# Presentation: 238850

## Hydrodynamic Models of Heavy-Ion Collisions

- Tetsufumi Hirano
*RIKEN BNL Research Center*

## 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

- Tetsufumi Hirano (RBRC)

## 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

- Tetsufumi Hirano (RBRC)

## 1. Why Hydrodynamics?

**1. Why Hydrodynamics?**

**Static**
**EoS from Lattice QCD**
**Finite *****T*****, **********  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:**

- Tetsufumi Hirano (RBRC)

## 1. Why Hydrodynamics (contd.)

**Transverse**

**Longitudinal**

***e *****(GeV/fm****3****)**

***e *****(GeV/fm****3****)**

**A full 3D hydrodynamic simulation with a CGC initial condition**
**Talk by Y.Nara**

**Space-time evolution of energy density in **
**sqrt(s****NN****)=200 GeV Au+Au collision at b=7.2fm**

**space-time rapidity**

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

- Tetsufumi Hirano (RBRC)

## 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

- Tetsufumi Hirano (RBRC)

## 2. How Hydrodynamics Works at RHIC

**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?**

- Tetsufumi Hirano (RBRC)

## Elliptic Flow of Charged Particles

**Elliptic Flow of Charged Particles**

- T.H.(’01)

- P.Huovinen(’03)

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

- P.Kolb et al.(’01)

- Tetsufumi Hirano (RBRC)

## 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.

- Tetsufumi Hirano (RBRC)

## Ideal hydro seems to give agood description at RHIC

**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***_

- Tetsufumi Hirano (RBRC)

## 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

- Tetsufumi Hirano (RBRC)

## 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!**

- Tetsufumi Hirano (RBRC)

## 3.1.1 Hydro as a Tool to Analyze Jet Quenching

**3.1.1 Hydro as a Tool to Analyze ****Jet Quenching**

**Color: parton density**
**Plot: mini-jets**

- Au+Au 200*A*GeV, *b*=8 fm
- transverse plane@midrapidity
- Fragmentation switched off

**hydro+jet model**

**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 **********(*****x*****) taken**
** ****from full 3D hydro simulations**

***x***

***y***

**GLV 1****st**** order formula (M.Gyulassy et al.(’00))**

- Movie and data of **(*x*) are available at
- http://quark.phy.bnl.gov/~hirano/

- Tetsufumi Hirano (RBRC)

## Interplay between Soft and Hard

**Interplay between Soft and Hard**

***N*****SOFT****~*****N*****HARD**

*p**T*

- (1/*p**T*)(*dN*/*dp**T*)

**Hydrodynamic**
**afterburner**

**Jet**
**quenching**

**Interesting region**
******Intermediate *****p******T***
**(2<*****p******T*****<3.5 GeV/*****c*****)**
**Pion ********hard****,**** ****Proton**** ********soft**

**It’s the very**
**heavy ion physics!**

- T.H & Y.Nara(’03)

**Crossing p****T**** moves**
**toward high p****T**

**soft**

**hard**

**Au+Au at b=2 fm**

- Tetsufumi Hirano (RBRC)

## Consequense from hadron species dependent pT,cross

**Hydro+Jet**

**Talk by R.Fries**

**Recombination**
**+Fragmentation**

- !?

***R******AA***

**Particle ratio**

**“****Scaling v****2****”**
**Interplay between soft and hard?**
**Recombination mechanism?**

- Tetsufumi Hirano (RBRC)

## 3.1.2 Hydro as a Tool to Analyze Electromagnetic Radiation

** ****probe of QGP      **     (E.Shuryak(’78))

**3.1.2 Hydro as a Tool to Analyze ****Electromagnetic Radiation**

***T*****, ********

***u*********

** ****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

- Tetsufumi Hirano (RBRC)

## Chemical Non-Equilibrium

| QGP phase | “Gluon Plasma (GP)”  QGP |
| --- | --- |
| Hadron phase | Chemical freezeout |

**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

- Tetsufumi Hirano (RBRC)

## Novel Temperature Evolution

_***Caveat***_**:**
**   ****one has to take account of**
**fugacity ********in calculating EM**
**spectra.**
**QGP phase: ********<1**
**Hadron phase: ********>1**
**Compensation between**
***T***** and ********? **
**                 ****Talk by H.Niemi**

