Fully corrected assorted $\pi^{0}$-hadron conditional pair distributions for $d$+Au collisions centrality 0-88% and $p$+$p$ collisions. The trigger $\pi^0$s are within 5 < $p_{T,trig}$ < 10 GeV/$c$ and are correlated with hadrons with $p_{T,assoc}$ of 1.5-2 GeV/$c$, 2-3GeV/$c$, 3-4 GeV/$c$, and 4-5 GeV/$c$.

Near- and far-side widths as a function of $p_{T, assoc}$ for charged hadron azimuthal correlations from minimumbias $d$+Au collisions.

Near-side width, far-side width as a function of $p_{T,assoc}$ for a charged pion and neutral pion triggers from the $p_{T,trig}$ range of 5-10 GeV/$c$ in minimum bias $d$+Au collisions.

Near-side width, far-side width as a function of $p_{T,assoc}$ for a charged pion and neutral pion triggers from the $p_{T,trig}$ range of 5-10 GeV/$c$ in minimum bias $d$+Au collisions.

Near- and far-side conditional yields as a function of $p_{T, assoc}$ for charged hadron triggers (2.5−4 GeV/$c$) and associated charged hadrons from $d$+Au collisions.

Near- and far-side conditional yields as a function of $p_{T, assoc}$ for charged hadron triggers (4−6 GeV/$c$) and associated charged hadrons from $d$+Au collisions.

Near- and far-side conditional yields as a function of $p_{T, assoc}$ for charged pion triggers (5−10 GeV/$c$) and associated charged hadrons from minimum-bias $d$+Au collisions.

Near- and far-side conditional yields as a function of $p_{T, assoc}$ for neutral pion triggers (5−10 GeV/$c$) and associated charged hadrons from minimum-bias $d$+Au collisions.

Near- and far-side widths and conditional yields as a function of $N_{coll}$ for charged hadron triggers (2.5−4 GeV/$c$) and associated charged hadrons (1–2.5 GeV/$c$) from $d$+Au collisions.

Near- and far-side widths and conditional yields as a function of centrality for neutral pion triggers (5−10 GeV/$c$) and associated charged hadrons (2–3 GeV/$c$) from $d$+Au collisions.

The extracted $\sqrt{<j^2_T>}$ for minimum-bias $d$+Au collisions from all four dihadron correlations. The trigger $p_T$ ranges are 3 - 5 GeV/$c$, 5 - 10 GeV/$c$ and 5 - 10 GeV/$c$ for $h^{\pm}$ - $h^{\pm}$, $\pi^0$ - $h^{\pm}$ and $\pi^{\pm}$ - $h^{\pm}$ assorted-$p_T$ correlations.

The extracted $\sqrt{<j^2_T>}$ for minimum-bias $d$+Au collisions from all four dihadron correlations. The trigger $p_T$ ranges are 3 - 5 GeV/$c$, 5 - 10 GeV/$c$ and 5 - 10 GeV/$c$ for $h^{\pm}$ - $h^{\pm}$, $\pi^0$ - $h^{\pm}$ and $\pi^{\pm}$ - $h^{\pm}$ assorted-$p_T$ correlations.

The extracted $\sqrt{<j^2_T>}$ for minimum-bias $d$+Au collisions from all four dihadron correlations. The trigger $p_T$ ranges are 3 - 5 GeV/$c$, 5 - 10 GeV/$c$ and 5 - 10 GeV/$c$ for $h^{\pm}$ - $h^{\pm}$, $\pi^0$ - $h^{\pm}$ and $\pi^{\pm}$ - $h^{\pm}$ assorted-$p_T$ correlations.

The extracted $\sqrt{<j^2_T>}$ for minimum-bias $d$+Au collisions from all four dihadron correlations. The trigger $p_T$ ranges are 3 - 5 GeV/$c$, 5 - 10 GeV/$c$ and 5 - 10 GeV/$c$ for $h^{\pm}$ - $h^{\pm}$, $\pi^0$ - $h^{\pm}$ and $\pi^{\pm}$ - $h^{\pm}$ assorted-$p_T$ correlations.

