Energy and system-size dependence of two- and four-particle $v_2$ measurements in heavy-ion collisions at RHIC and their implications on flow fluctuations and nonflow

Abstract: We present STAR measurements of azimuthal anisotropy by means of the two- and four-particle cumulants $v_2$ ($v_2{2}$ and $v_2{4}$) for Au+Au and Cu+Cu collisions at center of mass energies $\sqrt{s_{{\mathrm{NN}}}} = 62.4$ and 200 GeV. The difference between $v_2{2}^2$ and $v_2{4}^2$ is related to $v{2}$ fluctuations ($\sigma_{v_2}$) and nonflow $(\delta_{2})$. We present an upper limit to $\sigma_{v_2}/v_{2}$. Following the assumption that eccentricity fluctuations $\sigma_{\epsilon}$ dominate $v_2$ fluctuations $\frac{\sigma_{v_2}}{v_2} \approx \frac{\sigma_{\epsilon}}{\epsilon}$ we deduce the nonflow implied for several models of eccentricity fluctuations that would be required for consistency with $v_2{2}$ and $v_2{4}$. We also present results on the ratio of $v_2$ to eccentricity.