**proper time **

*T*c

**temperature**

**chemical non-eq.**

**chemical eq.**

- Tetsufumi Hirano (RBRC)

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

| Group | Hydro | Initial condition |
| --- | --- | --- |
| M.Gyulassy et al. | SHASTA (2+1D, Bjorken) | HIJING, event-by-event |
| C.Nonaka et al. | Lagrangian hydro (full 3D) | URASiMA, event average |
| B.Schlei et al. | HYLANDER (2+1D) | VNI, event average |
| C.E.Aguiar et al. | SPheRIO (full 3D) | NeXus, event-by-event |
| L.P.Csernai et al. | Particle-in-cell (full 3D) | String ropes, flux tubes, classical YM |
| K.Eskola et al. | SHASTA (2+1D, Bjorken) | pQCD + final state saturation |
| T.H. & Y.Nara |  coordinate (full 3D) | CGC, (kT2,x) a la Kharzeev & Levin |
| ... | ... | ... |

- Tetsufumi Hirano (RBRC)

## 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)**

- ***S**moothed **P**article **h**ydrodynamical **e**volution of **R**elativistic
- heavy **IO**n collisions  (**S**ao **P**aulo & **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)

- Tetsufumi Hirano (RBRC)

## 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!**

- Tetsufumi Hirano (RBRC)

## 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!

**p****T**** slope is not affected largely.**
****** ****v****2****(p****T****) and its fluctuation?**

**Now the hydro simulation becomes**
** ****close to experimental situations**
** ****like event-generators!**

- Tetsufumi Hirano (RBRC)

## 3.2.2 CGC+Hydro+Jet Model

**T.H. & Y.Nara**
**Talk by Y.Nara**

- Jet quenching

**Dense Medium**

- Color Glass Condensate

- These three physics closely related with each other!

**Elliptic flow**

**          ****Talk by**
** ****J.Jalilian-Marian**

**Talk by**
** ****I.Vitev**

- Tetsufumi Hirano (RBRC)

## 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**

***k******T***** factorization**

**Parton**
**energy loss**

**Initial condition of **
**energy density from CGC**
**Au+Au 200AGeV**
**b=7.2fm, ********************=0.6fm**

**transverse**

**longitudinal**

- Tetsufumi Hirano (RBRC)

## Results from CGC+hydro+jet

**Au+Au sqrt(s****NN****) = 200 GeV**

**For details, talk by Y.Nara**

**CGC initial condition**
**works very well!**
**(Energy, rapidity, centrality**
**dependences)**

- Tetsufumi Hirano (RBRC)

## 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

- Tetsufumi Hirano (RBRC)

## 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**

**1****st**** order correction to dist. fn.:**

**:Sound attenuation length**

**:Tensor part of thermodynamic force**

**Reynolds number in Bjorken flow**

- Nearly ideal hydro !?

**D.Teaney(’03)**

- Tetsufumi Hirano (RBRC)

## Break Down of Naive Navier-Stokes Eq. and a Relaxation Method

**Non-relativistic case (Based on discussion by Cattaneo (1948))**

**0: **Fourier’s law**

**: **“relaxation time”**

**Parabolic equation (heat equation)**
**ACAUSAL!! **
**                 ****Finite ****
**Hyperbolic equation (telegraph equation)**

**Balance eq.:**

**Constitutive eq.:**

**            ****Talk by D.Teaney**
**See also, A.Muronga (’02)**

- Tetsufumi Hirano (RBRC)

## 5. Summary

- Open our mind *!* Hydrodynamics can be used even for “high pT physics in HIC”.
- Jet tomography
- EM probe
- (J/ 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**

- Tetsufumi Hirano (RBRC)

## Thank you!

- Special thanks goes to:
- H.Niemi,
- D.Teaney,
- Y.Hama, T.Kodama
- (SPheRIO collaboration),
- Y.Nara,
- and
- L.McLerran

**Space-time evolution of energy density in **
**sqrt(s****NN****)=200 GeV Au+Au collision at b=7.2fm**

- Tetsufumi Hirano (RBRC)

## Spare Slides

- Tetsufumi Hirano (RBRC)

## No Boost Invariant Region at RHIC?

***Basic assumption***
**Finite **_**Bjorken**_** rod (-**********0****<**********s****<**********0****)**
**Massless pions**
**Thermalization and Boltzmann approximation**

- 2**0

- Space-time rapidity

- Not free streaming,
- but thermal fluctuation!

