Dark-Matter Decays and Self-Gravitating Halos
  We consider models in which a dark-matter particle decays to a slightly less
massive daughter particle and a noninteracting massless particle. The decay
gives the daughter particle a small velocity kick. Self-gravitating dark-matter
halos that have a virial velocity smaller than this velocity kick may be
disrupted by these particle decays, while those with larger virial velocities
will be heated. We use numerical simulations to follow the detailed evolution
of the total mass and density profile of self-gravitating systems composed of
particles that undergo such velocity kicks as a function of the kick speed
(relative to the virial velocity) and the decay time (relative to the dynamical
time). We show how these decays will affect the halo mass-concentration
relation and mass function. Using measurements of the halo mass-concentration
relation and galaxy-cluster mass function to constrain the
lifetime--kick-velocity parameter space for decaying dark matter, we find
roughly that the observations rule out the combination of kick velocities
greater than 100 km/s and decay times less than a few times the age of the
Universe.
