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

Hydromodels can describe m T (p T ) spectra Good agreement with hydrodynamic prediction at RHIC & SPS (2d only) RHIC: T th ~ 100 MeV,   T  ~ 0.55 c

Blastwave vs. Hydrodynamics T dec = 100 MeV Kolb and Rapp, PRC 67 (2003) Mike Lisa (QM04): Use it don’t abuse it ! Only use a static freeze-out parametrization when the dynamic model doesn’t work !!

Basics of hydrodynamics Hydrodynamic Equations Energy-momentum conservation Charge conservations (baryon, strangeness, etc…) For perfect fluids (neglecting viscosity), Energy densityPressure4-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 1 st principle with experiment Need equation of state (EoS) P(e,n B ) to close the system of eqs.  Hydro can be connected directly with lattice QCD

T chemical Input for Hydrodynamic Simulations Final stage: Hadronic interactions (cascade ?)  Need decoupling prescription Intermediate stage: Hydrodynamics can be applied if thermalization is achieved.  Need EoS (Lattice QCD ?) Initial stage: Pre-equilibrium, Color Glass Condensate ?  Instead parametrization (  ) for hydro simulations

Caveats of the different stages Initial stage Initial stage  Recently a lot of interest (Hirano et al., Heinz et al.)  Presently parametrized through initial thermalization time  0, initial entropy density s 0 and  parameter (pre-equilibrium ‘partonic wind’) QGP stage QGP stage  Which EoS ? Maxwell construct with hadronic stage ?  Nobody uses Lattice QCD EoS. Why not ? Hadronic stage Hadronic stage  Do we treat it as a separate entity with its own EoS  Hadronic cascade allows to describe data without an 

Interface 1: Initial Condition Need initial conditions (energy density, flow velocity,…) Parametrize initial hydrodynamic field Initial time  0 ~ thermalization time Hirano.(’02) Take initial distribution from other calculations e or s proportional to  part,  coll or a  part + b  coll Energy density from NeXus. (Left) Average over 30 events (Right) Event-by-event basis x xx yy

Main Ingredient: Equation of State Latent heat One can test many kinds of EoS in hydrodynamics. Typical EoS in hydro model H: resonance gas(RG) p=e/3 Q: QGP+RG EoS with chemical freezeout Kolb and Heinz (’03) Hirano and Tsuda(’02) PCE:partial chemical equiliblium CFO:chemical freeze out CE: chemical equilibrium

Interface 2: Hadronization TcTc QGP phase Hadron phase  Partial Chemical Equilibrium EOS Hirano & Tsuda; Teaney; Kolb & Rapp Teaney, Lauret & Shuryak; Bass & Dumitru T ch T th Hadronic Cascade Chemical Equilibrium EOS T th Kolb, Sollfrank, Huovinen & Heinz; Hirano;… Ideal hydrodynamics

The Three Pillars of Experimental Tests to Hydrodynamics Identified Spectra Identified Spectra  Radial Flow in partonic and hadronic phase Identified Elliptic Flow (v2) Identified Elliptic Flow (v2)  Spatial to Momentum anisotropy, mostly in partonic phase HBT results HBT results  Kinetic Freezeout Surface  Lifetime of Source Conclusions from hydro Conclusions from hydro  Early local thermalization  Viscosity, mean free path  Coupling, Collectivity

π -, K -, p : reasonable agreement Best agreement for : T dec = 100 MeV α = 0.02 fm -1 Best agreement for : T dec = 100 MeV α = 0.02 fm -1 α ≠ 0 : importance of inital conditions α ≠ 0 : importance of inital conditions Only at low p T (p T < 1.5 – 2 GeV/c) Only at low p T (p T < 1.5 – 2 GeV/c) Failing at higher p T (> 2 GeV/c) expected: Failing at higher p T (> 2 GeV/c) expected:  Less rescattering T dec = 165 MeV T dec = 100 MeV α : initial (at τ 0 ) transverse velocity : v T (r)=tanh(αr) Central Data Thermalization validity limit P.F. Kolb and R. Rapp, Phys. Rev. C 67 (2003)