$<sin^2(\phi_{jj})>$ for minimum bias $d$+Au collisions as function of associated particle $p_T$ for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ correlations where the trigger particles have a $p_T$ between 5 - 10 GeV/$c$.

$<sin^2(\phi_{jj})>$ for minimum bias $d$+Au collisions as function of associated particle $p_T$ for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ correlations where the trigger particles have a $p_T$ between 5 - 10 GeV/$c$.

$<sin^2(\phi_{jj})>$ for minimum bias $d$+Au collisions as function of trigger particle $p_T$ for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ correlations.

$<sin^2(\phi_{jj})>$ for minimum bias $d$+Au collisions as function of trigger particle $p_T$ for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ correlations.

Near-side and far-side $p_{out}$ distributions for minimum bias $d$+Au collisions obtained from $\pi^{\pm}$ - $h^{\pm}$ correlation. The trigger is 5 < $p_{T,trig}$ < 10 GeV/$c$, the associated particle is 0.5 < $p_{T,assoc}$ < 5.0 GeV/$c$.

Conditional yield as a function of $x_E$ for near-side and far-side for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ from minimum-bias $d$+Au collisions.

Conditional yield as a function of $x_E$ for near-side and far-side for $\pi^{\pm}$ - $h^{\pm}$ and $\pi^0$ - $h^{\pm}$ from minimum-bias $d$+Au collisions.

Conditional yield as a function of $x_E$ for near-side and far-side correlations for $\pi^{\pm}$ - $h^{\pm}$ correlations from minimum-bias $d$+Au collisions. The trigger pions are 5 < $p_{T,trig}$ < 6 GeV/$c$.

Conditional yield as a function of $x_E$ for near-side and far-side correlation for $\pi^{\pm}$ - $h^{\pm}$ correlation for several different trigger $p_T$s for minimum-bias $d$+Au collisions.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ for $\pi^{\pm}$ - $h^{\pm}$ correlation for minimum-bias $d$+Au collisions.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ for $\pi^{\pm}$ - $h^{\pm}$ correlation for minimum-bias $d$+Au collisions.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ for $\pi^{\pm}$ - $h^{\pm}$ correlation for minimum-bias $d$+Au collisions.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ for $\pi^{\pm}$ - $h^{\pm}$ correlation for minimum-bias $d$+Au collisions.

The comparison of the $\sqrt{<j^2_T>}$ values between $d$+Au and $p$+$p$ for the $\pi^{\pm}$ - $h^{\pm}$ correlations and $\pi^0$ - $h^{\pm}$ correlations. The trigger pion range is 5 - 10 GeV/$c$.

The comparison of the $\sqrt{<j^2_T>}$ values between $d$+Au and $p$+$p$ for the $\pi^{\pm}$ - $h^{\pm}$ correlations and $\pi^0$ - $h^{\pm}$ correlations. The trigger pion range is 5 - 10 GeV/$c$.

Quadrature difference between minimum-bias $d$+Au and $p$+$p$ $<sin^2(\phi_{jj})>$ values.

Quadrature difference between minimum-bias $d$+Au and $p$+$p$ $<sin^2(\phi_{jj})>$ values.

The comparison of the $p_{out}$ distribution at the near-side and far-side between central $d$+Au collisions and $p$+$p$ collisions. Results are obtained for $\pi^{\pm}$ - $h^{\pm}$ correlations with the associated hadron range 0.5 < $p_{T,assoc}$ < 5 GeV/$c$ and trigger pion range of 5 < $p_{T,trig}$ < 10 GeV/$c$.

