yuting bai (for the collaboration)
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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
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