# Presentation: 537193

## System size and beam energy dependence of azimuthal anisotropy from PHENIX

**Michael Issah**
**Vanderbilt University**
**for the PHENIX Collaboration**
**QM2008, Jaipur, India**

## Origin of azimuthal anisotropy

- Interactions among the produced particles lead to pressure gradients which generate an azimuthal anisotropy in particle emission or elliptic flow, measured by v2, from which can be obtained valuable information about the early dynamics after the collision

- Spatial anisotropy

- Momentum anisotropy

- QM 2008, Jaipur, India

## Azimuthal anisotropy at different beam energies in Au+Au collisions

-  Comparison between v2 for different pT and centralities show that the measured v2 is very similar at different beam energies
-  Suggests that v2 does not change much with beam energy over the range √s=62.4-200 GeV

**0-10%**

**10-20%**

**20-30%**

**30-40%**

- QM 2008, Jaipur, India

## Centrality and pT dependence of elliptic flow at different beam energies 

-  Detailed differential centrality and pT dependence of v2 show similar magnitudes at √s = 62.4, 130 and 200 GeV
-  Increase in measured v2 between SPS energies and RHIC energies

**PRL 94, 232302 (2005)**

- QM 2008, Jaipur, India

## Beam energy dependence of elliptic flow 

-  v2 saturates in the energy range √s=62.4-200 GeV suggesting a softening of the equation of state of matter at RHIC
-  Extracted value for <cs> ≈ 0.35 ± 0.05 or <cs2> ≈ 0.12 (PRL 98, 162301)
-  This value lies between the ideal gas limit (cs2=1/3) and mixed phase value (cs2=0)

**PRL 94, 232302 (2005)**

**F. Karsch, hep-lat/0601013**

- QM 2008, Jaipur, India

## Beam energy comparison in Cu+Cu

-  Measured v2 in Cu+Cu at √s = 62.4 GeV is observed to be of comparable magnitude or somewhat lower than v2 √s = 200 GeV.
-  Systematic errors are big.
-  The smaller size of the system and smaller energy densities created in Cu+Cu may be factors in explaining the difference observed in Cu+Cu compared Au+Au system

**0-10%**

**10-20%**

**20-30%**

**30-40%**

- QM 2008, Jaipur, India

##  Test of hydrodynamic behavior and partonic degrees of freedom in Au+Au collisions at √s = 200 GeV

**PRL. 98, 162301 (2007****)**

-  Hydrodynamic behavior tested by transverse kinetic energy scaling for low transverse kinetic energy KET =  mT – m
-  Baryon and mesons scale separately after KET  ≥ 1 GeV
-  Partonic recombination manifest by scaling  by the number of constituent quarks nq (NCQ scaling)
-  NCQ scaling is observed to break at around KET/nq ~1 GeV – see S. Huang’s talk later in the sesssion

** **Test of hydrodynamic behavior and partonic degrees of freedom in Au+Au collisions at √s = 200 GeV

- QM 2008, Jaipur, India

## Au + Au at √s = 62.4 GeV

-  Similar picture in Au+Au at 200 GeV and 62.4 GeV
-  Partonic degrees of freedom are manifest in Au+Au collisions at √s=62.4 GeV

- Au + Au at √s = 62.4 GeV

- QM 2008, Jaipur, India

## NCQ scaling across systems and beam energies

**Au+Au 200 GeV**

**Cu+Cu 200 GeV**

**Au+Au 62.4 GeV**

**PRL. 98, 162301 (2007)**

-  Number of constituent quark scaling holds in Au+Au and Cu+Cu colliding systems at 200 GeV at low KET
-  Suggests that coalescence of particles with the quantum numbers of quarks occurs over the energy range 62.4 – 200 GeV for colliding systems of different sizes

**Centrality 10-40%**

**min bias**

- QM 2008, Jaipur, India

## KET + Number of constituent Quarks (NCQ) scaling

- KET + Number of constituent Quarks (NCQ) scaling

-  Scaling seems to hold well for different centralities up to 60% centrality
-  The goodness of the scaling can be tested by fitting the scaled curves with a polynomial and taking ratio of data/fit

- QM 2008, Jaipur, India

## NCQ scaling and fit to data

-  Ratio of measured v2 to a fit to the data confirms that there is good NCQ scaling in the region where such scaling is expected to hold
-  Scaling fails at low KET/nq (<0.2). Could be due to feed down from resonances
-  More in-depth study of systematic errors needed at low KET as well as comparison to hydrodynamic models

- QM 2008, Jaipur, India

## Non-flow contributions in Au+Au at √s=200 GeV

-  Reaction plane v2 less affected by non-flow than cumulant v2 because of large rapidity gap between PHENIX central arms and BBCs
-  Non-flow mainly due to jet correlations
-  Differences between reaction plane and cumulant v2 measurements show that jet correlations become influential as from pT ~3.5 GeV/c at all centralities

- Non-flow contributions in Au+Au at √s=200 GeV

- PHENIX
- Preliminary

- QM 2008, Jaipur, India

## v4 of unidentified charged hadrons

- v4 of unidentified hadrons scale with integral flow between centrality 10-40%
- v4/(ε’)2 is well described by (v2/ε’)2 up to pT ≈ 2 GeV/c
- Ratio v4/v22 probes degree of thermalization
- Results for different particle species reported in S. Huang’s talk later in this session

- v4 of unidentified charged hadrons

- A.Taranenko
- Poster 212

- ε’ : <v2>

- QM 2008, Jaipur, India

## Summary

- Differential azimuthal anisotropy measurements in Au+Au and Cu+Cu at different beam energies and centralities indicate saturation of v2 with beam energy at RHIC
- Transverse kinetic energy (KET) scaling, as well as number of constituent quark scaling, is observed in both systems at different beam energies and for KET/nq  < 1 GeV and for centrality up to 60%
- More in depth study needed to look into the goodness of the KET/nq scaling at low KET
- Comparison between reaction plane and cumulant v2 shows that non-flow correlations due to jet correlations exist for different centralities as from pT ~3.0 – 4.0 GeV/c. May explain the break of the NCQ scaling at KET > 1 GeV
- Detailed study of different flow harmonics carried out in Run7. It is observed that v4 scales with eccentricity and with v22

- QM 2008, Jaipur, India

##    Thanks to: M. Shimomoura, H. Masui and A. Taranenko

- Acknowledgements

- QM 2008, Jaipur, India

## BACK UP

- QM 2008, Jaipur, India

## Eccentricity scaling across colliding systems

- k ~ 3.1 (from data )

-  Eccentricity scaling observed in hydrodynamic model over a broad range of centralities
-  v2 is observed to scale with eccentricity and across system size

**Hydrodynamic model simulations (Bhalerao, Blaizot, Borghini, Ollitrault , nucl-th/0508009****)**

- QM 2008, Jaipur, India

## Estimate of the speed of sound (I)

- Estimate of the speed of sound (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**

- QM 2008, Jaipur, India

## Eccentricity scaling from PHOBOS

- QM 2008, Jaipur, India