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Contents. Introduction 3-d Hydrodynamic Model Hydro + Cascade Model Results (hadron spectra, elliptic flow) Summary. Hydro + Cascade Model at RHIC. Duke University, Chiho Nonaka. In Collaboration with Steffen A. Bass (Duke University & RIKEN) October 30, 2004@DNP, Chicago.

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Hydro + Cascade Model at RHIC

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Hydro cascade model at rhic


  • Introduction

  • 3-d Hydrodynamic Model

  • Hydro + Cascade Model

  • Results (hadron spectra, elliptic flow)

  • Summary

Hydro + Cascade Model at RHIC

Duke University, Chiho Nonaka

In Collaboration with

Steffen A. Bass (Duke University & RIKEN)

October 30, 2004@DNP, Chicago



  • Hydrodynamic Model at RHIC



  • Single particle spectra

  • Elliptic flow

Morita, Muroya, CN and Hirano,


Hirano and Tsuda, PRC66

  • HBT

  • Elliptic flow

Morita et al., PRC66

Huovinen et.al, PLB503

Possible solution?

Freeze out final interactions

Freeze-out, Final Interactions


Thermal model

T = 177 MeV

 = 29 MeV


  • universal Tf for all hadrons in Hydro

  • Tf & 

  • Final interactions

Thermal + radial flow fit

STAR, nucl-ex/0307024

Markert @QM2004

  • Freeze-out is not universal for all hadron spectra.

  • Rescattering and regeneration is important.

Hydro cascade model

Hydro + Cascade Model

Bass and Dumitru, PRC61,064909(2000)

Teaney et al, nucl-th/0110037

  • Hydro + hadron transport model


    • Freeze-out condition ex. Chemical and kinetic freeze-out

    • Final interactions

Hirano and Tsuda, PRC66(2002)054905

Treatment of freeze-out in transport model is determined

by mean free path.



  • Full 3-d Hydrodynamics

    • EoS 1st order phase transition

    • QGP + excluded volume model

( Improved)


formula (Reco)



Monte Carlo

t fm/c

3 d hydrodynamic model

3-d Hydrodynamic Model

Hydrodynamic equation

Baryon number density conservation


Lagrangian hydrodynamics

Tracing the adiabatic path of each

volume element

Effects of phase transition of observables


Focusing on conservation law

Flux of


Trajectories on the phase diagram

Trajectories on the Phase Diagram

  • Lagrangian hydrodynamics

temperature and chemical

potential of volume element

of fluid

effect of

phase transition

C.N et al., Eur. Phys.J C17,663(2000)



  • Initial Conditions

    • Energy density

    • Baryon number density

    • Parameters

    • Flow

      longitudinal: Bjorken’s Solution

  • Equation of State

    • 1st order phase transition

    • QGP phase (Bag model), mixed phase,

      hadron phase (up to 2GeV)

      (excluded volume model)

    • Bag constant:

  • Hydro UrQMD

Hadron spectra i

Hadron Spectra (I)

  • Pure Hydro

    • Central collision

    • Parameters

  • Hydro works well up to PT ~ 2 GeV

Hadron spectra ii

Hadron Spectra (II)

  • Hydro + UrQMD

  • Many pions are produced in UrQMD.

  • Low PT resonances

  • High PT interactions

  • Transition temperature is too low.

  • PT slope becomes flatter.

  • Extra radial flow in UrQMD

The initial condition for Hydro + UrQMD

Is different from that for pure hydro.

Elliptic flow

Elliptic Flow

  • Pure Hydro

  • Centrality 5-10 %

  • Hydro works well.

Centrality dependence

Elliptic flow ii

Elliptic Flow (II)

  • Hydro + UrQMD


  • In UrQMD elliptic flow becomes small ?

  • Shape of elliptic flow as a function of 



  • Hydro + Cascade Model

    • Hadron Spectra, elliptic flow

    • Effect of resonances, final interactions in experimental data

  • Work in progress

    • Parameter

    • Initial Conditions

    • EoS (QCD critical point) ,CN and Asakawa nucl-th/0410078

    • Parton Cascade Model

    • Hadronization mechanism

      Recombination + Fragmentation model, Duke Group

Hydro cascade model at rhic


Numerical calculation

Numerical Calculation

Step 1.

Step 2.

Step 3.

Coordinates move in parallel

with baryon number current

and entropy density current.

local velocity:

from hydro eq.

temperature and chemical potential

CPU time is almost

proportional of # of lattice points.

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