slide1 l.
Skip this Video
Loading SlideShow in 5 Seconds..
Huichao Song PowerPoint Presentation
Download Presentation
Huichao Song

Loading in 2 Seconds...

play fullscreen
1 / 19

Huichao Song - PowerPoint PPT Presentation

  • Uploaded on

Viscous hydrodynamics for relativistic heavy-ion collisions. Huichao Song. Department of Physics. The Ohio State University. 191 West Woodruff Avenue. Columbus, OH 43210. 2007 National Nuclear Summer School. FSU, FL. July 8 – July 21, 2007. Advisor: U. Heinz, Supported by DOE.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Huichao Song' - ezekial

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Viscous hydrodynamics for relativistic heavy-ion collisions

Huichao Song

Department of Physics

The Ohio State University

191 West Woodruff Avenue

Columbus, OH 43210

2007 National Nuclear Summer School

FSU, FL. July 8 – July 21, 2007

Advisor: U. Heinz, Supported by DOE

the qgp shear viscosity
The QGP Shear Viscosity

The QGP shear viscosity of is in hot theoretical debates recently:

-Weakly coupled QCD prediction:

P.Arnold,G.Moore,&Y.Yaffe, 00,03

-Strongly coupled AdS/CFT prediction:

D.T. Son, et,al. 03

The first estimation of the QGP shear viscosity from the experimental data (RHIC):

--blast wave model + the first order theory corrections

D. Teaney, PRC 68 (2003) 034913

Blast wave model analysis:

-only counts the viscous corrections to the

spectra during freeze-out procedure

-neglects shear viscosity effects on hydro dynamic evolution before freeze-out

Viscous hydrodynamics is needed!

ideal hydrodynamics

Input: “EOS”

Ideal hydrodynamics




-A macroscopic tool to describe the expansion of QGP or hadronic matter

Conservation laws

5 equ. 14 independent variables

-reduce # of independent variables (ideal hydro)

-Provide more equations? (viscous hydro)

Ideal hydrodynamics: reduce the independent variable from 14 to 6,

causal viscous hydrodynamics

Dissipative flows

charge flow

energy flow

bulk pressure

shear pressure tensor

entropy flow

Causal viscous hydrodynamics

Full tensor decomposition in frame of:

Besides these modified transport equations for, one need more equations

for these dissipative flows:

The first order theory formulism:

--- Eckart, Landau & Lifishitz around 1950’s

Problems in the first order theory formulism:

-Acuasl, infinite speed of signal propagation

-process instabilities

causal viscous hydrodynamics6

Dissipative flows

charge flow

energy flow

bulk pressure

shear pressure tensor

entropy flow

Causal viscous hydrodynamics

Full tensor decomposition in frame of:

W. Israel, J.Stewart 79

The 2nd order Israel-Stewart formulation:

--expansion the entropy current to the 2nd order of dissipative flows,

causal viscous hydro in 2 1 d


-Bjorken approximation:

Causal viscous hydro in (2+1)-d

U. Heinz, H. Song & A. Chaudhuri, PRC 73(2006) 034904

3+1 2+1

-zero net baryon density, zero bulk pressure, zero heat conduction

Equivalent to the modified transport equations for

where, the transport equations for energy momentum tensor are explicit written as:

viscous vs ideal hydro temperature entropy

Initial & final conditions: (viscous & ideal)

Other viscous hydro parameter: Shear viscosity& relaxation time

Viscous vs. ideal hydro: temperature & entropy

-slowing down of cooling process due to decelerated longitudinal expansion initially ,

but faster cooling in middle and late stages due to stronger transverse expansion

-viscous effects are larger in early and middle stages, but neglectable in late stage

viscous vs ideal hydro radial flow spectra
Viscous vs. ideal hydro: radial flow & spectra

-More radial flow, flatter spectra

-the viscous effects to the hadron spectra could be absorbed by starting viscous

hydro later with lower initial energy density

viscous vs ideal hydro elliptical flow

-Both the evolution corrections (viscous corrections to ) and spectra corrections

initial energy density distribution

(viscous corrections to ) have significant effects to , for low region evolution

correction dominant.

Viscous vs. ideal hydro: elliptical flow

For non-central collisions:

-Elliptical flow is very sensitive to even minimal shear viscosity.

summery and conclusions
Summery and Conclusions

- Shear viscosityresults inslowing down of the cooling process in early stage due

to decelerated longitudinal expansion, faster cooling in middle and late stages due

to stronger transverse expansion.

-Shear viscosity leads to more radial flow generation and flatter spectra, the effects

of which could be absorbed by starting viscous hydro later with lower initial energy


-elliptical flow is very sensitive to shear viscosity, even the minimum value from

AdS/CFT could result in a great suppression of .

  • in contrast with the Teaney’s blast wave model method, which only counts viscous

spectra corrections during freeze-out procedure, our results shows that evolution

  • corrections ( ) are the main factor to influence the low spectra elliptical flow.

-Do the results indicate that the QGP viscosity smaller than the AdS/CFT lowest

limit? Need more investigations in the at least flowing aspects:

a)Different initial conditions

b) more realistic descriptions of the hadronic stage

1 st order theory vs 2 nd order theory

vs. different relaxation time

1st theory vs. 2nd order theory



1st order theory vs. 2nd order theory

As the relaxation time reduces to zero, the 2nd order theory formulism returns to the 1st order one. First order theory , instable ?

a)calculated with the same velocity profile from the 2nd theory by

not the real 1st order Navier-Stokes hydrodynamics

b)Smaller relaxation time reduces the viscous effects on suppression of

blast wave model vs real viscous hydrodynamics
Blast wave model vs. real viscous hydrodynamics

Blast wave model


viscous hydrodynamics

+ the1st order theory corrections

(the 2 order theory Israel-Stewart formulation)

--with only spectra corrections

--with both evolution and spectra corrections

Compare the spectra corrections from blast wave model and from real hydrodynamics:

-Spectra corrections are sensitive to the details of flow pattern at freeze out, and are

not easily captured with blast-wave model parametrizations.

where ideal hydro works
Where ideal hydro works

Hydro: U Heinz & P.Kolb Data: STAR PHENIX

spectra for both central collision and noncentral collisions :

where ideal hydro works19
Where ideal hydro works



Elliptic flow coefficient at noncentral collisions:

as a function of centrality

for different identified hadrons

-Ideal hydro describes the data well at

-It also gives a correct mass splitting of at low region