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

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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

- 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

coordinate-space-anisotropy momentum-space-anisotropy

y

py

px

x

Initial/final conditions, dof, EOS

Elliptic flow strength determined principally by initial conditions, initial eccentricity and EoS

CIPANP 2006, Puerto Rico

PRL87, 052301 (2001)

peripheral collisions

Central collisions

Extrapolation From ET Distributions

- High energy densities are achieved, higher than required for phase transition to occur (~ 1 GeV/fm3)

thermalization time

(t0 ~ 0.2 – 1 fm/c)

eBj~ 5 – 15 GeV/fm3

CIPANP 2006, Puerto Rico

PRC 72 (05) 014904

200 GeV Au+Au

min-bias

Hydro by Huovinen et al.

hydro tuned to fit central

spectra data.

PRL 91, 2003 (PHENIX)

- 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 ?

CIPANP 2006, Puerto Rico

- 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

CIPANP 2006, Puerto Rico

- 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

STAR Collaboration

CIPANP 2006, Puerto Rico

Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009

Eccentricity scaling observed in hydrodynamic model over a broad range of centralities

R: measure of

size of system

CIPANP 2006, Puerto Rico

k ~ 3.1 (obtained from data )

PHENIX Preliminary

v2 scales with eccentricity and across system size

CIPANP 2006, Puerto Rico

- Saturation of azimuthal anisotropy observed at RHIC energies
- Suggests the matter has a soft EoS

CIPANP 2006, Puerto Rico

- Energy dependence at RHIC energies seem to indicate a soft equation of state. How soft ?
- Estimate of cs from elliptic flow measurementscan be made from eccentricity scaled v2

Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009

CIPANP 2006, Puerto Rico

Assume simple EoS: relation between pressure and energy density

v2/ε for <pT> ~ 0.45 GeV/c

cs ~ 0.35 ±0.05

(cs2 ~ 0.12), soft EOS

F. Karsch, hep-lat/0601013

CIPANP 2006, Puerto Rico

Scaling breaks

See H. Masui’s talk

in this session

Baryons scale together

Mesons scale together

PHENIX preliminary

Kinetic energy of a particle in a relativistic fluid:

= mT – m

- 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

CIPANP 2006, Puerto Rico

PHENIX preliminary

Transverse kinetic energy scaling works

for a large selection of particles

CIPANP 2006, Puerto Rico

STAR preliminary

200 GeV Au+Au

PHENIX preliminary

- 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 !

CIPANP 2006, Puerto Rico

Chiho Nonaka: 3-D Hydro

PHENIX preliminary

R. Fries, SQM2006

- 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

CIPANP 2006, Puerto Rico

KET/n scaling observed across centralities

CIPANP 2006, Puerto Rico

- 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

CIPANP 2006, Puerto Rico