- Tetsufumi Hirano (RBRC)

## Thermalization?

- Hydro people often used
**0 =0.2-1.0 fm/c
- at RHIC energies to get large v2.

- pQCD +Boltzmann eq. analyses :
- Elastic (gggg) collisions:**eq>6-10 fm/c
- Inelastic (ggggg) collisions:**eq=2-3fm/c

- A.H.Mueller, R.Baier et al., J.Serreau et al., A.Dumitru et al.,
- J.Bjoraker et al. ...

- Thermalization controlled by
- non-perturbative physics?

- Tetsufumi Hirano (RBRC)

## Protons with pT=4 GeV/c in hydro?

**Proton: **
***p******T*****=4 GeV/*****c***** in lab. frame**
***p******T*****~2.4GeV/*****c***** in local rest frame with *****v******T*****=0.5*****c***** **

**No!**

**Lorentz tr.**
**Suppose momentum parallel to flow**

- Tetsufumi Hirano (RBRC)

## Recombination + Fragmentation?

- Work in intermediate and high pT
- Parameterized flow
- How do we obtain such a large flow
- (vT~0.55c) at T=Tc?
- What happens for high pT v2 if a
-  realistic density profile is used instead
-  of hard sphere?

- Work in low and high pT
- Flow is dynamically obtained.
- Radial flow in hadron phase
-  is also important.
-  At T=Tc,            <vT>~0.25c
-       T=100 MeV, <vT>~0.55c

**Talk by R.Fries**

**T.H. & Y.Nara**

**Hydro + Jet ?**

- Tetsufumi Hirano (RBRC)

## Hydro + Rate Eq. in QGP phase

**Including gg********qqbar and gg********ggg**

**Collision term:**

- T.S.Biro et al.,Phys.Rev.C48(’93)1275.

**Assuming “multiplicative” fugacity, EoS is unchanged. **

- Tetsufumi Hirano (RBRC)

## Hydro+Jet Model

**Hydro+Jet Model**

*N*

*N*

- 3

- 4

**Fragmentation:**
**Independent**
**Fragmentation**
**Model**

- PYTHIA

- 3D Hydro

- PYTHIA

**hadrons**

**hadrons**

**PDF:**
**Collinear: CTEQ5LO**
**k****T****: Gaussian**

**Parton energy loss**

**pQCD LO:**

- *Initial and final state radiation are included.

- Tetsufumi Hirano (RBRC)

## Initial energy density fluctuation

**Suppose massless free EoS,**

**Multiplicity is proportional to the entropy.**

- The 1st order term vanishes.

- In the conventional approach,
- one uses average
-  initial energy density

- Multiplicity **WITH** fluctuation **<** Multiplicity **WITHOUT** fluctuation

- Tetsufumi Hirano (RBRC)

## dN/d from a Saturation Model

**dN/d******** from a Saturation Model**

*Q*s2

**

*k**T**2*

- 0

- ggg

- D. Kharzeev and E. Levin, Phys.Lett.B523,79(2001)

- Parton-hadron duality

- s

- Tetsufumi Hirano (RBRC)

## Initial Condition from CGC

**“****CGC +**** Hydro + Jet model”**

**Saturation scale at a transverse position: **

**Momentum rapidity *****y***** ******** space time rapidity **********s**** **

**Input for hydrodynamics**

**where**

**Unintegrated gluon distribution can be written**

- Tetsufumi Hirano (RBRC)

## v2() from CGC+Hydro

- Tetsufumi Hirano (RBRC)

## 2nd order formula...

- 14 equations...

- 1st order

- 2nd order

- How obtain additional equations?

- In order to ensure the second law of thermodynamics               , one can choose

- Balance eqs.

- Constitutive eqs.

- Tetsufumi Hirano (RBRC)