Scaling Properties of Azimuthal Anisotropy in $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ Collisions at $\sqrt{s_{\mathrm{NN}}}=200\mathrm{GeV}$

Differential measurements of elliptic flow ($v_2$) for $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200\mathrm{GeV}$ are used to test and validate predictions from perfect fluid hydrodynamics for scaling of $v_2$ with eccentricity, system size, and transverse kinetic energy (${\mathrm{KE}}_T$). For ${\mathrm{KE}}_T\equiv m_T-m$ up to $\sim 1\mathrm{GeV}$ the scaling is compatible with hydrodynamic expansion of a thermalized fluid. For large values of ${\mathrm{KE}}_T$ mesons and baryons scale separately. Quark number scaling reveals a universal scaling of $v_2$ for both mesons and baryons over the full ${\mathrm{KE}}_T$ range for $\mathrm{Au}+\mathrm{Au}$. For $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ the scaling is more pronounced in terms of ${\mathrm{KE}}_T$, rather than transverse momentum.

Figure 1

$v_2$ vs $p_T$ for charged hadrons obtained in (a) $\mathrm{Au}+\mathrm{Au}$ and (b) $\mathrm{Cu}+\mathrm{Cu}$ collisions for the centralities indicated. (c) $v_2(\mathrm{\text{centrality}},p_T)$ divided by $k=3.1$ (see text) times the $p_T$-integrated value $v_2(\mathrm{\text{centrality}})$ for $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$.

Figure 2

(a) $v_2$ vs $p_T$ and (b) $v_2$ vs ${\mathrm{KE}}_T$ for identified particle species obtained in minimum-bias $\mathrm{Au}+\mathrm{Au}$ collisions. The STAR data are from Refs. [24, 43].

Figure 3

(a) $v_2/n_q$ vs $p_T/n_q$ and (b) $v_2/n_q$ vs ${\mathrm{KE}}_T/n_q$ for identified particle species obtained in minimum-bias $\mathrm{Au}+\mathrm{Au}$ collisions. The STAR data are from Refs. [24, 43].