Michael Issah Stony Brook University for the PHENIX Collaboration CIPANP 2006, Puerto Rico

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


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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


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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

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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


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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


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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 )


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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


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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


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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


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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


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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

Documents

Michael Issah Stony Brook University for the PHENIX Collaboration CIPANP 2006, Puerto Rico