Rapidity Dependence of Elliptic Flow from Hydrodynamics

1
Rapidity Dependence ofElliptic Flowfrom
Hydrodynamics

• Tetsufumi Hirano
• RIKEN BNL Research Center
• (Collaboration with Yasushi Nara, Univ. of
  Arizona)

2
Outline

• Introduction
• Results so far
• Tth dependence of v2(h)
• Initial condition from the CGC and its
  consequence
• Summary discussion

3
Introduction
v2(y) is supposed to reflect global dynamics
? How obtain by hydrodynamics?
Non-central coll. ? No cylindrical
sym. Non-Bjorken behavior ? No scaling
ansatz High energy collisions (_at_RHIC) ? No
Cartesian coordinate? Need full 3D
hydro simulations in t-h coordinate

T.H., PRC65,011901(2002).
From Experimental Point of View Need broad
acceptance in longitudinal direction See
S.Manlys talk
4
Results so far (1)
T.H., PRC65,011901(2002).

• The shape of v2(h) depends largely on initial
  longitudinal profile

dN/dh
v2(h)
5
Local Rapidity Shift
Direct charged, Tth140MeV, b6.9fm

• Local rapidity shift
• (J.Sollfrank et al., Eur.Phys.J.C6,525(1999))

v2(h)
dN/dh
z
x
E(x,hs) at b6.9fm
Shape at hs4.5
hs
Third flow? (L.P.Csernai and D.Rohrich, PL B458,
454(1999))
x
6
Results so far (2)
T.H. and K.Tsuda, PRC66,054905(2002).

• v2 is reduced by chemical
• non-equilibrium property

• Space-time evolution is completely
• different from conventional
• (chemically equilibrated) EOS.

7
v2(h) and v2(y)
Jacobian as an weight fn.
P. Kolb, Heavy Ion Phys.15, 279(2002).
Jacobian between y and h
Result from 3D hydro
8
Summary (part 1)

• Ambiguity of init. condition.
• ?Smaller flat region would be good.
• ?No local rapidity shift
• Realistic EOS (chemically non-eq.)

Return game in 200 GeV collisions
9
Initial Condition in Long. Direction
hflat
(x,y)(0,0)
Emax
hGauss

• Emax45 GeV/fm3
• hflat 2.0
• hGauss 0.8
• No local rapidity shift

of binary coll. scaling for finite b. Works
well as centrality dep. for initial
condition. (P.Kolb et al., Nucl.Phys.A696,197,(200
1))
10
Tth Dependence of v2
As far as pions, Tth is not determined by pT
slope within chemically non-equilibrium EOS model.

• v2 glows also in hadron phase.
• Eventually, v2(y) becomes flat
• as Tth decreases

11
dN/dh from a Saturation Model
D. Kharzeev and E. Levin, Phys.Lett.B523,79(2001)
gg?g
Parton-hadron duality
f
1/as
Qs2
kT2
0
12
Initial Condition from CGC(hydrodynamic
afterburner for CGC)
Saturation scale at a transverse position
where
K0.7 k20.94 (Tth100MeV) l0.2
Unintegrated gluon distribution can be written
Momentum rapidity y ? space time rapidity hs
Input for hydrodynamics
CGC Hydro ( Jet) model
13
Initial Energy Density Distributionand dNch/dh
b2.4fm
dET/dhs
e(y0,hs0)
14
v2(h) from CGCHydro
CGCHydro
FlatGaussian initialization

• Slightly suppressed near midrapidity region
• Pressure gradient in longitudinal direction
• Pressure gradient in transverse direction
• ?Stronger longitudinal flow and weaker
  transverse flow
• in CGChydro case than in flatGaussian case.

15
Summary Discussion

• There IS a solution for v2(h) from
  hydrodynamics.
• Further systematic studies are needed.
• Initial condition? Tth dependence ? EOS ?
• CGChydro(jet) model (Improvement of I.C.)

• Consistency check
• ltpTgt(y) pT spectra in forward rapidity (BRAHMS
  data)
• v2(pT) _at_ forward rapidity region ?
• ? v1(y) ??? ?third flow components ?

16
Thank you!
CGChydro at b6.9fm in transverse plane
17
Flat Energy Flat dN/dy

• Basic assumption
• Finite Bjorken rod (-h0lthslth0)
• Massless pions
• Constant T and Boltzmann approximation

2h0
18
Accepted Events by PHOBOS
Not minimus bias!
In hydro, average over Npart in multiples of 25
up to 325.
B.B.Back et al.(PHOBOS), PRL89,222301(2002).
19
Mean pT as a Function of y
J.H.Lee(BRAHMS), talk at Forward Physics at RHIC,
Oct.9, 2003,BNL
20
Blast Wave Fit in Forward Rapidity Region by
BRAHMS
R.Debbie (BRAHMS), proceeding for The 8th
Conference on Intersections of Particle And
Nuclear Physics (CIPANP2003), New York City, New
York (May 19-24, 2003).
21
v2(pT) _at_ 130AGeV
Chemical eq. model
Chemical non-eq. model
Table. Tth dependence for pions
pT slope v2(pT)
Chem. eq. yes no
Chem. non-eq. no yes
22
Freezeout Hypersurface
100-120MeV
120-140MeV
140- MeV
tau (fm)
PCE
CE
Initial temperature (b6.9fm)
7.8
8.7
9.6
23
Movie
CGC
FlatGaussian
24
Longitudinal Acceleration
Initial transverse energy
YL-hs Deviation from scaling flow