The azimuthal anisotropic flow of identified and unidentified charged particles has been systematically studied in Cu+Au collisions at $\sqrt{s_{_{NN}}}$ = 200 GeV for harmonics $n=$ 1-4 in the pseudorapidity range $|\eta|<1$. The directed flow in Cu+Au collisions is compared with the rapidity-odd and, for the first time, the rapidity-even components of charged particle directed flow in Au+Au collisions at $\sqrt{s_{_{NN}}}$ = 200~GeV. The slope of the directed flow pseudorapidity dependence in Cu+Au collisions is found to be similar to that in Au+Au collisions, with the intercept shifted toward positive $\eta$ values, i.e., the Cu-going direction. The mean transverse momentum projected onto the spectator plane, $\langle p_x\rangle$, in Cu+Au collision also exhibits approximately linear dependence on $\eta$ with the intercept at about $\eta\approx-0.4$, closer to the rapidity of the Cu+Au system center-of-mass. The observed dependencies find natural explanation in a picture of the directed flow originating partly due the "tilted source" and partly due to the rapidity dependent asymmetry in the initial density distribution. Charge-dependence of the $\langle p_x\rangle$ was also observed in Cu+Au collisions, indicating an effect of the initial electric field created by charge difference of the spectator protons in two colliding nuclei. The rapidity-even component of directed flow in Au+Au collisions is close to that in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ = 2.76 TeV, indicating a similar magnitude of dipole-like fluctuations in the initial-state density distribution. Higher harmonic flow in Cu+Au collisions exhibits similar trends to those observed in Au+Au and Pb+Pb collisions and is qualitatively reproduced by a viscous hydrodynamic model and a multi-phase transport model. For all harmonics with $n\ge2$ we observe an approximate scaling of $v_n$ with the number of constituent quarks.
Directed flow $v_1(\eta)$ and $<p_x>(\eta)$ of charged particles measured with respect to the target and projectile spectator planes in 10%-40% centrality for Cu+Au collisions.
Directed flow $v_1(\eta)$ and $<p_x>(\eta)$ of charged particles measured with respect to the target and projectile spectator planes in 10%-40% centrality for Au+Au collisions.
Conventional and fluctuation components of directed flow $v_1(\eta)$ and momentum shift $<p_x>/<p_T>(\eta)$ of charged particles in 10%-40% centrality for Cu+Au and Au+Au collisions.
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