  The unique properties of dark matter are revealed during collisions between
clusters of galaxies, like the bullet cluster (1E 0657-56) and baby bullet
(MACSJ0025-12). These systems provide evidence for an additional, invisible
mass in the separation between the distribution of their total mass, measured
via gravitational lensing, and their ordinary 'baryonic' matter, measured via
its X-ray emission. Unfortunately, the information available from these systems
is limited by their rarity. Constraints on the properties of dark matter, such
as its interaction cross-section, are therefore restricted by uncertainties in
the individual systems' impact velocity, impact parameter and orientation with
respect to the line of sight.
  Here we develop a complementary, statistical measurement in which every piece
of substructure falling into every massive cluster is treated as a bullet. We
define 'bulleticity' as the mean separation between dark matter and ordinary
matter, and we measure the signal in hydrodynamical simulations. The phase
space of substructure orbits also exhibits symmetries that provide an
equivalent control test.
  Any detection of bulleticity in real data would indicate a difference in the
interaction cross-sections of baryonic and dark matter that may rule out
hypotheses of non-particulate dark matter that are otherwise able to model
individual systems. A subsequent measurement of bulleticity could constrain the
dark matter cross-section. Even with conservative estimates, the existing HST
archive should yield an independent constraint tighter than that from the
bullet cluster. This technique is then trivially extendable to, and benefits
enormously from larger, future surveys.