π -, K -, p : apparent disagreement? Predictions normalized to data Predictions normalized to data Limited range of agreement Limited range of agreement Hydro starts failing at 62 GeV? Hydro starts failing at 62 GeV? different feed-down treatment in data and hydro? different feed-down treatment in data and hydro? Different initial / final conditions than at 200 GeV ? Different initial / final conditions than at 200 GeV ?  Lower T dec at 62 GeV ?  Larger τ 0 at 62 GeV ? Increasing τ 0 gives much better agreement! Increasing τ 0 gives much better agreement!  T dec = 100 MeV STAR preliminary data

PHENIX proton and pion spectra vs. hydro

Conclusions from spectra Central spectra well described either by including a pre- equilibrium transverse flow or by using a hadron cascade for the hadronic phase. Central spectra well described either by including a pre- equilibrium transverse flow or by using a hadron cascade for the hadronic phase. Multistrange Baryons can be described with common decoupling temperature. Different result than blast wave fit. Blast wave fit is always better. Multistrange Baryons can be described with common decoupling temperature. Different result than blast wave fit. Blast wave fit is always better. Centrality dependence poorly described by hydro Centrality dependence poorly described by hydro Energy dependence (62 to 200 GeV) indicates lower decoupling temperature and longer initial thermalization time at lower energy. System thermalizes slower and stays together longer. Energy dependence (62 to 200 GeV) indicates lower decoupling temperature and longer initial thermalization time at lower energy. System thermalizes slower and stays together longer.

Collective anisotropic flow x y z

Elliptic Flow (in the transverse plane) for a mid-peripheral collision Dashed lines: hard sphere radii of nuclei Reaction plane In-plane Out-of-plane Y X Re-interactions  FLOW Re-interactions among what? Hadrons, partons or both? In other words, what equation of state? Flow

Anisotropic Flow A.Poskanzer & S.Voloshin (’98) z x x y Transverse planeReaction plane 0 th : azimuthally averaged dist.  radial flow 1 st harmonics: directed flow 2 nd harmonics: elliptic flow …  “Flow” is not a good terminology especially in high p T regions due to jet quenching.

Large spatial anisotropy turns into momentum anisotropy, IF the particles interact collectively ! High pT protons Low pT protons

How does the system respond to the initial spatial anisotropy ? Ollitrault (’92) Hydrodynamic expansion Initial spatial anisotropy Final momentum anisotropy INPUT OUTPUT Rescattering dN/d   Free streaming 0 22 dN/d   0 22 2v22v2 x y 

Hydrodynamics describes the data Hydrodynamics: strong coupling, small mean free path, lots of interactions NOT plasma-like Strong collective flow: elliptic and radial expansion with mass ordering

# III: The medium consists of constituent quarks ? baryons mesons

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

How strong is the coupling ? Navier-Stokes type calculation of viscosity – near perfect liquid Viscous force ~ 0 Simple pQCD processes do not generate sufficient interaction strength (2 to 2 process = 3 mb) v2 pT (GeV/c)

Remove your organic prejudices Remove your organic prejudices  Don’t equate viscous with “sticky” ! Think instead of a not-quite-ideal fluid: Think instead of a not-quite-ideal fluid:  “not-quite-ideal”  “supports a shear stress”  Viscosity  then defined as  Dimensional estimate:  Viscosity increases with temperature F Large cross sections  small viscosity Viscosity Primer

Ideal Hydrodynamics Why the interest in viscosity? Why the interest in viscosity? A.) Its vanishing is associated with the applicability of ideal hydrodynamics (Landau, 1955): A.) Its vanishing is associated with the applicability of ideal hydrodynamics (Landau, 1955): B.) Successes of ideal hydrodynamics applied to RHIC data suggest that the fluid is “as perfect as it can be”, that is, it approaches the (conjectured) quantum mechanical limit B.) Successes of ideal hydrodynamics applied to RHIC data suggest that the fluid is “as perfect as it can be”, that is, it approaches the (conjectured) quantum mechanical limit See “A Viscosity Bound Conjecture”, P. Kovtun, D.T. Son, A.O. Starinets, hep-th/ P. KovtunD.T. SonA.O. Starinetshep-th/ P. KovtunD.T. SonA.O. Starinetshep-th/

Consequences of a perfect liquid All “realistic” hydrodynamic calculations for RHIC fluids to date have assumed zero viscosity  = 0  “perfect fluid” All “realistic” hydrodynamic calculations for RHIC fluids to date have assumed zero viscosity  = 0  “perfect fluid”  But there is a (conjectured) quantum limit  Where do “ordinary” fluids sit wrt this limit?  RHIC “fluid” might be at ~2-3 on this scale (!) 400 times less viscous than water, 10 times less viscous than superfluid helium ! T=10 12 K 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)

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 ?

