  In symmetric gravitating systems experiencing rapid mass loss, particle
orbits change almost instantaneously, which can lead to the development of a
sharply contoured density profile, including singular caustics for
collisionless systems. This framework can be used to model a variety of
dynamical systems, such as accretion disks following a massive black hole
merger and dwarf galaxies following violent early star formation feedback.
Particle interactions in the high-density peaks seem a promising source of
observable signatures of these mass loss events (i.e. a possible EM counterpart
for black hole mergers or strong gamma-ray emission from dark matter
annihilation around young galaxies), because the interaction rate depends on
the square of the density. We study post-mass-loss density profiles, both
analytic and numerical, in idealised cases and present arguments and methods to
extend to any general system. An analytic derivation is presented for particles
on Keplerian orbits responding to a drop in the central mass. We argue that
this case, with initially circular orbits, gives the most sharply contoured
profile possible. We find that despite the presence of a set of singular
caustics, the total particle interaction rate is reduced compared to the
unperturbed system; this is a result of the overall expansion of the system
dominating over the steep caustics. Finally we argue that this result holds
more generally, and the loss of central mass decreases the particle interaction
rate in any physical system.
