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, $N_{\rm part}$. We observe that $v_2$ divided by eccentricity ($\varepsilon$) monotonically increases with $N_{\rm part}$ and scales as ${N_{\rm part}^{1/3}}$. The Cu$+$Cu data at 62.4 GeV falls below the other scaled $v_{2}$ data. For identified hadrons, $v_2$ divided by the number of constituent quarks $n_q$ is independent of hadron species as a function of transverse kinetic energy $KE_T=m_T-m$ between $0.1