The comparison of the $x_E$ distribution from $\pi^{\pm}$ - $h^{\pm}$ correlation at the near-side and far-side between minimum bias $d$+Au collisions and $p$+$p$ collisions. The trigger $\pi^{\pm}$ are from 5 - 10 GeV/$c$.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ from $p$+$p$ collisions, triggers are $\pi^{\pm}$ from 5 - 10 GeV/$c$.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ from $p$+$p$ collisions, triggers are $\pi^{\pm}$ from 5 - 10 GeV/$c$.

Far-side conditional yield as a function of $p_{T,trig}$ for different ranges of $x_E$ from $p$+$p$ collisions, triggers are $\pi^{\pm}$ from 5 - 10 GeV/$c$.

The fitted fractional change in $dN/d_{x_E}$ per unit $p_{T,trig}$ of the far-side conditional yield for different ranges of $x_E$.

Centrality dependent near and far $CY(p_T)$ for $\pi^{\pm}$ - $h^{\pm}$ correlations and $\pi^0$ - $h^{\pm}$ correlations.

Centrality dependent near and far $CY(p_T)$ for $\pi^{\pm}$ - $h^{\pm}$ correlations and $\pi^0$ - $h^{\pm}$ correlations.

Centrality dependence to the ratio of near and far $CY(p_T)$ for $d$+Au to $p$+$p$.

Centrality dependence to the ratio of near and far $CY(p_T)$ for $d$+Au to $p$+$p$.

Near- and far-side widths as a function of $p_{T, trig}$ for charged pion triggers and associated charged hadrons (2–4.5 Gev/$c$) from minimum-bias $d$+Au collisions.

Near- and far-side widths as a function of $p_{T, trig}$ for neutral pion triggers and associated charged hadrons (2–4.5 Gev/$c$) from minimum-bias $d$+Au collisions.

$v_3\{\Psi_1\}$ vs. centrality for $\pi^+$, $\pi^-$, and protons using the event plane method in $\sqrt{s_{\textrm{NN}}}=3$ GeV Au+Au collisions at STAR.

$v_3\{\Psi_1\}$ vs. centrality for $K^+$, and $K^-$ using the event plane method in $\sqrt{s_{\textrm{NN}}}=3$ GeV Au+Au collisions at STAR.

$v_3\{\Psi_1\}$ vs. centrality for $K^+$, and $K^-$ using the event plane method in $\sqrt{s_{\textrm{NN}}}=3$ GeV Au+Au collisions at STAR.

$v_3\{\Psi_1\}$ vs. rapidity for protons in three large centrality bins from a symmetric acceptance across midrapidity in $\sqrt{s_{\textrm{NN}}}=3$ GeV Au+Au collisions at STAR. Protons exhibit an increasingly negative slope as the centrality increases.

$v_3\{\Psi_1\}$ vs. rapidity for protons in three large centrality bins from a symmetric acceptance across midrapidity in $\sqrt{s_{\textrm{NN}}}=3$ GeV Au+Au collisions at STAR. Protons exhibit an increasingly negative slope as the centrality increases.

$v_3\{\Psi_1\}$ vs. rapidity for protons in three large centrality bins from only the backward region in $\sqrt{s_{\textrm{NN}}}=3$ GeV Au+Au collisions at STAR. Note that the $p_{\mathrm{T}}$ acceptance extends to a lower limit than in Fig. 6.

$v_3\{\Psi_1\}$ vs. rapidity for protons in three large centrality bins from only the backward region in $\sqrt{s_{\textrm{NN}}}=3$ GeV Au+Au collisions at STAR. Note that the $p_{\mathrm{T}}$ acceptance extends to a lower limit than in Fig. 6.

$v_3\{\Psi_1\}$ vs. $p_{\mathrm{T}}$ for protons in three large centrality bins in $\sqrt{s_{\textrm{NN}}}=3$ GeV Au+Au collisions at STAR. $v_3\{\Psi_1\}$ becomes increasingly negative as $p_{\mathrm{T}}$ and centrality increase.

