"Appendix 1.1" of "Measurement of the higher-order anisotropic flow coefficients for identified hadrons in Au$+$Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV"

Measurements of the anisotropic flow coefficients $v_2\{\Psi_2\}$, $v_3\{\Psi_3\}$, $v_4\{\Psi_4\}$, and $v_4\{\Psi_2\}$ for identified particles ($\pi^{\pm}$, $K^{\pm}$, and $p+\bar{p}$) at midrapidity, obtained relative to the event planes $\Psi_m$ at forward rapidities in Au$+$Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV, are presented as a function of collision centrality and particle transverse momenta $p_T$. The $v_n$ coefficients show characteristic patterns consistent with hydrodynamical expansion of the matter produced in the collisions. For each harmonic $n$, a modified valence quark number $N_q$ scaling (plotting $v_n\{\Psi_m\}/(N_q)^{n/2}$ versus ${\rm KE}_T/N_q$) is observed to yield a single curve for all the measured particle species for a broad range of transverse kinetic energies ${\rm KE}_T$. A simultaneous blast-wave model fit to the observed $v_n\{\Psi_m\}(p_T)$ coefficients and published particle spectra identifies radial flow anisotropies $\rho_n\{\Psi_m\}$ and spatial eccentricities $s_n\{\Psi_m\}$ at freeze-out. These are generally smaller than the initial-state participant-plane (PP) geometric eccentricities $\varepsilon_n\{\Psi_m^{\rm PP}\}$, as also observed in the final eccentricity from quantum interferometry measurements with respect to the event plane.