# Presentation: 847387

## The effect of early chemical freeze out on hydrodynamic evolution from a full 3D hydrodynamic model

- Tetsufumi Hirano

*Physics Dept., Univ. of  Tokyo*

- hirano@nt.phys.s.u-tokyo.ac.jp

- Contents:
- Introduction
- EOS of chemically
-   non-equilibrium matter
- Hydrodynamic simulations
*p*t spectra & elliptic flow
- Summary

- Talk based on
- T. Hirano and K. Tsuda, nucl-th/0202033.
- See also
- T. Hirano, PRC**65**, 011901 (2002).
- T. Hirano, PRL**86**, 2754 (2001).

## Introduction

**Region between chemical**
**and thermal freeze-out lines**
- Chemically frozen
- but
-  thermally equilibrated

- We want to describe this region
- in terms of
- hydrodynamics.

- Figure from U. Heinz, hep-ph/0109006.

- Chemical parameters  particle ratio
- Thermal parameters  *p*t spectra

## Motivation

- Conventional hydrodynamic models fail to reproduce particle ratios and spectra simultaneously.
- Low *p*t spectrum ? (U.Ornik and R.M.Weiner, PLB263(1991)5503.)
- Elliptic flow at low *p*t ? (T.Hirano, PRL86(2001)2754.)
*T*th and *v*r from thermal models ? (W.Florkowski et al., Acta Phys.Polon.B33(2002)753.)
- Can we resolve the following problems in hydrodynamics ?
- Anti-proton puzzle: *p/p|*measure >> *p/p|*hydro @SPS
-                                      (R.Rapp and E.V.Shuryak, PRL86(2001)2980.)
- Low mass dilepton  (R.Rapp and J.Wambach, Eur.Phys.A6(1999)415.)
- HBT puzzle ? (U.Heinz and P.Kolb, hep-ph/0111075.)

- Need to consider early chemical freeze out
- in hydrodynamics

- Results from *T*ch=*T*th

## Conventional Hydrodynamic Model

- Chemical & thermal equilibrium
*T*ch=*T*th (~100-140 MeV)

- Hydrodynamic Model in Next Generation
- Separate freeze-out temperature (*T*ch > *T*th)

- 1st trial calculation
- Description at _RHIC_ energies

- Including baryon & isospin chemical potentials
- Detailed description of particle ratio & spectra
-     at SPS and RHIC energies

- Our Roadmap

## Model EOS

- Mixed phase (*T*c=170 MeV)
- Hadron Phase
- (All hadrons up to **(1232) are taken into account.)
- Model 1. Chemical Equilibrium (CE)
- Model 2. Chemical Freeze-Out (CFO)
- Model 3. Partial Chemical Equilibrium (PCE)

## Illustration of Models 

- Let’s suppose a fluid element in the hadron phase
- including _only____and___.

*N*=const.
*N*=const. *S  *=const.

*N*+2*N*=const.          *S *= const.

*S*=const.

- (*See, for example, H.Bebie *et al*., Nucl.Phys.**B378**(1992)95.)

## Equation of State

-  are very similar
-  to each other.

- Larger *E* in PCE and CFO
- at a fixed *T *than in CE due to
- large fraction of resonances
- PCE looks like CFO
- rather than CE.

- CE: Chemical Equilibrium
- PCE: Partial Chemical Equilibrium
- CFO: Chemical Freeze-Out

## Time Evolution of E and T

- Initial condition for central collisions
- at the RHIC energy:
- 0=0.6 fm, *b*=2.4 fm
*E*0=28.9 GeV/fm3, *T*0=349.5 MeV

- We cannot distinguish
- between three models !

## Time Evolution of 

- CE

- PCE

- Reaction Plane

- Transverse Plane

*T*=171 MeV
*T*=169 MeV
*T*=140 MeV

- mixed
- phase

- hadron
- phase

- QGP
- phase

- Time Evolution of
- Freeze-Out Hypersurface

##  Time Evolution of Freeze-Out 

- Hypersurface at Midrapidity

- Model PCE

- Model CE

- Au + Au 130 A GeV central collision

- The system does not expand explosively
- in the model PCE.
- The effect on HBT radii ?

## Tth vs. <vr> from hydrodynamics

**J.Burward-Hoy **
- Talk at Thermal Fest (BNL)
-     Hydrodynamics-based fitting
-     for , K and p in low pt region
-     Resonance decays are not included.
**Broniowski & Florkowski**
- PRL87,272302(2001).
*    *Another parameterization
*    **T*th=*T*ch is assumed.
-     Resonance decays are included.

- @ midrapidity

- Radial flow is suppressed!

- More detailed analyses with both hydro and thermal
- models are needed for understanding thermal freeze-out.

## Pseudorapidity Distribution of Charged 

-  Particles in Au+Au 130 A GeV

- Data:A.H.Wuosmaa *et al.* (PHOBOS), Nucl.Phys.A698(2002)88c.

- model PCE:*T*f=140 MeV

- Initial condition:
- 0=0.6 fm
*E*0=28.9 GeV/fm3
*T*0=349.5 MeV

- For initial transverse and
- longitudinal profiles, see
- T. Hirano, PRC65,011901(2002).

## pt spectrum & v2(pt) of Charged 

- Data: STAR, PRL**87**, 112303(2001) & PRL**86**,402(2001).

- Almost independent of *T*th

- Smaller *T*th, larger *v*2

- Our results with *T*th~140 MeV are consistent with
-  experimental data of both *p*t spectrum and *v*2(*p*t)
-  below 1 GeV/*c*.
- Onset of hard processes  ~1 GeV/*c *?

*p*t spectrum & *v*2(*p*t) of Charged
-  Particles in Au+Au 130 A GeV

- minimum bias

- negative charged hadron

- average over
- particle spectrum

## v2() of Charged Particles

-  in Au+Au 130 A GeV

- Is early thermalization achieved only near midrapidity ?
-                See, e.g., T.Hirano, PRC65,011901(2002).

*v*2 is almost flat in –2<<2.

- Data:I. Park (PHOBOS), Nucl.Phys.A698(2002)564c.

- model PCE

- model CE

## Summary

- Hydrodynamic model with chemically non-equilibrium EOS
- In comparison with conventional EOS (chemical equilibrium),
- the system cools down more rapidly.
- radial and elliptic flow are suppressed.
*T*th~140 MeV and <*v*r>~0.35 are consistent with experimental data.

## The END...

- Energy density
- in the reaction plane

- Pressure in the
- transverse plane

- Au+Au 130 A GeV
- central collision (*b*=2.4 fm)

- Movies are available at
- http://tkynt2.phys.s.u-tokyo.ac.jp/~hirano