Non-flow correlations and elliptic flow fluctuations in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

This article presents results on event-by-event elliptic flow fluctuations in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=$ 200 GeV, where the contribution from non-flow correlations has been subtracted. An analysis method is introduced to measure non-flow correlations, relying on the assumption that non-flow correlations are most prominent at short ranges ($\left|\Delta \eta \right|<2$). Assuming that non-flow correlations are of the order that is observed in $p+p$ collisions for long-range correlations ($\left|\Delta \eta \right|>2$), relative elliptic flow fluctuations of approximately 30–40% are observed. These results are consistent with predictions based on spatial fluctuations of the participating nucleons in the initial nuclear overlap region. It is found that the long-range non-flow correlations in $\mathrm{Au}+\mathrm{Au}$ collisions would have to be more than an order of magnitude stronger compared to the $p+p$ data to lead to the observed azimuthal anisotropy fluctuations with no intrinsic elliptic flow fluctuations.

Figure 1

Second Fourier coefficient of the correlation function $R_n(\Delta \varphi ,{\eta }_1,{\eta }_2)$ as a function of ${\eta }_1$ and ${\eta }_2$ for the 40–45% central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=$ 200 GeV. The ridge along ${\eta }_1={\eta }_2$ represents the region where non-flow contributions are most prominent.

Figure 2

Flow (left) and non-flow (right) components of $v_2^2({\eta }_1,{\eta }_2)$ in Fig. 1 obtained by Eqs. (9) and (10) assuming non-flow correlations at $\left|\Delta \eta \right|>2$ are negligible.

Figure 3

Measured value of the non-flow ratio ($\langle \delta \rangle /\langle v_2^2\rangle$) as a function of the $\Delta \eta$ cut ($\Delta {\eta }_c$) where non-flow correlations are assumed to be zero for $\left|\Delta \eta \right|>\Delta {\eta }_c$ for different centrality bins. The black circles (one for each panel) show values for $\Delta {\eta }_c=2.1$ with the gray band denoting the 90% C.L. systematic errors on those results as described in the text. The gray squares show values for $1.2⩽\Delta {\eta }_c⩽2.7$, which are used in the systematic error estimation. Open squares show values for $\Delta {\eta }_c<1$.

Figure 4

The magnitude of non-flow correlations ($\delta$) scaled by the charged particle multiplicity ($n$) in the pseudorapidity range $\left|\eta \right|<3$ as a function of particle pair pseudorapidity separations ($\Delta \eta$) for $p+p$ data and different Monte Carlo generators with no flow correlations at $\sqrt{s_{\mathit{NN}}}=$ 200 GeV. The results for $p+p$ data (squares) with 90% C.L. systematic errors are obtained from two particle $\Delta \eta ,\Delta \varphi$ correlations [22]. Statistical errors are not shown.

Figure 5

The non-flow ratio ($\langle \delta \rangle /\langle v_2^2\rangle$) in the PHOBOS octagon detector acceptance as a function of number of participating nucleons ($N_{\mathrm{part}}$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=$ 200 GeV. The black squares show the results with the assumption that non-flow correlations are negligible at $\left|\Delta \eta \right|>2$. The shaded band shows the 90% confidence systematic errors. The lines show different assumptions about non-flow at $\left|\Delta \eta \right|>2$. The open circles with 90% C.L. systematic errors, show the upper limit on $\langle \delta \rangle /\langle v_2^2\rangle$ obtained by assuming that the measured dynamic fluctuations in $v_2$ are due to non-flow alone.

Figure 6

Relative elliptic flow fluctuations (${\sigma }_{\mathrm{flow}}/\langle v_2\rangle {}_{\mathrm{flow}}$) as a function of number of participating nucleons ($N_{\mathrm{part}}$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=$ 200 GeV. The black circles show the results with the assumption that non-flow correlations are negligible at $\left|\Delta \eta \right|>2$. The shaded band shows the 90% confidence systematic errors. The thin lines show results for different assumptions on the magnitude of non-flow at $\left|\Delta \eta \right|>2$. The continuous and dashed thick lines show $\sigma ({\epsilon }_{\mathrm{part}})/\langle {\epsilon }_{\mathrm{par}\mathrm{t}}\rangle$ values calculated in Glauber MC [11] and CGC [24] models, respectively.

Figure 7

Dynamic $v_2$ fluctuations (${\sigma }_{\mathrm{dyn}}/\langle v_2\rangle$) as a function of elliptic flow fluctuations (${\sigma }_{\mathrm{flow}}/\langle v_2\rangle {}_{\mathrm{flow}}$) and the non-flow ratio ($\langle \delta \rangle /\langle v_2^2\rangle$) for ${\sigma }_n/\langle v_2\rangle {}_{\mathrm{flow}}=0.6$. The observed values of dynamic $v_2$ fluctuations are roughly given by ${\sigma }_{\mathrm{dyn}}/\langle v_2\rangle \approx$ 40% [11].