Transcript Document
Anisotropic Flow
and Ideal Hydrodynamic Limit
Yuting Bai
(for the
Collaboration)
International Conference on Strangeness in
Quark Matter 2008
Oct. 6 -10, 2008
Beijing, China
Outline
Introduction
Anisotropic flow
The success and uncertainties in ideal
hydro calculations
Results
How much deviation from ideal hydro
Conclusions
Yuting Bai, SQM2008
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Anisotropic Flow
y
py
x
y
x
z
v2 cos2 r
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
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Ideal hydro success and uncertainties
C. Alt et.al;
Phys.Rev.C68,034903(2003)
Hydro limits from P.Kolb,
J.Sollfrank,U.Heinz;
Phys.ReV.C62:054909,2000
v2/e 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)
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Choices of v2 and e
y
y’
x’
x
Standard eccent ricity : ε std
RP
y2 x 2
y2 x 2
(σ 2y σ 2x ) 2 4σ 2xy
P articipant eccent ricity : ε part
σ 2y σ 2x
,
σ 2x x 2 x , σ 2y y 2 y , σ xy xy x y
2
ε{2}
2
ε2
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
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}, epart and
e{2} sensitive to
anisotropy w.r.t the
participant plane PP
v2{4},v2{ZDCSMD} and
estd sensitive to
anisotropy w.r.t the
reaction plane RP
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Flow increases
STAR Preliminary
standard eccentricity from
Glauber model
eccentricity from CGC
(nucl-th/0605012)
Scaled v2 increases with centrality over large pt range
Peak position of v2/e shifts to higher pt in more central collision
The system seems more close to thermalization for most
central collisions
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How much deviation from ideal hydro
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/e
dependence has been
parameterized as
function of K
Fit data to extract
v2hydro/e and s
hydro
v2 v2
ε
ε
1
1 K K0
Knudsen number : K λ R
T henumber of collisionsper part icle:
1 K (σ S)(dN dy )cs
σ : part oniccross sect ion
K 0 0.7,c s 1
K 0:
v2
3
hydro
Hydrodynamic limit
ε
K : c ss
1 dN
Low densit y limit (LDL)
S dy
R.Bhalerao,J-P.Blaizot,N.Borghini and JY.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, JY.Ollitrault; Phys. Rev. C 76, 024905 (2007)
Yuting Bai, SQM2008
How much deviation from ideal hydro
STAR Preliminary
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/e is considerably
away from hydro limit
independent of choices
of e
K decreases with the
increasing of particle
density. But still finite
in the most central
collisions
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Hiroshi Masui Parallel Session I: 15:40—16:00
How much deviation from ideal hydro
STAR Preliminary
PHENIX p, K and p: nucl-ex/0604011, STAR Ks0, L: Phys. ReV. C 77 054901 (2008)
With the assumption that parton cross section (s) is same
for all identified particles, a universal trend of approaching
hydro limit is established. In central collisions, the ratio of
v2/e is considerably away from hydro limit
Yuting Bai, SQM2008
Constraint on EoS
STAR Preliminary
cs
s K 0 const.
c
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Constraint on h/s
Temperature from:
A.Adare nucl-ex/08044168
STAR Preliminary
η
λT
T
T
T
1
0.316 0.316
0.316
0.316
1
dN
1
s
c
csn
σcs 1 dN
cσ
S dy R/(cs /c)
SR dy
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Charged particle v4/v22
STAR Preliminary
Hydro, Boltzmann calculations:J-Y. Ollitrault
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
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Conclusions
v2/e, examined with transport motivated formula,
approaches ideal hydro limit for all identified
hadrons. In central Au+Au collisions, v2/e 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, h/s versus centrality is extracted.
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Choices of v2 and e
G. Wang QM2005
Au +Au 200 GeV
STAR Preliminary
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
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