Martin D. Weinberg
Department of Physics and Astronomy,
University of Massachusetts, Amherst, MA 01003-4525, USA
Gravitational amplification of Poisson noise in stellar systems is important on large scales. For example, it increases the dipole noise power by roughly a factor of six and the quadrupole noise by 50% for a King model profile. The dipole noise is amplified by a factor of fifteen for the core-free Hernquist model. The predictions are computed using the dressed-particle formalism of Rostoker & Rosenbluth (1960) and are demonstrated by n-body simulation.
This result implies that a collisionless n-body simulation is impossible; The fluctuation noise which causes relaxation is an intrinic part of self gravity. In other words, eliminating two-body relaxation does not eliminate relaxation altogether.
Applied to dark matter halos of disk galaxies, particle numbers of
at least 
will be necessary to suppress this noise at a level
that does not dominate or significantly affect the disk response.
Conversely, halos are most likely far from phase-mixed equilibrium
and the resulting noise spectrum may seed or excite observed
structure such as warps, spiral arms and bars. For example,
discreteness noise in the halo, similar to that due to a population
of 
black holes can produce observable warping and
possibly excite or seed other disk structure.
