Yuting Bai

(for the Collaboration)

Anisotropic Flow and Ideal Hydrodynamic Limit

International Conference on Strangeness in Quark Matter 2008

Oct. 6 -10, 2008

Beijing, China

Yuting Bai, SQM2008 2

Outline Introduction

Anisotropic flow The success and uncertainties in ideal

hydro calculations Results

How much deviation from ideal hydro Conclusions

Yuting Bai, SQM2008 3

Anisotropic Flow

The spatial anisotropy is transformed into a momentum anisotropy by the multiple interactions

Established early, self-quenching, therefore sensitive to the early stage of the collisions

Depending on rescattering, sensitive to the degree of thermalization

xz

y

px

pyy

x

v2 cos 2 r

reac

tion

plan

e

Yuting Bai, SQM2008 4

Ideal hydro success and uncertainties

v2/ was considered to approach the ideal hydro limit in central collisions

Uncertainties: Choice of EoS - affects Hydro limits The initial conditions: Glauber, Color Glass Condensate

(CGC)

C. Alt et.al; Phys.Rev.C68,034903(2003) Hydro limits from P.Kolb, J.Sollfrank,U.Heinz; Phys.ReV.C62:054909,2000

Yuting Bai, SQM2008 5

Choices of v2 and The number of individual

nucleons participating in the collision as well as their position could fluctuate from event to event. The center of the overlap zone can be shifted and the orientation of the principal axes of the interaction zone can be rotated

v2{EP}, v2{2}, part and {2} sensitive to anisotropy w.r.t the participant plane PP

v2{4},v2{ZDCSMD} and std sensitive to anisotropy w.r.t the reaction plane RP

2

xy

222y

222x

2x

2y

2xy

22x

2y

part

22

22

std

εε{2}

yxxyσ,yyσ,xxσ

,σσ

4σ)σ(σε:tyeccentricit Participan

xy

xyε:tyeccentrici Standard

y

x

x’

y’

M.Miller and R.Snellings;nucl-ex/0312008

R.Bhalerao and J- Y.Ollitrault; Phys.Lett.B 614(2006)260

S.Voloshin, A.Poskanzer, A.Tang and G.Wang; Phys.Lett.B 659(2008)537

RP

PP

Yuting Bai, SQM2008 6

Flow increases

Scaled v2 increases with centrality over large pt range Peak position of v2/ shifts to higher pt in more central collision The system seems more close to thermalization for most central

collisions

eccentricity from CGC (nucl-th/0605012)

standard eccentricity from Glauber model

STAR Preliminary

Yuting Bai, SQM2008

How much deviation from ideal hydro

R.Bhalerao,J-P.Blaizot,N.Borghini and J-Y.Ollitrault;Phys.Lett.B 627:49-54,2005

C.Gombeaud and J-Y.Ollitrault; Phys. Rev. C 77, 054904 (2008)

H-J.Drescher, A.Dumitru, C.Gombeaud, J-Y.Ollitrault; Phys. Rev. C 76, 024905 (2007)

Try to use the data to constrain the hydro limit

Use relativistic Boltzmann calculations to calculate how v2 approaches hydro as function of cross section and density

Based on these calculations the v2/ dependence has been parameterized as function of K

Fit data to extract v2

hydro/ and

(LDL)limit density Low dy

dN

S

1c :K

limit icHydrodynam ε

v :0K

31c0.7,K

section cross partonic :σ

)cdydN)(Sσ(K1

:particleper collisions ofnumber The

Rλ K :numberKnudsen

KK1

1

ε

v

ε

v

s

hydro2

s0

s

0

hydro22

Yuting Bai, SQM2008 8

How much deviation from ideal hydro

The estimates depend on the initial conditions. A softer EoS is required for CGC

Ideal hydro limit is not reached at top RHIC energy. The ratio of v2/ is considerably away from hydro limit independent of choices of

K decreases with the increasing of particle density. But still finite in the most central collisions

STAR Preliminary

Yuting Bai, SQM2008

How much deviation from ideal hydro

With the assumption that parton cross section () is same for all identified particles, a universal trend of approaching hydro limit is established. In central collisions, the ratio of v2/ is considerably away from hydro limit

PHENIX p, K and p: nucl-ex/0604011, STAR Ks0, : Phys. ReV. C 77 054901 (2008)

STAR Preliminary

Hiroshi Masui Parallel Session I: 15:40—16:00

Yuting Bai, SQM2008 10

Constraint on EoS

.0 constKc

cs

STAR Preliminary

Yuting Bai, SQM2008 11

Constraint on s

dydN

SR1

1

σc

T0.316

/c)R/(c1

dydN

S1

cσ

T0.316

nc

T0.316

c

λT0.316

s

η

s

s

Temperature from:

A.Adare nucl-ex/08044168

STAR Preliminary

Yuting Bai, SQM2008 12

Charged particle v4/v22

It’s expected that v4/v22 decreases with K-1.

Consistent with Boltzmann calculation with K> 0.5 Measured ratios indicate that ideal hydro limit is not

reached

Hydro, Boltzmann calculations:J-Y. Ollitrault

STAR Preliminary

Yuting Bai, SQM2008 13

Conclusions

v2/, examined with transport motivated formula, approaches ideal hydro limit for all identified hadrons. In central Au+Au collisions, v2/ is still considerably away from Hydro limit. The conclusion is independent of initial conditions.

Results of charged hadron v4/v22 are consistent with

above

Constraint on EoS obtained.

For the first time, /s versus centrality is extracted.

Yuting Bai, SQM2008 14

Choices of v2 and

v2{4}: measured with the 4-particle cumulant method v2{ZDCSMD}: measured with the first order event plane

reconstructed with STAR’s ZDC-SMD non-flow effects are reduced in both methods

Au +Au 200 GeV

G. Wang QM2005

STAR Preliminary