System Size and Energy Dependence of Elliptic Flow

The elliptic flow v2 is presented for the Cu+Cu collisions at √ sNN = 62.4 and 200 GeV, as a function of pseudorapidity. Comparison to results for the Au+Au collisions at the same energies shows a reduction of about 20% in the flow observed for a centrality selection of 0-40%. The centrality dependent flow, expressed as a function of the number of participants Npart, is compared for the Cu+Cu and Au+Au systems using two definitions of eccentricity, the standard definition εstandard and a participant eccentricity εpart. The v2/〈εpart〉 as a function of Npart, for the Au+Au and Cu+Cu collisions are consistent within errors, while v2/〈εstandard〉 gives unrealistically large values for Cu+Cu, especially for central collision. INTRODUCTION The azimuthal correlations of produced particles have proven to be a sensitive measure of the initial conditions and subsequent dynamics in relativistic heavy ion collisions. The elliptic flow v2, as inferred from the angular distribution of particles with respect to the reaction plane, provides important constraints on hydrodynamical descriptions about the evolution of the collision [1]. The large pseudorapidity coverage (|η| ≤ 5.4) and the near symmetric azimuthal acceptance for charged hadrons of the PHOBOS detector at RHIC make it excellent for the investigation of the systematics of the flow measurements, as a function of energy, system size, centrality and pseudorapidity. This contribution will concentrate on v2 measurements for the Cu+Cu collisions at √ sNN = 1 Collaboration: B.Alver4, B.B.Back1, M.D.Baker2, M.Ballintijn4, D.S.Barton2, R.R.Betts6, R.Bindel7, W.Busza4, Z.Chai2, V.Chetluru6, E.García6, T.Gburek3, K.Gulbrandsen4, J.Hamblen8,I.Harnarine6, C.Henderson4, D.J.Hofman6, R.S.Hollis6, R.Hołyński3, B.Holzman2, A.Iordanova6, J.L.Kane4, P.Kulinich4,vC.M.Kuo5, W.Li4, W.T.Lin5, C.Loizides4, S.Manly8, A.C.Mignerey7, R.Nouicer2, A.Olszewski3, R.Pak2, C.Reed4, E.Richardson7, C.Roland4, G.Roland4, J.Sagerer6, I.Sedykh2, C.E.Smith6, M.A.Stankiewicz2,P.Steinberg2, G.S.F.Stephans4, A.Sukhanov2, A.Szostak2, M.B.Tonjes7, A.Trzupek3, G.J.van Nieuwenhuizen4, S.S.Vaurynovich4, R.Verdier4, G.I.Veres4, P.Walters8, E.Wenger4, D.Willhelm7, F.L.H.Wolfs8, B.Wosiek3, K.Woźniak3, S.Wyngaardt2, B.Wysłouch4. 1 Argonne National Laboratory, Argonne, IL 60439-4843, USA. 2 Brookhaven National Laboratory, Upton, NY 11973-5000, USA. 3 Institute of Nuclear Physics PAN, Kraków, Poland. 4 Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA. 5 National Central University, Chung-Li, Taiwan. 6 University of Illinois at Chicago, IL 60607-7059, USA. 7 University of Maryland, MD 20742, USA. 8 University of Rochester, Rochester, NY 14627, USA. -5 0 5 10 15 20 25 30 35 40 0 0.01 0.02 0.03 0.04 0.05 0.06 -4 -2 0 2 4 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 -4 -2 0 2 4 -4 -2 0 2 4 -4 -2 0 2 4 2 v η η η η 19.6 GeV 62.4 GeV 130 GeV 200 GeV PHOBOS Au-Au Cu-Cu Cu-Cu Preliminary Preliminary FIGURE 1. Measured v2(η) from Au+Au and Cu+Cu collisions at RHIC energies and for the centrality range of 0-40%. Only the 1σ statistical error bars are shown for clarity. The full systematic errors can be found in Ref. [3] for the Au+Au data and Ref. [5] for the Cu+Cu data. 62.4 and 200 GeV and a comparison to previously reported Au+Au results. Details of the PHOBOS detector and the experimental technique used to extract the flow can be found in references [2, 3, 4]. RESULTS AND CONCLUSIONS The pseudorapidity distributions of the elliptic flow, v2(η), for the Au+Au and Cu+Cu collisions over broad range of center-of-mass energies and for a centrality of 0-40% are shown in Fig. 1. The triangular shape first observed for Au+Au collisions [3] is also apparent in the Cu+Cu data [5]. The measurements of v2 for Cu+Cu collisions is only about 20% lower than that for Au+Au results, even though the Cu+Cu system size is about a third of that of Au+Au. The measured pseudorapidity density of charged hadrons, dNch dη , for Cu+Cu and Au+Au collisions at √ sNN = 200 GeV, is essentially the same at a given Npart [6], but the elliptic flow is different due to the difference in system size. While 〈Npart〉 of 100 corresponds to a 3-6% centrality selection for the Cu+Cu system, 〈Npart〉 of 99 corresponds to only 35-40% central for Au+Au. This implies different initial geometrical overlaps for the two systems with the same energy density (as reflected in the near identical dNch dη ). The measured v2 for Au+Au and Cu+Cu collisions at the same energy, 200 GeV, expressed as a function of Npart is shown in Fig. 2. This discrepancy in elliptic flow for the two systems can be accounted for if v2 is normalized by the eccentricity of the system. Two definitions of eccentricity have been used, based on a simple Glauber model [5, 6]. The standard eccentricity, εstandard, is defined in the frame of the original impact parameter; a participant eccentricity, εpart, is obtained from the geometry of the participants that define Npart, and is influenced by fluctuations in the participant positions. This is more important for the much smaller Cu+Cu system than for Au+Au, as seen in Fig. 3(a), where the mean eccentricities derived from the two approaches are compared. The v2 normalized by the two eccentricities is shown 0 50 100 150 200 250 300 350 0 0.02 0.04 0.06 0.08 0.1