Suggested Reading November, 2005 issue of Scientific American November, 2005 issue of Scientific American “The Illusion of Gravity” by J. Maldacena A test of this prediction comes from the Relativistic Heavy Ion Collider (RHIC) at BrookhavenNational Laboratory, which has been colliding gold nuclei at very high energies. A preliminary analysis of these experiments indicates the collisions are creating a fluid with very low viscosity. Even though Son and his co-workers studied a simplified version of chromodynamics, they seem to have come up with a property that is shared by the real world. Does this mean that RHIC is creating small five- dimensional black holes? It is really too early to tell, both experimentally and theoretically. (Even if so, there is nothing to fear from these tiny black holes-they evaporate almost as fast as they are formed, and they "live" in five dimensions, not in our own four- dimensional world.) A test of this prediction comes from the Relativistic Heavy Ion Collider (RHIC) at BrookhavenNational Laboratory, which has been colliding gold nuclei at very high energies. A preliminary analysis of these experiments indicates the collisions are creating a fluid with very low viscosity. Even though Son and his co-workers studied a simplified version of chromodynamics, they seem to have come up with a property that is shared by the real world. Does this mean that RHIC is creating small five- dimensional black holes? It is really too early to tell, both experimentally and theoretically. (Even if so, there is nothing to fear from these tiny black holes-they evaporate almost as fast as they are formed, and they "live" in five dimensions, not in our own four- dimensional world.)

χ 2 minimum result D->e 2σ 4σ 1σ Even charm flows strong elliptic flow of electrons from D meson decays → v 2 D > 0 strong elliptic flow of electrons from D meson decays → v 2 D > 0 v 2 c of charm quarks? v 2 c of charm quarks? recombination Ansatz: (Lin & Molnar, PRC 68 (2003) ) recombination Ansatz: (Lin & Molnar, PRC 68 (2003) ) universal v 2 (p T ) for all quarks universal v 2 (p T ) for all quarks simultaneous fit to , K, e v 2 (p T ) simultaneous fit to , K, e v 2 (p T ) a = 1 b = 0.96  2 /ndf: 22/27 within recombination model: charm flows like light quarks! within recombination model: charm flows like light quarks!

Constraining medium viscosity  /s Simultaneous description of Simultaneous description of STAR R(AA) and PHENIX v2 for charm. (Rapp & Van Hees, PRC 71, 2005) Ads/CFT ==  /s ~ 1/4  ~ 0.08 Ads/CFT ==  /s ~ 1/4  ~ 0.08 Perturbative calculation of D (2  t) ~6 Perturbative calculation of D (2  t) ~6 (Teaney & Moore, PRC 71, 2005) ==  /s~1 transport models require transport models require  small heavy quark relaxation time  small diffusion coefficient D HQ x (2  T) ~ 4-6  this value constrains the ratio viscosity/entropy ratio viscosity/entropy   /s ~ (1.3 – 2) / 4   within a factor 2 of conjectured lower quantum bound  consistent with light hadron v 2 analysis  electron R AA ~  0 R AA at high p T - is bottom suppressed as well?

An alternate idea (Abdel-Aziz & Gavin) viscous liquid pQGP ~ HRG ~ 1 fm nearly perfect sQGP ~ (4  T c ) -1 ~ 0.1 fm Abdel-Aziz & S.G Level of viscosity will affect the diffusion of momentum correlations kinematic viscosity effect on momentum diffusion: limiting cases: wanted: rapidity dependence of momentum correlation function Broadening from viscosity QGP + mixed phase + hadrons  T(  )  = width of momentum covariance C in rapidity

we want: STAR measurement STAR measures: maybe  n  2  * STAR, PRC 66, (2006) uncertainty range  *    2  *  0.08   s  0.3 density correlation function density correlation function may differ from  r g