# Presentation: 008366

## Elliptic flow and HBT radii from a relativistic hydrodynamic modelwith early chemical freeze out

- Tetsufumi Hirano
*Physics Dept., Univ. of Tokyo*
- hirano@nt.phys.s.u-tokyo.ac.jp

- Contents:
- Introduction & motivation
- EOS of chemically equilibrium &
-   non-equilibrium hadronic matter
- Hydrodynamic simulations
*p*t spectra, *v*2 & HBT radii
- Summary & discussion

- Talk based on
- T. Hirano and K. Tsuda, nucl-th/0205043.
- T. Hirano and K. Tsuda, nucl-th/0202033.
- See also,
- T. Hirano, PRC**65**, 011901 (2002).
- T. Hirano, PRL**86**, 2754 (2001).

- Workshop on two-particle interferometry and elliptic flow at RHIC, June 14-15, 2002, BNL.

## Full 3D Hydro in the -s Coordinate*

- Full 3D Hydro in the **-**s Coordinate*

- No cylindrical symmetry
-  Enables us to simulate non-central collisions.
-  Elliptic flow, HBT radii in          collisions
- No Bjorken’s scaling ansatz (*            *)
-  Enables us to obtain the (pseudo-)rapidity
-      dependence of observable.
-  *v*2(**), *R**i*(*Y*) (*i*=out, side, long), etc.
- Not the Cartesian coordinate, but the **-**s coordinate
-  It is relevant to the collider energies.
-  Observables at RHIC

- *T.Hirano, Phys.Rev.C **65**,** **011901 (2002).

## Early Chemical Freeze Out

- In the conventional hydrodynamics, one assumes

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

- “*Early*” means that chemical freeze out in our model happens
- earlier than in the conventional one. So, in our hydro model,
-                        (Approximation **B=0 for the RHIC energy)

- motivation

**Chemically frozen ****but**
** ****thermally equilibrated**

- See, for example, T.Hirano and K.Tsuda, nucl-th/0205043; D.Teaney, nucl-th/0204023.

## Model EOS

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

*S*, *N*=*N*+2*N*

*S, N**, N*

*S*

- 140
-      (=*T*th)

- 170
-      (=*T*ch)

- Model 3*
- (PCE)

- Model 2
- (CFO)

- Model 1
- (CE)

- Temp.
- (MeV)

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- Conserved
- quantities

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

- 

**Notes:**
We use three models EOS and compare the results with each other. The QGP phase is composed of massless free up, down, strange quarks and gluons and this is common to three models. As for the hadron phase, we introduce three models. First one is a conventional resonance gas model with chemical equilibrium, which I call `model CE’. Second and third models are new EOS. Second one is the simplest model to describe the chemical freeze-out property of nuclear matter, which I call `model CFO’. Third one is more realistic model, which I call `model PCE’. 

## Equation of State

- Three models are very
- similar to each other.

- TEMPERATURE:
- At a fixed *T*,* E* in PCE and
-  CFO are larger than in CE due
-  to large fraction of resonances.
- PCE looks like CFO rather
-  than CE.

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

- Approximation **B=0 for the RHIC energy

**Notes:**
Let me show you the result of EOS. This figure shows the pressure as a function of energy density. This region corresponds to the hadron phase, this region corresponds the mixed phase, and this region corresponds to the QGP phase. As I enlarge the hadron phase, we find three models are very similar to each other.

On the other hand, these three models split when we represent the temperature as a function of energy density. Here, red line shows the conventional EOS and brack and blue lines are new EOS. This is an enlargement of the hadron phase. At a fixed temperature, for example, 140 MeV, energy density in models PCE and CFO is larger than that in conventional model due to large fraction of resonance particles. This is a reson why the difference appears in this figure.

## Time Evolution of E and T

- Time Evolution of *E* and *T*

- Chemical freeze-out makes the hadron phase cool down
- more rapidly !

**Initial condition in central**
**collisions at the RHIC energy:**
**0 = 0.6 fm
*b  *= 2.4 fm
*E*(**0,**0**) = 33.7 GeV/fm3
*T*(**0,**0**) = 357.5 MeV

- Energy density:
- Not distinguishable

## Time Evolution of Hypersurface

- Chemical Equilibrium model
- Explosive expansion in the
-  hadron phase

- Partial Chemical Equilibrium
- Expansion is not so
-  explosively due to early
-  chemical freeze out.

- Effects on HBT Radii ?  I’ll show you later.

- CE

- PCE

## Tth vs. <vr> at s=0

*T*th vs. <*v*r> at **s=0

- Radial flow is suppressed.
- Chemical freeze-out affects the *p*t slope.

