Systematic Study of Azimuthal Anisotropy in Cu$+$Cu and Au$+$Au Collisions at $\sqrt{s_{{}_{NN}}}=62.4$ and 200 GeV

We have studied the dependence of azimuthal anisotropy $v_2$ for inclusive and identified charged hadrons in Au$+$Au and Cu$+$Cu collisions on collision energy, species, and centrality. The values of $v_2$ as a function of transverse momentum $p_T$ and centrality in Au$+$Au collisions at $\sqrt{s_{{}_{NN}}}$=200 GeV and 62.4 GeV are the same within uncertainties. However, in Cu$+$Cu collisions we observe a decrease in $v_2$ values as the collision energy is reduced from 200 to 62.4 GeV. The decrease is larger in the more peripheral collisions. By examining both Au$+$Au and Cu$+$Cu collisions we find that $v_2$ depends both on eccentricity and the number of participants, $N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}$. We observe that $v_2$ divided by eccentricity ($\epsilon$) monotonically increases with $N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}$ and scales as ${N_{\rm part}^{1/3}}$\mathrm{.}TheCu$+$Cudataat62.4GeVfallsbelowtheotherscaled$v_{2}$data\mathrm{.}Foridentifiedhadrons,$v_2$ divided by the number of constituent quarks $n_q$ is independent of hadron species as a function of transverse kinetic energy $K{E}_T=m_T-m$ between $0.1<K{E}_T\mathrm{/}{n}_q<1$ GeV. Combining all of the above scaling and normalizations, we observe a near-universal scaling, with the exception of the Cu$+$Cu data at 62.4 GeV, of $v_2\mathrm{/}(n_q\cdot \epsilon \cdot N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}^{1\mathrm{/}3})$ vs $K{E}_T\mathrm{/}{n}_q$ for all measured particles.