  Caustics are a generic feature of the nonlinear growth of structure in the
dark matter distribution. If the dark matter were absolutely cold, its mass
density would diverge at caustics, and the integrated annihilation probability
would also diverge for individual particles participating in them. For
realistic dark matter candidates, this behaviour is regularised by small but
non-zero initial thermal velocities. We present a mathematical treatment of
evolution from Hot, Warm or Cold Dark Matter initial conditions which can be
directly implemented in cosmological N-body codes. It allows the identification
of caustics and the estimation of their annihilation radiation in fully general
simulations of structure formation.

Astrophysics