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.