$v_3\{\Psi_1\}$ vs. $p_{\mathrm{T}}$ for protons in three large centrality bins in $\sqrt{s_{\textrm{NN}}}=3$ GeV Au+Au collisions at STAR. $v_3\{\Psi_1\}$ becomes increasingly negative as $p_{\mathrm{T}}$ and centrality increase.

Centrality dependence of (a) $v_2${2} and (b) $v_2${4}. (a) The red points indicate no pseudorapidity gap whereas the magenta points indicate a pseudorapidity gap of |$\Delta\eta$| > 2.0. (b) The black points indicate $v_2${4} with no pseudorapidity gap, the blue points indicate a two-subevent method with |$\Delta\eta$| > 2.0 but where some short-range pairs are allowed, and the red points indicate a two-subevent method with |$\Delta\eta$| > 2.0 where no short-range pairs are allowed.

Centrality dependence of (a) $v_2${2} and (b) $v_2${4}. (a) The red points indicate no pseudorapidity gap whereas the magenta points indicate a pseudorapidity gap of |$\Delta\eta$| > 2.0. (b) The black points indicate $v_2${4} with no pseudorapidity gap, the blue points indicate a two-subevent method with |$\Delta\eta$| > 2.0 but where some short-range pairs are allowed, and the red points indicate a two-subevent method with |$\Delta\eta$| > 2.0 where no short-range pairs are allowed.

Multi-particle $v_2$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The magenta open diamonds indicate the $v_2${SP }, the blue open squares indicate $v_2${4}, the black open circles indicate $v_2${6}, and the green filled diamonds indicate $v_2${8}.

Multi-particle $v_2$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The magenta open diamonds indicate the $v_2${SP }, the blue open squares indicate $v_2${4}, the black open circles indicate $v_2${6}, and the green filled diamonds indicate $v_2${8}.

Multi-particle $v_2$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The magenta open diamonds indicate the $v_2${SP }, the blue open squares indicate $v_2${4}, the black open circles indicate $v_2${6}, and the green filled diamonds indicate $v_2${8}.

Multi-particle $v_2$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The magenta open diamonds indicate the $v_2${SP }, the blue open squares indicate $v_2${4}, the black open circles indicate $v_2${6}, and the green filled diamonds indicate $v_2${8}.

Cumulant method estimate of $\sigma_{v_{2}}$ / $\langle v_{2} \rangle$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The data are shown as black open squares. The same calculation as done in data is done in ampt, shown as a solid green line. Calculations of $\sigma_{\epsilon_{2}}$ /$ \langle\epsilon_{2}\rangle$ performed in the Monte Carlo Glauber model are shown as blue lines. The solid blue line is the Monte Carlo Glauber calculation done using the same estimate as the data, the dashed blue line is the direct calculation of the moments of the MC Glauber $\epsilon_{2}$ distribution.

Centrality dependence of $v_3${2, |$\Delta\eta$| > 2} in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, shown as magenta diamonds. The systematic uncertainty is indicated as a shaded magenta band. Also shown as black squares are $\sqrt{\langle v^{2}_{3}\rangle}$ as determined from the folding analysis, which is shown in the next section.

Centrality dependence of $v_3${2, |$\Delta\eta$| > 2} in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, shown as magenta diamonds. The systematic uncertainty is indicated as a shaded magenta band. Also shown as black squares are $\sqrt{\langle v^{2}_{3}\rangle}$ as determined from the folding analysis, which is shown in the next section.

Centrality dependence of $c_3${4} for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (a) Calculations using both arms: $c_3${4} (black circles), $c_3${4}$_{ab|ab}$ (blue diamonds), $c_3${4}$_{aa|bb}$ (red squares), and comparison to STAR [36] (black stars). (b) Comparison of $c_3${4} determined using both arms (open symbols) and a single arm (closed symbols). Note that the open black circles are the same in (a) and (b).

