Dark Matter Substructure in Numerical Simulations: A Tale of
  Discreteness Noise, Runaway Instabilities, and Artificial Disruption
  To gain understanding of the complicated, non-linear and numerical processes
associated with the tidal evolution of dark matter subhaloes in numerical
simulation, we perform a large suite of idealized simulations that follow
individual N-body subhaloes in a fixed, analytical host halo potential. By
varying both physical and numerical parameters, we investigate under what
conditions the subhaloes undergo disruption. We confirm the conclusions from
our more analytical assessment in van den Bosch et al. that most disruption is
numerical in origin; as long as a subhalo is resolved with sufficient mass and
force resolution, a bound remnant survives. This implies that state-of-the-art
cosmological simulations still suffer from significant overmerging. We
demonstrate that this is mainly due to inadequate force-softening, which causes
excessive mass loss and artificial tidal disruption. In addition, we show that
subhaloes in N-body simulations are susceptible to a runaway instability
triggered by the amplification of discreteness noise in the presence of a tidal
field. These two processes conspire to put serious limitations on the
reliability of dark matter substructure in state-of-the-art cosmological
simulations. We present two criteria that can be used to assess whether
individual subhaloes in cosmological simulations are reliable or not, and
advocate that subhaloes that satisfy either of these two criteria be discarded
from further analysis. We discuss the potential implications of this work for
several areas in astrophysics.
