michael issah stony brook university for the phenix collaboration cipanp 2006, puerto rico
DESCRIPTION
What do the scaling characteristics of elliptic flow reveal about the properties of the matter at RHIC ?. Michael Issah Stony Brook University for the PHENIX Collaboration CIPANP 2006, Puerto Rico. Outline. Motivation Eccentricity scaling and thermalization - PowerPoint PPT PresentationTRANSCRIPT
What do the scaling What do the scaling characteristics of elliptic flow characteristics of elliptic flow
reveal about the properties of the reveal about the properties of the matter at RHIC ?matter at RHIC ?
Michael IssahStony Brook University
for the PHENIX Collaboration
CIPANP 2006, Puerto Rico
CIPANP 2006, Puerto Rico
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OutlineOutline
Motivation Eccentricity scaling and thermalization Equation of state and speed of sound estimation Dependence of elliptic flow on kinetic energy and
degrees of freedom Summary
CIPANP 2006, Puerto Rico
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Elliptic FlowElliptic Flow
y
x
py
px
coordinate-space-anisotropy momentum-space-anisotropy
Initial/final conditions, dof, EOS
Elliptic flow strength determined principally by initial conditions, initial eccentricity and
EoS
v2 px
2 py2
px2 py
2
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• High energy densities are achieved, higher than required for phase transition to occur (~ 1 GeV/fm3)
Are energy densities high enough?Are energy densities high enough?
PRL87, 052301 (2001)
Central collisionsperipheral collisionsthermalization time
(0 ~ 0.2 – 1 fm/c)Bj~ 5 – 15 GeV/fm3
dydE
RT
Bj0
2
11
Extrapolation From EExtrapolation From ETT DistributionsDistributions
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Elliptic flowElliptic flow at RHICat RHIC
Large v2 created at RHIC Indicates early thermalization Elliptic flow data agrees well with hydrodynamic predictions Can one exploit scaling properties of v2 to get insight into the degree of thermalization and test for hydrodynamic behavior ?
Hydr
o by
Huo
vine
n et
al.
hydr
o tu
ned
to fi
t cen
tral
spec
tra d
ata.
PRC 72 (05) 014904
200 GeV Au+Aumin-bias
PRL 91, 2003 (PHENIX)
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Eccentricity scaling as a test for the degree of Eccentricity scaling as a test for the degree of thermalizationthermalization
Large v2 indicative of high degree of thermalization of produced matter
Are there other observables showing that the matter is thermalized ? Eccentricity scaled v2
Ideal hydrodynamics is scale invariant. If the matter behaves hydrodynamically and is thermalized, v2 should be independent of system size
Do we observe such independence in the data? Data for different colliding systems (Au+Au,
Cu+Cu) available to test this
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Determination of eccentricityDetermination of eccentricity
Eccentricity usually obtained from a Glauber Model
One can also use experimental quantity sensitive to initial eccentricity, like the integrated v2
Integrated v2 is proportional to the eccentricity
2 2
2 2
y x
y x
STAR Collaboration
CIPANP 2006, Puerto Rico
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Eccentricity scalingEccentricity scaling
Eccentricity scaling observed in hydrodynamic model over a broad range of centralities
Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009
R: measure ofsize of system
CIPANP 2006, Puerto Rico
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Eccentricity scaling and system sizeEccentricity scaling and system size
v2 scales with eccentricity and across system size
PHENIX Preliminary
k ~ 3.1 (obtained from data )
CIPANP 2006, Puerto Rico
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Energy dependence of elliptic flowEnergy dependence of elliptic flow
Saturation of azimuthal anisotropy observed at RHIC energies Suggests the matter has a soft EoS
CIPANP 2006, Puerto Rico
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Estimate of the speed of soundEstimate of the speed of sound (I)(I) Energy dependence at RHIC energies seem to indicate a soft equation of
state. How soft ? Estimate of cs from elliptic flow measurements can be made from
eccentricity scaled v2
Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009
CIPANP 2006, Puerto Rico
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Estimation of the speed of sound (II)Estimation of the speed of sound (II)
Assume simple EoS: relation between pressure and
energy density
cs ~ 0.35 ± 0.05(cs
2 ~ 0.12), soft EOSF. Karsch, hep-lat/0601013
v2/ε for <pT> ~ 0.45 GeV/c
CIPANP 2006, Puerto Rico
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Scaling breaks
Elliptic flow scales with KET up to KET ~1 GeV Indicates hydrodynamic behavior Possible hint of quark degrees of freedom become apparent at higher KET
Baryons scale together
Mesons scale together
PHENIX preliminary
See H. Masui’s talkin this session
Kinetic energy of a particle in a relativistic fluid:
= mT – m
Scaling vScaling v22 with kinetic energy (I) with kinetic energy (I)
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PHENIX preliminary
Transverse kinetic energy scaling works for a large selection of particles
Scaling vScaling v2 2 with kinetic energy (II) with kinetic energy (II)
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Constituent quark scaling works better with KET as compared to pT Hadron mass (hydro) scaling at low KET (KET < 1 GeV) is not perturbed by constituent quark scaling at higher KET !
Test for partonic degrees of freedomTest for partonic degrees of freedom
PHENIX preliminary
STAR preliminary
200 GeV Au+Au
CIPANP 2006, Puerto Rico
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KEKET T /n scaling and hydrodynamics/n scaling and hydrodynamics
Scaling works for a broad set of particles Supports the observation that all particles emerge from a common flow field Hydrodynamic calculation not incompatible with KET/n scaling
PHENIX preliminary Chiho Nonaka: 3-D Hydro
R. Fries, SQM2006
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KEKETT/n scaling across collision centralities/n scaling across collision centralities
KET/n scaling observed across centralities
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SummarySummary
Scaling properties of elliptic flow provide a way to infer some properties of the matter formed in heavy-ion collisions at RHIC
Eccentricity scaling shows that the medium is highly thermalized, with a soft EoS
Transverse kinetic energy scaling indicates perfect fluid hydrodynamic behavior
In addition, scaling with KET/n leads to comprehensive scaling of elliptic flow data, which prevails over a broad range of centralities
Taken together, these observations show that the matter is highly thermalized, has a soft equation of state and is made up of flowing constituent quarks