrons, partons or both?

In other words, what equation of state?

Flow

Flo

w

Page 17: Hydrodynamics in High-Density Scenarios

Anisotropic FlowAnisotropic Flow

A.Poskanzer & S.Voloshin (’98)

z

x

x

y

Transverse plane Reaction plane

0th: azimuthally averaged dist. radial flow1st harmonics: directed flow2nd harmonics: elliptic flow…

“Flow” is not a good terminologyespecially in high pT regions

due to jet quenching.

Page 18: Hydrodynamics in High-Density Scenarios

Large spatial anisotropy Large spatial anisotropy turns intoturns into

momentum anisotropy, IF momentum anisotropy, IF the particles interact the particles interact

collectively !collectively !

High pTprotons

Low pTprotons

Page 19: Hydrodynamics in High-Density Scenarios

How does the system respond to the How does the system respond to the initial spatial anisotropy ?initial spatial anisotropy ?

Ollitrault (’92) Hydrodynamic expansion

Initial spatial anisotropy

Final momentum anisotropy

INPUT

OUTPUT

Rescattering

dN/d

Free streaming

0 2dN

/d

0 2

2v2

x

y

Page 20: Hydrodynamics in High-Density Scenarios

Hydrodynamics describes the data

Hydrodynamics:strong coupling,small mean free path,lots of interactionsNOT plasma-like

Strong collective flow:elliptic and radial expansion withmass ordering

Page 21: Hydrodynamics in High-Density Scenarios

# III: The medium consists of constituent quarks ?

baryonsbaryons

mesonsmesons

Page 22: Hydrodynamics in High-Density Scenarios

Ideal liquid dynamics –reached at RHIC for the 1st time

Page 23: Hydrodynamics in High-Density Scenarios

How strong is the coupling ?Navier-Stokes type calculationof viscosity – near perfect liquidViscous force ~ 0

Simple pQCD processes do not generate sufficient interaction strength (2 to 2 process = 3 mb)

v2

pT (GeV/c)

Page 24: Hydrodynamics in High-Density Scenarios

Remove your organic prejudicesRemove your organic prejudices Don’t Don’t equate viscous with “sticky” ! equate viscous with “sticky” !

Think instead of a not-quite-ideal fluid:Think instead of a not-quite-ideal fluid: ““not-quite-ideal” not-quite-ideal” “supports a shear stress” “supports a shear stress” Viscosity Viscosity

then defined asthen defined as

Dimensional Dimensional estimate:estimate:

ViscosityViscosityincreasesincreases with withtemperaturetemperature

LargeLarge cross sections cross sections smallsmall viscosity viscosity

Viscosity Primer

yv

AF xx

σmkT

η)(

σσ1

)()(η

gasidealnearlyafor

pn

pnmfppn

pathfreemeandensitymomentum

Page 25: Hydrodynamics in High-Density Scenarios

Ideal Hydrodynamics Why the interest in viscosity?Why the interest in viscosity?

A.) Its vanishing is associated with the applicability of ideal A.) Its vanishing is associated with the applicability of ideal hydrodynamics (Landau, 1955):hydrodynamics (Landau, 1955):

B.) Successes of ideal hydrodynamics applied to RHIC data B.) Successes of ideal hydrodynamics applied to RHIC data suggest that the fluid is “as perfect as it can be”, that is, it suggest that the fluid is “as perfect as it can be”, that is, it approaches the (conjectured) quantum mechanical limitapproaches the (conjectured) quantum mechanical limit

See “See “A Viscosity Bound ConjectureA Viscosity Bound Conjecture”, ”, P. P. KovtunKovtun, , D.T. SonD.T. Son, , A.O. A.O. StarinetsStarinets, , hep-th/0405231hep-th/0405231

11 so )(

1Forces DragForces Inertial

Number Reynolds Hydro Ideal

mfpL

mfpvLV

mfpv

LV

thermal

BULKthermal

BULK

s

4

)densityentropy (4

Page 26: Hydrodynamics in High-Density Scenarios

Consequences of a perfect liquid All “realistic” hydrodynamic calculations for RHIC fluids to date All “realistic” hydrodynamic calculations for RHIC fluids to date

have assumed zero viscosity have assumed zero viscosity = 0 = 0 “perfect fluid” “perfect fluid” But there is a (conjectured) quantum limitBut there is a (conjectured) quantum limit

Where do Where do “ordinary” “ordinary” fluids sit wrt fluids sit wrt this limit?this limit?

RHIC “fluid” RHIC “fluid” mightmightbe at ~2-3 on this be at ~2-3 on this scale (!)scale (!)

400 times less viscous than water,400 times less viscous than water,10 times less viscous than 10 times less viscous than superfluid helium !superfluid helium !

sDensityEntropy

4

)(4

T=10T=101212 KK

Motivated by calculation of lower viscosity bound in black hole via supersymmetric N=4 Yang Mills theory in AdS (Anti deSitter) space (conformal field theory)

Page 27: Hydrodynamics in High-Density Scenarios

Viscosity in Collisions Hirano & Gyulassy, Teaney, Moore, Yaffe, Gavin, etc.

supersymmetric Yang-Mills: s pQCD and hadron gas: s ~ 1

liquid ?

liquid

plasma

gas

d.o.f. in perfect liquid ? Bound states ?, constituent quarks ?, heavy resonances ?

