  Measurements of galaxy cluster kinematics are important in understanding the
dynamical state and evolution of clusters of galaxies, as well as constraining
cosmological models. While it is well established that clusters exhibit
non-spherical geometries, evident in the distribution of galaxies on the sky,
azimuthal variations of galaxy kinematics within clusters have yet to be
observed. Here we measure the azimuthal dependence of the line-of-sight
velocity dispersion profile in a stacked sample of 1743 galaxy clusters from
the Sloan Digital Sky Survey (SDSS). The clusters are drawn from the SDSS DR8
redMaPPer catalog. We find that the line-of-sight velocity dispersion of
galaxies lying along the major axis of the central galaxy is larger than those
that lie along the minor axis. This is the first observational detection of
anisotropic kinematics of galaxies in clusters. We show that the result is
consistent with predictions from numerical simulations. Furthermore we find
that the degree of projected anisotropy is strongly dependent on the
line-of-sight orientation of the galaxy cluster, opening new possibilities for
assessing systematics in optical cluster finding.
