On the cross-section of Dark Matter using substructure infall into
  galaxy clusters
  We develop a statistical method to measure the interaction cross-section of
Dark Matter, exploiting the continuous minor merger events in which small
substructures fall into galaxy clusters. We find that by taking the ratio of
the distances between the galaxies and Dark Matter, and galaxies and gas in
accreting sub-halos, we form a quantity that can be statistically averaged over
a large sample of systems whilst removing any inherent line-of-sight
projections. In order to interpret this ratio as a cross-section of Dark Matter
we derive an analytical description of sub-halo infall which encompasses; the
force of the main cluster potential, the drag on a gas sub-halo, a model for
Dark Matter self-interactions and the resulting sub-halo drag, the force on the
gas and galaxies due to the Dark Matter sub-halo potential, and finally the
buoyancy on the gas and Dark Matter. We create mock observations from
cosmological simulations of structure formation and find that collisionless
Dark Matter becomes physically separated from X-ray gas by up to 20h^-1 kpc.
Adding realistic levels of noise, we are able to predict achievable constraints
from observational data. Current archival data should be able to detect a
difference in the dynamical behaviour of Dark Matter and standard model
particles at 6 sigma, and measure the total interaction cross-section sigma/m
with 68% confidence limits of +/- 1cm2g^-1. We note that this method is not
restricted by the limited number of major merging events and is easily extended
to large samples of clusters from future surveys which could potentially push
statistical errors to 0.1cm^2g^-1.