Centrality dependence of $c_3${4} for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (a) Calculations using both arms: $c_3${4} (black circles), $c_3${4}$_{ab|ab}$ (blue diamonds), $c_3${4}$_{aa|bb}$ (red squares), and comparison to STAR [36] (black stars). (b) Comparison of $c_3${4} determined using both arms (open symbols) and a single arm (closed symbols). Note that the open black circles are the same in (a) and (b).

Centrality dependence of $c_3${4} for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (a) Calculations using both arms: $c_3${4} (black circles), $c_3${4}$_{ab|ab}$ (blue diamonds), $c_3${4}$_{aa|bb}$ (red squares), and comparison to STAR [36] (black stars). (b) Comparison of $c_3${4} determined using both arms (open symbols) and a single arm (closed symbols). Note that the open black circles are the same in (a) and (b).

Folding results for (a) $v_2$, (b) $\sigma_{v_{2}}$ , and (c) $\sigma_{v_{2}}$ / $\langle v_{2}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. In the case of $\langle v_{2}\rangle$, the statistical uncertainties at the 68.27% confidence level are too small to be seen, and the uncertainties at the 95.45% confidence level are visible but noticeably smaller than the marker size. Shown as blue squares are the same quantities as determined using the cumulant based calculation—these points are slightly offset in the x-coordinate to improve visibility.

Folding results for (a) $v_2$, (b) $\sigma_{v_{2}}$ , and (c) $\sigma_{v_{2}}$ / $\langle v_{2}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. In the case of $\langle v_{2}\rangle$, the statistical uncertainties at the 68.27% confidence level are too small to be seen, and the uncertainties at the 95.45% confidence level are visible but noticeably smaller than the marker size. Shown as blue squares are the same quantities as determined using the cumulant based calculation—these points are slightly offset in the x-coordinate to improve visibility.

Folding results for (a) $v_2$, (b) $\sigma_{v_{2}}$ , and (c) $\sigma_{v_{2}}$ / $\langle v_{2}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. In the case of $\langle v_{2}\rangle$, the statistical uncertainties at the 68.27% confidence level are too small to be seen, and the uncertainties at the 95.45% confidence level are visible but noticeably smaller than the marker size. Shown as blue squares are the same quantities as determined using the cumulant based calculation—these points are slightly offset in the x-coordinate to improve visibility.

Folding results for (a) $\langle v_{3}\rangle$, (b) $\sigma_{v_{3}}$ , and (c) $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. The $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$ values are all ≈ 0.52, the apparent limiting value of this quantity for the Bessel-Gaussian distribution.

Folding results for (a) $\langle v_{3}\rangle$, (b) $\sigma_{v_{3}}$ , and (c) $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. The $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$ values are all ≈ 0.52, the apparent limiting value of this quantity for the Bessel-Gaussian distribution.

Folding results for (a) $\langle v_{3}\rangle$, (b) $\sigma_{v_{3}}$ , and (c) $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. The $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$ values are all ≈ 0.52, the apparent limiting value of this quantity for the Bessel-Gaussian distribution.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV.

$v_2$ for inclusive charged hadrons in Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV compared with 200 GeV.

$v_2$ for inclusive charged hadrons in Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV compared with 200 GeV.

$v_2$ for inclusive charged hadrons in Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV compared with 200 GeV.

Comparison of integrated $v_2$ at $\sqrt{s_{NN}}$ = 62.4 and 200 GeV. Au+Au reaction.

Comparison of integrated $v_2$ at $\sqrt{s_{NN}}$ = 62.4 and 200 GeV. Au+Au reaction.

Comparison of integrated $v_2$ at $\sqrt{s_{NN}}$ = 62.4 and 200 GeV. Cu+Cu reaction.

Comparison of integrated $v_2$ at $\sqrt{s_{NN}}$ = 62.4 and 200 GeV. Cu+Cu reaction.

The comparison of integrated $v_2$ as a function of centrality.

The comparison of the normalized $v_2$/$\epsilon$ vs. centrality.

