  The azimuthal angle dependence of quark spin polarization in the longitudinal
beam direction of non-central relativistic heavy ion collisions is studied in
the chiral kinetic approach. Contrary to the prediction from models based on
the assumption of thermal equilibrium of spin degrees of freedom that the quark
spin polarization always points along the direction of local vorticity field,
we find the two can have opposite directions due to the effect from the
transversal component of vorticity field, which can lead to a redistribution of
axial charges in the produced matter. Our finding is consistent with the
azimuthal angle dependence of the longitudinal spin polarization of $\Lambda$
hyperons, which is mainly determined by that of the strange quark, recently
measured in the experiments by the STAR Collaboration at the Relativistic Heavy
Ion Collider (RHIC).