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

- Suppression of <*v*r>:
-  17.7 % (*T*th=140 MeV)
-  22.5 % (*T*th=120 MeV)

-          : average over thermal
- freeze out hypersurface

## Single Particle Distribution of Charged Particles in Au+Au 130A GeV Collisions

- Single Particle Distribution of Charged Particles in Au+Au 130*A* GeV Collisions

- Pseudorapidity distribution

- Transverse momentum spectra

*   **T*th=140 MeV
-    Binary collision scaling

- Data from PHOBOS (QM2001)

- Data from STAR, PRL87, 112303 (2001);nucl-ex/0111004.

- Almost *T*th independent !
- Due to suppression of transverse flow in the
- model PCE

- Model PCE

## v2(pt) for Charged Hadrons

*v*2(*p*t) for Charged Hadrons

- Chemical Equilibrium

- Partial Chemical Equilibrium

- Almost *T*th independent

*v*2 depends on *T*th
- in the model PCE !
*T*th=140 MeV ?

- Data from STAR, PRL86,402(2001).

## v2() for Charged Hadrons

*v*2(**) for Charged Hadrons

- Note: *v*2 in forward and backward region is sensitive
- to the initial shape of energy density.  Detailed analyses are needed !

- Our results:
-    0<*p*t<2 GeV/*c*
- PHOBOS:
-    All *p*t
- STAR:
-    0.1<*p*t<2 GeV/*c*

- Elliptic flow is also suppressed !

- Data from PHOBOS, (QM2001); STAR, PRL86,402(2001).

*T*th=140 MeV

## KT dependence of HBT Radii

*K*T dependence of HBT Radii

*R*side

*R*out

*R*long

*R*out/*R*side

*T*th=140 MeV, negative pions, neglecting resonance decays.

- Data from STAR, PRL87, 082301 (2001), PHENIX, PRL88, 192302 (2002).

## Summary

- Fully 3D hydrodynamic simulations at the RHIC energy by using
-  EOS with/without chemical equilibrium
- In comparison with the model CE, the model PCE shows that
- radial flow is suppressed.
- temporal/spatial size of the fluid is reduced.
- elliptic flow is also suppressed and the resultant *v*2 depends on *T*th.
- HBT radii are also reduced.
- Nevertheless, it is not enough to completely interpret the HBT puzzle.

- Anyway, one should really include the properties of
-  chemical freeze out in hydrodynamic simulations !

## Initial Condition of Energy Density

- Initial energy density
- in the reaction plane

- transverse

- longitudinal

- Binary collision scaling:
*W* = *T*(*x*+*b*/2,*y*)*T*(*x*-*b*/2,*y*)

- Parameters for central collisions:
* **b*=2.4 fm
**0=0.6 fm
* **E*max=35 GeV/fm3
**flat=5.8
**Gauss=0.2

## Local Rapidity Shift

*z*

*z*

- BEFORE

- AFTER

- Local rapidity shift

**s0(*x*>0)>0

**s0(*x*<0)<0

- Global center of rapidity = 0

*x*

*x*

## pt Spectra for Identified Particles

*p*t Spectra for Identified Particles

- Chemical Equilibrium

- Partial Chemical Equilibrium

- Data from PHENIX, nucl-ex/0112006.

- The *p*t slope depends on *T*th
- in the conventional model EOS.

- The slopes of  are almost
- independent of *T*th.

## v2(pt) for Pions, Kaons and Protons

*v*2(*p*t) for Pions, Kaons and Protons

- 

*K*

*p*

- Chemical Equilibrium

- Partial Chemical Equilibrium

## v2(pt) for direct and indirect pions

*v*2(*p*t) for direct and indirect pions

- Population of resonances is very important
- in low pt region !
-  Need to include early chemical freeze out.

- Resonance decays
- dilute elliptic flow
- from direct pions.
- For its mechanism, see,
-  T.Hirano,PRL**86**,2754(2001).

## Variance of Initial Energy Density in the Transverse Plane

- with

- Variance of Initial Energy Density in the Transverse Plane

- Results (fm):
- 3.26  (binary collision scaling, *b*=2.4 fm)
- 3.40  (binary collision scaling, *b*=0 fm)
- 3.74  (wounded nucleon model, *b*=2.4 fm)
- 3.88  (wounded nucleon model, *b*=0 fm)
- 4.44  (prop. to Woods-Saxon)
- 5.78  (flat + Gauss)

## HBT Radii in Non-Central Collisions

*K*T(GeV/c)
- 0.2
- 0.4
- 0.6
- 0.8
- 1.0
- 0.

*K*T(GeV/c)
- 0.
- 0.2
- 0.4
- 0.6
- 0.8
- 1.0

## Discussion

*p*t spectra

*v*2(*p*t)

*R*side, *R*out

- ???

*p*t spectra

*v*2(*p*t)

*R*side, *R*out

- Transverse dynamics

- present initial condition

- future !?

- Are there any initial conditions
- compatible with all three
- observables ?