New PHENIX 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 $p+bar{p}$) obtained relative to the event planes $Psi_n$ in Au$+$Au collisions at $sqrt{s_{_{NN}}}$ = 200 GeV are presented as functions 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 $v_n/(n_q)^{n/2}$ 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 particle spectra and $v_n(p_T)$ coefficients identifies spatial eccentricities $s_n$ at freeze-out, which are much smaller than the initial-state geometric values.
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