The comparison of integrated $v_2$ as a function of centrality.

The comparison of the normalized $v_2$/$\epsilon$ vs. centrality.

The comparison of integrated $v_2$ as a function of centrality.

The comparison of the normalized $v_2$/$\epsilon$ vs. centrality.

The comparison of integrated $v_2$ as a function of centrality.

The comparison of the normalized $v_2$/$\epsilon$ vs. centrality.

Comparison of $v_2$ ($p_T$) at 200 GeV for two example systems with different collision size.

Comparison of $v_2$ ($p_T$) at 200 GeV for two example systems with different collision size.

Comparison of $v_2$ ($p_T$) at 200 GeV for two example systems with different collision size.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for the indicated hadrons emitted from central Au+Au collisions at 62.4 GeV.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for the indicated hadrons emitted from central Au+Au collisions at 62.4 GeV.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for the indicated hadrons emitted from central Au+Au collisions at 62.4 GeV.

$v_2$ vs. $p_T$ and $v_2$/($\epsilon * N^{1/3}_{part} * n_q$) vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ in Au+Au at 200 GeV, in Au+Au at 62.4 GeV, and in Cu+Cu at 200 GeV. The values of $v_2$ and $p_T$ in Au+Au at 200 GeV, in Au+Au at 62.4 GeV, and in Cu+Cu at 200 GeV are the same for as figure 14, and the values of $v_2$, $n_q$, and $KE_T$ in Au+Au at 200 GeV, in Au+Au at 62.4 GeV, and in Cu+Cu at 200 GeV are the same for as figure 18.

Transverse momentum spectra for the jet region, obtained as toward-transverse. Events with a leading track with PT>5 GEV at midrapidity are selected. The spectrum is shown in Figure 1 (right panel).

Coalescence parameter B2 as a function of the transverse momentum per nucleon pT/A, in the underlying event (transverse region). Events with a leading track with PT>5 GEV at midrapidity are selected. The B2 is shown in Figure 2 (both panels).

Coalescence parameter B2 as a function of the transverse momentum per nucleon pT/A, in the jet (transverse-toward region). Events with a leading track with PT>5 GEV at midrapidity are selected. The B2 is shown in Figure 2 (both panels).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) from UrQMD model in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 -200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, UrQMD calculation is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Fifth-to-first (KS5/KS1) and sixth-to-second (KS6/KS2) order K-statistic ratios of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0-40$\%$ and 50-60$\%$ centrality.

Net-proton cumulant ratio C6/C2 and corresponding K-statistic ratio (0-40$\%$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of sample size. Uncertainties are only statistical.

Cumulant ratios C4/C2, C5/C1, C6/C2 and C3/C1 of net-proton distributions measured with half rapdity coverage (-0.5 $<$ y $<$ 0) in 0-40$\%$ central Au+Au collisions for collider energies from $\sqrt{s_{NN}}$ = 7.7 - 54.4 GeV.

Cumulant ratios C5/C1 of net-proton distributions measured in 40-50$\%$, 60-70$\%$, and 70-80$\%$ Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. This is supplemental data and was not part of the original paper.

The minimum $\chi^2$ and the parameters $T_{fo}$ and $\beta^{max}_T$ for each of the five centrality selections. The best fit parameters are determined by averaging all parameter pairs within the 1$\sigma$ contour. The errors correspond to the standard deviation of the parameter pairs within the 1$\sigma$ $\chi^2$ contour.

Fit parameters for each particle species using Equations $\frac{dN}{dy}$ = $C \cdot$ ($N_{part}$)$^{\alpha_{part}}$ and $\frac{dN}{dy}$ = $C^{\prime} \cdot$ ($N_{coll}$)$^{\alpha_{coll}}$.

