  There is strong evidence that cosmological N-body simulations dominated by
Warm Dark Matter (WDM) contain spurious or unphysical haloes, most readily
apparent as regularly spaced low-mass haloes strung along filaments. We show
that spurious haloes are a feature of traditional N-body simulations of
cosmological structure formation models, including WDM and Cold Dark Matter
(CDM) models, in which gravitational collapse proceeds in an initially
anisotropic fashion, and arises naturally as a consequence of
discreteness-driven relaxation. We demonstrate this using controlled N-body
simulations of plane-symmetric collapse and show that spurious haloes are
seeded at shell crossing by localised velocity perturbations induced by the
discrete nature of the density field, and that their characteristic separation
should be approximately the mean inter-particle separation of the N-body
simulation, which is fixed by the mass resolution within the volume. Using
cosmological N-body simulations in which particles are split into two
collisionless components of fixed mass ratio, we find that the spatial
distribution of the two components show signatures of discreteness-driven
relaxation in their spatial distribution on both large and small scales.
Adopting a spline kernel gravitational softening that is of order the comoving
mean inter-particle separation helps to suppress the effect of
discreteness-driven relaxation, but cannot eliminate it completely. These
results provide further motivation for recent developments of new algorithms,
which include, for example, revisions of the traditional N-body approach by
means of spatially adaptive anistropric gravitational softenings or explicit
solutions for the evolution of dark matter in phase space.
