Yuting Bai (for the Collaboration) Anisotropic Flow and Ideal Hydrodynamic Limit International Conference on Strangeness in Quark Matter 2008 Oct , 2008 Beijing, China

Yuting Bai, SQM20082 Outline  Introduction Anisotropic flow The success and uncertainties in ideal hydro calculations  Results How much deviation from ideal hydro  Conclusions

Yuting Bai, SQM20083 Anisotropic Flow  The spatial anisotropy is transformed into a momentum anisotropy by the multiple interactions  Established early, self-quenching, therefore sensitive to the early stage of the collisions  Depending on rescattering, sensitive to the degree of thermalization x z y pxpx pypy y x reaction plane

Yuting Bai, SQM20084 Ideal hydro success and uncertainties  v 2 / was considered to approach the ideal hydro limit in central collisions  Uncertainties: Choice of EoS - affects Hydro limits The initial conditions: Glauber, Color Glass Condensate (CGC) C. Alt et.al; Phys.Rev.C68,034903(2003) Hydro limits from P.Kolb, J.Sollfrank,U.Heinz; Phys.ReV.C62:054909,2000

Yuting Bai, SQM20085 Choices of v 2 and   The number of individual nucleons participating in the collision as well as their position could fluctuate from event to event. The center of the overlap zone can be shifted and the orientation of the principal axes of the interaction zone can be rotated  v 2 {EP}, v 2 {2},  part and {2} sensitive to anisotropy w.r.t the participant plane  PP  v 2 {4},v 2 {ZDCSMD} and  std sensitive to anisotropy w.r.t the reaction plane  RP y x x’ y’ M.Miller and R.Snellings;nucl-ex/ R.Bhalerao and J- Y.Ollitrault; Phys.Lett.B 614(2006)260 S.Voloshin, A.Poskanzer, A.Tang and G.Wang; Phys.Lett.B 659(2008)537  RP  PP

Yuting Bai, SQM20086 Flow increases  Scaled v 2 increases with centrality over large p t range  Peak position of v 2 / shifts to higher p t in more central collision  The system seems more close to thermalization for most central collisions eccentricity from CGC (nucl-th/ ) standard eccentricity from Glauber model STAR Preliminary

Yuting Bai, SQM2008 How much deviation from ideal hydro R.Bhalerao,J-P.Blaizot,N.Borghini and J- Y.Ollitrault;Phys.Lett.B 627:49-54,2005 C.Gombeaud and J-Y.Ollitrault; Phys. Rev. C 77, (2008) H-J.Drescher, A.Dumitru, C.Gombeaud, J- Y.Ollitrault; Phys. Rev. C 76, (2007)  Try to use the data to constrain the hydro limit  Use relativistic Boltzmann calculations to calculate how v 2 approaches hydro as function of cross section and density  Based on these calculations the v 2 / dependence has been parameterized as function of K  Fit data to extract v 2 hydro / and 

Yuting Bai, SQM20088 How much deviation from ideal hydro  The estimates depend on the initial conditions. A softer EoS is required for CGC  Ideal hydro limit is not reached at top RHIC energy. The ratio of v 2 / is considerably away from hydro limit independent of choices of   K decreases with the increasing of particle density. But still finite in the most central collisions STAR Preliminary

Yuting Bai, SQM2008 How much deviation from ideal hydro  With the assumption that parton cross section () is same for all identified particles, a universal trend of approaching hydro limit is established. In central collisions, the ratio of v 2 / is considerably away from hydro limit PHENIX p, K and p: nucl-ex/ , STAR K s 0, : Phys. ReV. C (2008) STAR Preliminary Hiroshi Masui Parallel Session I: 15:40—16:00

Yuting Bai, SQM Constraint on EoS STAR Preliminary

Yuting Bai, SQM Constraint on s Temperature from: A.Adare nucl-ex/ STAR Preliminary

Yuting Bai, SQM Charged particle v 4 /v 2 2  It’s expected that v 4 /v 2 2 decreases with K -1.  Consistent with Boltzmann calculation with K> 0.5  Measured ratios indicate that ideal hydro limit is not reached Hydro, Boltzmann calculations:J-Y. Ollitrault STAR Preliminary

Yuting Bai, SQM Conclusions v 2 /, examined with transport motivated formula, approaches ideal hydro limit for all identified hadrons. In central Au+Au collisions, v 2 / is still considerably away from Hydro limit. The conclusion is independent of initial conditions. Results of charged hadron v 4 /v 2 2 are consistent with above Constraint on EoS obtained. For the first time, /s versus centrality is extracted.

Yuting Bai, SQM Choices of v 2 and   v 2 {4}: measured with the 4-particle cumulant method  v 2 {ZDCSMD}: measured with the first order event plane reconstructed with STAR’s ZDC-SMD  non-flow effects are reduced in both methods Au +Au 200 GeV G. Wang QM2005 STAR Preliminary