Fluctuations in finite-N equilibrium stellar systems

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 6 and the quadrupole noise by 50 per cent for a King model profile. The dipole noise is amplified by a factor of 15 for the core-free Hernquist model. The predictions are computed by summing over the wakes caused by each star in the system — the dressed-particle formalism of Rostoker & Rosenbluth — 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 scattering at interparticle scales does not eliminate relaxation altogether. Applied to dark matter haloes of disc galaxies, particle numbers of at least 106 will be necessary to suppress this noise at a level that does not dominate or significantly affect the disc response. Conversely, haloes 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 caused by a population of 106-M⊙ black holes, can produce observable warping and possibly excite or seed other disc structure