Inclusive charged hadron elliptic flow in Au $+$ Au collisions at $\sqrt{s_{NN}}=7.7$–39 GeV

A systematic study is presented for centrality, transverse momentum ($p_T$), and pseudorapidity ($\eta$) dependence of the inclusive charged hadron elliptic flow ($v_2$) at midrapidity ($\left|\eta \right|<1.0$) in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, and 39 GeV. The results obtained with different methods, including correlations with the event plane reconstructed in a region separated by a large pseudorapidity gap and four-particle cumulants ($v_2\left\{4\right\}$), are presented to investigate nonflow correlations and $v_2$ fluctuations. We observe that the difference between $v_2\left\{2\right\}$ and $v_2\left\{4\right\}$ is smaller at the lower collision energies. Values of $v_2$, scaled by the initial coordinate space eccentricity, $v_2/\varepsilon$, as a function of $p_T$ are larger in more central collisions, suggesting stronger collective flow develops in more central collisions, similar to the results at higher collision energies. These results are compared to measurements at higher energies at the Relativistic Heavy Ion Collider ($\sqrt{s_{NN}}=62.4$ and 200 GeV) and at the Large Hadron Collider ($\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV). The $v_2\left(p_T\right)$ values for fixed $p_T$ rise with increasing collision energy within the $p_T$ range studied ($<$$2\mathrm{GeV}/c$). A comparison to viscous hydrodynamic simulations is made to potentially help understand the energy dependence of $v_2\left(p_T\right)$. We also compare the $v_2$ results to UrQMD and AMPT transport model calculations, and physics implications on the dominance of partonic versus hadronic phases in the system created at beam energy scan energies are discussed.

Figure 1

Distribution of uncorrected multiplicity $N_{\mathrm{ch}}^{\mathrm{raw}}$ measured within $\left|\eta \right|<0.5$ in the TPC from $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$ to 39 GeV in Au $+$ Au collisions shown as black points. The red curves show the multiplicity distributions at $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$ to 39 GeV from MC Glauber simulations. See text for more details about simulations.

Figure 2

The event-plane resolutions for Au $+$ Au collisions at $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$, 11.5, 19.6, 27, and 39 GeV as a function of collision centrality. Panel (a) shows the resolution of the second harmonic event plane from the TPC ($\left|\eta \right|<1$). Panel (b) shows the resolution for second harmonic event plane from the FTPCs ($2.5<\left|\eta \right|<4.0$) for 39 GeV and second harmonic event-plane resolution correction using the first-order event plane from the BBCs ($3.8<\left|\eta \right|<5.2$) for 7.7, 11.5, 19.6, and 27 GeV.

Figure 3

The comparison of $v_2$ as a function of $p_T$ between GF-cumulant (open symbols) and $Q$-cumulant (solid symbols) methods in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{\mathit{s}}_{\mathit{NN}}}=39$ GeV. $v_2\left\{4\right\}$ fails in most central ($0\%–5\%$) collisions owing to the small values of $v_2$ and large $v_2$ fluctuations.

Figure 4

The $p_T$ ($>$$0.2$ GeV/$c$) and $\eta$ ($\left|\eta \right|<1$) integrated $v_2$ as a function of collision centrality for Au $+$ Au collisions at $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$ GeV (a1), 11.5 GeV (b1), 19.6 GeV (c1), 27 GeV (d1), and 39 GeV (e1). The results in the top panels are presented for several methods of obtaining $v_2$. The bottom panels show the ratio of $v_2$ obtained using the various techniques, with respect to $v_2\left\{2\right\}$. The error bars shown are statistical.

Figure 5

The $v_2$ as a function of $p_T$ for $20\%–30\%$ central Au $+$ Au collisions at midrapidity for $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$ GeV (a1), 11.5 GeV (b1), 19.6 GeV (c1), 27 GeV (d1), and 39 GeV (e1). The top panels show $v_2$ vs $p_T$ using various methods as labeled in the figure and discussed in the text. The bottom panels show the ratio of $v_2$ measured using the various methods with respect to $v_2\left\{2\right\}$.