Page 28: Hydrodynamics in High-Density Scenarios

Suggested Reading November, 2005 issue of Scientific November, 2005 issue of Scientific AmericanAmerican““The Illusion of Gravity” by J. The Illusion of Gravity” by J.

Maldacena Maldacena

A test of this prediction comes from the A test of this prediction comes from the Relativistic Heavy Ion Collider (RHIC) Relativistic Heavy Ion Collider (RHIC) at BrookhavenNational Laboratory, at BrookhavenNational Laboratory, which has been colliding gold nuclei at which has been colliding gold nuclei at very high energies. A preliminary very high energies. A preliminary analysis of these experiments indicates analysis of these experiments indicates the collisions are creating a fluid with the collisions are creating a fluid with very low viscosity. Even though Son and very low viscosity. Even though Son and his co-workers studied a simplified his co-workers studied a simplified version of chromodynamics, they seem to version of chromodynamics, they seem to have come up with a property that is have come up with a property that is shared by the real world. shared by the real world. Does this mean Does this mean that RHIC is creating small five-that RHIC is creating small five-dimensional black holes? It is really too dimensional black holes? It is really too early to tell,early to tell, both experimentally and both experimentally and theoretically. (Even if so, there is nothing theoretically. (Even if so, there is nothing to fear from these tiny black holes-they to fear from these tiny black holes-they evaporate almost as fast as they are evaporate almost as fast as they are formed, and they "live" in five formed, and they "live" in five dimensions, not in our own four-dimensions, not in our own four-dimensional world.)dimensional world.)

Page 29: Hydrodynamics in High-Density Scenarios

χ2 minimum resultD->e

Even charm flows strong elliptic flow of electrons from D strong elliptic flow of electrons from D

meson decays meson decays → v→ v22DD > 0 > 0

vv22cc of charm quarks? of charm quarks?

recombination Ansatz: recombination Ansatz: (Lin & Molnar, PRC 68 (2003) 044901)(Lin & Molnar, PRC 68 (2003) 044901)

universal vuniversal v22(p(pTT) for all quarks) for all quarks

simultaneous fit to simultaneous fit to , K, e v, K, e v22(p(pTT))

eT

D

cqT

D

uqT

D vpm

mbvp

m

mavpv 2222 )()()(

a = 1

b = 0.96

2/ndf: 22/27

within recombination model: charm within recombination model: charm flows like light quarks!flows like light quarks!

Page 30: Hydrodynamics in High-Density Scenarios

Constraining medium viscosity /s Simultaneous description of Simultaneous description of

STAR R(AA) and PHENIX v2STAR R(AA) and PHENIX v2for charm. for charm. (Rapp & Van Hees, PRC 71, 2005)(Rapp & Van Hees, PRC 71, 2005)

Ads/CFT == Ads/CFT == /s ~ 1/4/s ~ 1/4 ~ 0.08 ~ 0.08 Perturbative calculation of D (2Perturbative calculation of D (2t) ~6t) ~6

(Teaney & Moore, PRC 71, 2005) (Teaney & Moore, PRC 71, 2005) == == /s~1/s~1

transport models requiretransport models require small heavy quark small heavy quark

relaxation timerelaxation time small diffusion coefficient small diffusion coefficient

DDHQHQ x (2 x (2T) ~ 4-6T) ~ 4-6 this value constrains the this value constrains the

ratio viscosity/entropyratio viscosity/entropy /s ~ (1.3 – 2) / 4/s ~ (1.3 – 2) / 4 within a factor 2 of within a factor 2 of conjectured lower conjectured lower quantum boundquantum bound consistent with light hadron consistent with light hadron

vv22 analysis analysis electron Relectron RAAAA ~ ~ 00 R RAAAA at high p at high pTT - - is bottom suppressed as well?is bottom suppressed as well?

Page 31: Hydrodynamics in High-Density Scenarios

An alternate idea (Abdel-Aziz & Gavin)

viscous liquid pQGP ~ HRG ~ 1 fm

nearly perfect sQGP ~ (4 Tc)-1 ~ 0.1 fm

Abdel-Aziz & S.G

Ts

Level of viscosity will affect the diffusion of momentum correlationskinematic viscosity

effect on momentum diffusion:

limiting cases:

wanted:wanted: rapidity dependence of momentum correlation rapidity dependence of momentum correlation functionfunction

T 1( /s)

Broadening from viscosity

d

d 2

4 ( ) 2 ,

QGP + mixed phase + hadrons T()

= width of momentum covariance C in rapidity

Page 32: Hydrodynamics in High-Density Scenarios

we want: 2

2

1t

jitjti ppp

NC

STAR measurement

STAR measures:STAR measures:

maybe maybe n n 2 2**

STAR, PRC 66, 044904 (2006) STAR, PRC 66, 044904 (2006)

uncertainty range uncertainty range

** 2 2**

0.08 0.08 s s 0.3 0.3

N p t :n pti pt ptj pt ij

N2C pt

2(density correlations)

density correlation functiondensity correlation function may differ from rg