A test for skewed distributions of dark matter and a possible detection
  in galaxy cluster Abell 3827
  Simulations of self-interacting dark matter (SIDM) predict that dark matter
should lag behind galaxies during a collision. If the interaction is mediated
by a high-mass force carrier, the distribution of dark matter can also develop
asymmetric dark matter tails. To search for this asymmetry, we compute the
gravitational lensing properties of a mass distribution with a free {\em
skewness} parameter. We apply this to the dark matter around the four central
galaxies in cluster Abell~3827. In the galaxy whose dark matter peak has
previously been found to be offset, we tentatively measure a skewness
$s=0.23^{+0.05}_{-0.22}$ in the same direction as the peak offset. Our method
may be useful in future gravitational lensing analyses of colliding galaxy
clusters and merging galaxies.