Values of the parameters $n_{pp}$ and $x$ from fitting Equation $R \equiv \frac{dN/dy}{N_{part}}$ = (1-$x$) $\cdot n_{pp} \frac{1}{2}$ + $x \cdot n_{pp} \frac{N_{coll}}{N_{part}}$ = $n_{pp}$ [$\frac{1}{2}$ + $x$($\frac{N_{coll}}{N_{part}}$ - $\frac{1}{2})$]to the observed $dN$/$dy$ per $N_{part}$.

Invariant yields for $\pi^{\pm}$ measured in minimum-bias events at midrapidity and normalized to one rapidity unit.

Invariant yields for $K^{\pm}$ measured in minimum-bias events at midrapidity and normalized to one rapidity unit.

Invariant yields for (anti)$p$ measured in minimum-bias events at midrapidity and normalized to one rapidity unit.

Pion invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

Pion invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

Kaon invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

Kaon invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

(Anti)proton invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

(Anti)proton invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

(Anti)proton invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

(Anti)proton invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

(Anti)proton invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

(Anti)proton invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

(Anti)proton invariant yields in each event centrality and $p_T$ bin measured at midrapidity, normalized to one rapidity unit.

Minimum-bias invariant yields for $\pi^{\pm}$ in equal $p_T$ bins.

Minimum-bias invariant yields for $K^{\pm}$ in equal $p_T$ bins.

Minimum-bias invariant yields for (anti)$p$ in equal $p_T$ bins.

Pion invariant yields in each event centrality normalized to one rapidity unit at midrapidity.

Pion invariant yields in each event centrality normalized to one rapidity unit at midrapidity.

Kaon invariant yields in each event centrality normalized to one rapidity unit at midrapidity.

(Anti)proton invariant yields in each event centrality normalized to one rapidity unit at midrapidity.

(Anti)proton invariant yields in each event centrality normalized to one rapidity unit at midrapidity.

The integrated mean $p_T$ for pions, kaons, and (anti)protons produced in the five different classes of event centrality.

The expansion parameters $T_{fo}$ and $\beta^{max}_T$ as a function of the number of participants.

<p>Charged hadron spectra for centrality selected d+Au collisions.</p>

<p>Charged hadron spectra for centrality selected d+Au collisions.</p>

<p>Charged hadron spectra for centrality selected N+Au collisions. All centralities.</p>

<p>Charged hadron spectra for centrality selected N+Au collisions. Centrality A (Central).</p>

<p>Charged hadron spectra for centrality selected N+Au collisions. Centrality B.</p>

<p>Charged hadron spectra for centrality selected N+Au collisions. Centrality C.</p>

<p>Charged hadron spectra for centrality selected N+Au collisions. Centrality D (Peripheral).</p>

<p>$R_{dAu}$ as a function of $p_T$.</p>

<p>$R_{dAu}$ as a function of $p_T$.</p>

<p>$R_{dAu}$ as a function of $p_T$.</p>

<p>$R_{dAu}$ as a function of $p_T$.</p>

<p>$R_{NAu}$ as a function of $p_T$. Centrality A (Peripheral).</p>

<p>$R_{NAu}$ as a function of $p_T$. Centrality B.</p>

<p>$R_{dAu}$ as a function of $p_T$. Centrality C.</p>

<p>$R_{dAu}$ as a function of $p_T$. Centrality D (Central).</p>

<p>$R_{dAu}$ values averaged in three momentum ranges as functions of $\nu−1$. Horizontal bars show the uncertainty in the value of $\nu$ for each centrality class.</p>

<p>$R_{NAu}$ values averaged in three momentum ranges as functions of $\nu−1$. Horizontal bars show the uncertainty in the value of $\nu$ for each centrality class.</p>

<p>Charged hadron spectra for centrality selected d+Au collisions.</p>

The second-order Fourier coefficients $v_2 (p_T)$ for charge-combined identified hadrons $\pi^{\pm}$, $K^{\pm}$, $ p$, and $\bar{p}$ measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for the centrality classes marked in each panel.

