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Hydrodynamic Models of Heavy-Ion Collisions: 

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

Parallel Talks Based on Hydro: 

Parallel Talks Based on Hydro Jan. 13 H. Niemi, Photon production from non-equilibrium QGP in heavy-ion collisions M. Csanad, Indication for quark deconfinement and evidence for a Hubble flow in Au+Au collisions at RHIC Jan. 15 Y. Nara, CGC, hydrodynamics and the parton energy loss E. Shuryak, Why does the QGP behaves like a perfect fluid? U. Heinz, Rapidity dependence of momentum anisotropies in nuclear collisions D. Teaney, Viscosity and thermalization

Outline: 

Outline Why hydrodynamics? How hydrodynamics works at RHIC Hybrid models based on hydrodynamics Information of the inside (jet quenching , EM probe) Improvement of initial stage Improvement of ideal hydro (viscosity) Summary

1. Why Hydrodynamics?: 

1. Why Hydrodynamics? Static EoS from Lattice QCD Finite T, m field theory Critical phenomena Chiral property of hadron Dynamic Phenomena in HIC Expansion, Flow Space-time evolution of thermodynamic variables Once we accept local thermalization 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 (contd.): 

1. Why Hydrodynamics (contd.) A full 3D hydrodynamic simulation with a CGC initial condition Talk by Y.Nara Space-time evolution of energy density in sqrt(sNN)=200 GeV Au+Au collision at b=7.2fm Animation is here in the presentation. If you need, please ask me (hirano@bnl.gov).

Slide6: 

Hydrodynamics provides us a very intuitive and simple description of relativistic heavy ion collisions.

Outline: 

Outline Why hydrodynamics? How hydrodynamics works at RHIC Hybrid models based on hydrodynamics Information of the inside (jet quenching , EM probe) Improvement of initial stage Improvement of ideal hydro (viscosity) Summary

2. How Hydrodynamics Works at RHIC: 

:P.Kolb(’03), talk by A.Poskanzer 2. How Hydrodynamics Works at RHIC Elliptic flow (J.-Y.Ollitrault (’92)) How does the system respond to initial spatial anisotropy? A.Poskanzer & S.Voloshin (’98) Dense or dilute? If dense, thermalization? If thermalized, EoS?

Elliptic Flow of Charged Particles: 

Elliptic Flow of Charged Particles T.H.(’01) P.Huovinen(’03) P.Kolb et al.(’01)

Slide10: 

Roughly speaking, ideal hydro gives a good description For improvement of models, talk by U.Heinz

More on Elliptic Flow: 

More 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.

Ideal hydro seems to give agood description at RHIC: 

What’s next? Ideal hydro seems to give a good description at RHIC Making the most use of hydro models to study the RHIC physics Checking how robust the current results are when hydro models are improved

Outline: 

Outline Why hydrodynamics? How hydrodynamics works at RHIC Hybrid models based on hydrodynamics Information inside fluids (jet quenching , EM probe) Improvement of initial stage Improvement of ideal hydro (viscosity) Summary

3.1 Information inside fluids: 

3.1 Information inside fluids Jet quenching is a manifestation of interaction between matter and partons (Talks by G.Moore and I.Vitev) For quantitative analysis, the information about the space-time evolution of matter is indispensable!

3.1.1 Hydro as a Tool to Analyze Jet Quenching: 

3.1.1 Hydro as a Tool to Analyze Jet Quenching Jet quenching analysis taking account of (2+1)D hydro results (M.Gyulassy et al.(’02)) Hydro+Jet model (T.H. & Y.Nara (’02)) Parton density r(x) taken from full 3D hydro simulations GLV 1st order formula (M.Gyulassy et al.(’00)) Movie and data of r(x) are available at http://quark.phy.bnl.gov/~hirano/ Animation is here in the presentation. If you need, please ask me hirano@bnl.gov

Interplay between Soft and Hard: 

Interplay between Soft and Hard NSOFT~NHARD pT (1/pT)(dN/dpT) Hydrodynamic afterburner Jet quenching Interesting region Intermediate pT (2<pT<3.5 GeV/c) Pion hard, Proton soft It’s the very heavy ion physics! T.H & Y.Nara(’03) Crossing pT moves toward high pT soft hard Au+Au at b=2 fm

Consequense from hadron species dependent pT,cross: 

Consequense from hadron species dependent pT,cross Hydro+Jet Talk by R.Fries Recombination +Fragmentation RAA Particle ratio

Slide18: 

“Scaling v2” Interplay between soft and hard? Recombination mechanism?