Figure 6

The $v_2$ over $\varepsilon$ (Glauber) as a function of $p_T$ for various collision centralities ($10\%–20\%$, $30\%–40\%$ and $50\%–60\%$) in $\mathrm{Au}+\mathrm{Au}$ collisions at midrapidity. Panels (a), (b), (c), (d), and (e) show the results for $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$, 11.5, 19.6, 27, and 39 GeV, respectively. The data are from $v_2\left\{\mathrm{EtaSubs}\right\}$. The error bars and shaded boxes represent the statistical and systematic uncertainties, respectively, as described in Sec. 4c.

Figure 7

The $v_2$ over $\varepsilon$ (CGC) as a function of $p_T$ for various collision centralities ($10\%–20\%$, $30\%–40\%$, and $50\%–60\%$) in $\mathrm{Au}+\mathrm{Au}$ collisions at midrapidity. Panels (a), (b), (c), (d), and (e) show the results for $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$, 11.5, 19.6, 27, and 39 GeV, respectively. The data are from $v_2\left\{\mathrm{EtaSubs}\right\}$. The error bars and shaded boxes represent the statistical and systematic uncertainties respectively, as described in Sec. 4c.

Figure 8

Panel (a) shows the $v_2\left\{\mathrm{EP}\right\}$ vs $\eta$ for $10\%–40\%$ centrality in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV. Panel (c) shows the ratio of $v_2$ vs $\eta$ for all $\sqrt{{\mathit{s}}_{\mathit{NN}}}$ with respect to the fit curve. Panel (b) shows the $v_2\left\{\mathrm{EP}\right\}$ vs $\eta /y_{\mathrm{beam}}$. Panel (d) shows the ratio of $v_2$ vs $\eta /y_{\mathrm{beam}}$ for all $\sqrt{{\mathit{s}}_{\mathit{NN}}}$ with respect to the fit curve. The data for $\sqrt{{\mathit{s}}_{\mathit{NN}}}=62.4$ and 200 GeV are from Refs. [12, 61, 62]. The dashed red curves show the empirical fit to the results from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$ GeV. The bands show the systematic uncertainties as described in Sec. 4c.

Figure 9

The top panels show $v_2\left\{4\right\}$ vs $p_T$ at midrapidity for various collision energies ($\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$ GeV to 2.76 TeV). The results for $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$ to 200 GeV are for Au $+$ Au collisions and those for 2.76 TeV are for $\mathrm{Pb}+\mathrm{Pb}$ collisions. The dashed red curves show the empirical fits to the results from Au $+$ Au collisions at $\sqrt{{\mathit{s}}_{\mathit{NN}}}=200$ GeV. The bottom panels show the ratio of $v_2\left\{4\right\}$ vs $p_T$ for all $\sqrt{{\mathit{s}}_{\mathit{NN}}}$ with respect to the fit curve. The results are shown for three collision centrality classes: $10\%–20\%$ (a1), $20\%–30\%$ (b1), and $30\%–40\%$ (c1). Error bars are shown only for the statistical uncertainties.

Figure 10

The experimental data (symbols) are the same as in Fig. 9 (b2). The lines represent the viscous hydrodynamic calculations from Ref. [5] based on (a) MC-Glauber initial conditions and $\eta /s=0.08$ and (b) MC-KLN initial conditions and $\eta /s=0.20$.

Figure 11

The top panels show $v_2\left\{\mathrm{EtaSubs}\right\}$ vs $p_T$ at midrapidity for various collision energies ($\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$ GeV to 39 GeV). The bottom panels show the ratio of $v_2\left\{\mathrm{EtaSubs}\right\}$ vs $p_T$ for all $\sqrt{{\mathit{s}}_{\mathit{NN}}}$ with respect to the 39-GeV data. The results are shown for three collision centrality classes: $10\%–20\%$ (a1), $20\%–30\%$ (b1), and $30\%–40\%$ (c1). Error bars are shown only for the statistical uncertainties.

Figure 12

The $v_2\left\{4\right\}$ as a function of $p_T$ for $20\%–30\%$ Au $+$ Au collisions at $\sqrt{{\mathit{s}}_{\mathit{NN}}}=7.7$, 11.5, 39, and 200 GeV compared to corresponding results from UrQMD, AMPT default version, and AMPT with string melting version (3 and 10 mb). The shaded boxes show the systematic uncertainties for the experimental data of 7.7, 11.5, and 39 GeV. The bottom panels show the ratio of data to the fit results of the models.