The second-order Fourier coefficients $v_2 (p_T)$ for charge-combined identified hadrons $\pi^{\pm}$, $K^{\pm}$, $ p$, and $\bar{p}$ measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for the centrality classes marked in each panel.

The second-order Fourier coefficients $v_2 (p_T)$ for charge-combined identified hadrons $\pi^{\pm}$, $K^{\pm}$, $ p$, and $\bar{p}$ measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for the centrality classes marked in each panel.

The second-order Fourier coefficients $v_2 (p_T)$ for charge-combined identified hadrons $\pi^{\pm}$, $K^{\pm}$, $ p$, and $\bar{p}$ measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for the centrality classes marked in each panel.

The second-order Fourier coefficients $v_2 (p_T)$ for charge-combined identified hadrons $\pi^{\pm}$, $K^{\pm}$, $ p$, and $\bar{p}$ measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for the centrality classes marked in each panel.

The third-order Fourier coefficients $v_3(p_T)$ for charge-combined identified hadrons $\pi^{\pm}$, $K^{\pm}$, $p$, and $\bar{p}$ measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for 0%-30% centrality.

The third-order Fourier coefficients $v_3(p_T)$ for charge-combined identified hadrons $\pi^{\pm}$, $K^{\pm}$, $p$, and $\bar{p}$ measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for 0%-30% centrality.

The third-order Fourier coefficients $v_3(p_T)$ for charge-combined identified hadrons $\pi^{\pm}$, $K^{\pm}$, $p$, and $\bar{p}$ measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for 0%-30% centrality.

The first-order Fourier coefficients $v_1(p_T)$ for charge-combined $\pi^{\pm}$, $K^{\pm}$, $ p$, and $\bar{p}$ identified hadrons measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for 10%-50% centrality.

The first-order Fourier coefficients $v_1(p_T)$ for charge-combined $\pi^{\pm}$, $K^{\pm}$, $ p$, and $\bar{p}$ identified hadrons measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV for 10%-50% centrality.

Scaled second-order Fourier coefficients $v_2(p_T)/\epsilon_2$ for charged hadrons measured at midrapidity in Cu + Cu collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/\epsilon_2$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/\epsilon_2$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/\epsilon_2$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/\epsilon_2$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/\epsilon_2$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/\epsilon_2$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/\epsilon_2$ for charged hadrons measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/(\epsilon_2 N^{1/3}_{part})$ for charged hadrons measured at midrapidity in Cu + Cu collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/(\epsilon_2 N^{1/3}_{part})$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/(\epsilon_2 N^{1/3}_{part})$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/(\epsilon_2 N^{1/3}_{part})$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/(\epsilon_2 N^{1/3}_{part})$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/(\epsilon_2 N^{1/3}_{part})$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/(\epsilon_2 N^{1/3}_{part})$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled second-order Fourier coefficients $v_2(p_T)/(\epsilon_2 N^{1/3}_{part})$ for charged hadrons measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled third-order Fourier coefficients $v_3(p_T)/\epsilon_3$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled third-order Fourier coefficients $v_3(p_T)/\epsilon_3$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled third-order Fourier coefficients $v_3(p_T)/\epsilon_3$ for charged hadrons measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled third-order Fourier coefficients $\frac{v_3}{($_3 N_{part}^{1/3})}$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled third-order Fourier coefficients $\frac{v_3}{(e_3 N_{part}^{1/3})}$ for charged hadrons measured at midrapidity in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

Scaled third-order Fourier coefficients $\frac{v_3}{(e_3 N_{part}^{1/3})}$ for charged hadrons measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV.

The second-order Fourier coefficients $v_2$($p_T$ ) for charged hadrons measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV in comparison with hydrodynamics calculations for the centrality classes marked in each panel.

The third-order Fourier coefficients $v_3(p_T)$ for charged hadrons measured at midrapidity in Cu + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV in comparison with hydrodynamics calculations for the centrality classes marked in each panel.