3.1.2 Hydro as a Tool to Analyze Electromagnetic Radiation: 

Thermal photon is a penetrating probe of QGP (E.Shuryak(’78)) 3.1.2 Hydro as a Tool to Analyze Electromagnetic Radiation um Production rate (Number per unit space-time volume) Invariant 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 profile

Chemical Non-Equilibrium: 

Chemical Non-Equilibrium Talk by H.Niemi Hydro + rate eq. Smaller d.o.f.  Larger initial T T.H. & K.Tsuda(’02) Hydro( ) Overpopulation of resonance  Rapid 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 phase Hadron phase 100 200 300 400 500 600 700 800 Temperature (MeV) 0

Novel Temperature Evolution: 

Novel Temperature Evolution Caveat: one has to take account of fugacity l in calculating EM spectra. QGP phase: l<1 Hadron phase: l>1 Compensation between T and l? Talk by H.Niemi proper time Tc temperature chemical non-eq. chemical eq.

3.2 Improvement of Initial Condition -Toward an unified model in HIC-: 

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

3.2.1 SPheRIO*: 

3.2.1 SPheRIO* Main features: “Particle” method (a kind of Lagrangian hydro) Numerical cost cheaper than conventional finite grids method (Even in 3+1 D, any geometry) Event-by-event physics (NeXus + SPheRIO=NeXSPheRIO) (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 density of single event Spectra from Energy density of single event Spectra from Conventional approach SPheRIO Similar approach based on HIJING: M.Gyulassy et al.(’97)

Initial Conditions in NeXSPheRIO: 

Initial Conditions in NeXSPheRIO Single event (b=0fm) Average over 30 events (b=0fm) Energy density in the transverse plane (z=0) Bumpy!

Results from NeXSPheRIO: 

Results from NeXSPheRIO Pb+Pb 17.3A GeV Multiplicity is reduced by ~10%! :(event average) Effect of initial energy density fluctuation (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 Model: 

3.2.2 CGC+Hydro+Jet Model T.H. & Y.Nara Talk by Y.Nara Dense Medium These three physics closely related with each other! Talk by J.Jalilian-Marian Talk by I.Vitev

CGC+Hydro+Jet Model (contd.): 

CGC+Hydro+Jet Model (contd.) Full 3D hydro evolution pQCD parton dilute time momentum scale ggg 22 CGC small x dense collinear factorization kT factorization Parton energy loss Initial condition of energy density from CGC Au+Au 200AGeV b=7.2fm, t0 =0.6fm transverse longitudinal

Results from CGC+hydro+jet: 

Results from CGC+hydro+jet Au+Au sqrt(sNN) = 200 GeV For details, talk by Y.Nara CGC initial condition works very well! (Energy, rapidity, centrality dependences)

Outline: 

Outline Why hydrodynamics? How hydrodynamics works at RHIC Hybrid models based on hydrodynamics Information of the inside (jet quenching , EM probe) Improvement of initial stage Improvement of ideal hydro (viscosity) Summary

4. Viscosity: 

4. Viscosity Change not only the equations of motion but 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 Navier-Stokes Eq. and a Relaxation Method: 

Break Down of Naive Navier-Stokes Eq. and a Relaxation Method Non-relativistic case (Based on discussion by Cattaneo (1948)) t0: Fourier’s law t : “relaxation time” Parabolic equation (heat equation) ACAUSAL!! Finite t Hyperbolic equation (telegraph equation) Balance eq.: Constitutive eq.: Talk by D.Teaney See also, A.Muronga (’02)

5. Summary: 

5. Summary Open our mind ! Hydrodynamics can be used even for “high pT physics in HIC”. Jet tomography EM probe (J/Y suppression) … Keep in mind ! How robust is the current agreement of hydro?: Chemical non-eq.? Initial fluctuation? Viscosity? Thermalization? EoS? (Freeze-out?) Hydrodynamics is one of the valuable tools at RHIC energies