Disruption of dark matter substructure: fact or fiction?

Accurately predicting the demographics of dark matter (DM) substructure is of paramount importance for many fields of astrophysics, including gravitational lensing, galaxy evolution, halo occupation modelling, and constraining the nature of DM. Because of its strongly nonlinear nature, DM substructure is typically modelled using N-body simulations, which reveal that large fractions of DM subhaloes undergo complete disruption. In this paper, we use both analytical estimates and idealized numerical simulations to investigate whether this disruption is mainly physical, due to tidal heating and stripping, or numerical (i.e. artificial). We show that, contrary to naive expectation, subhaloes that experience a tidal shock E that exceeds the subhalo's binding energy, |E b |, do not undergo disruption, even when E/|E b | is as large as 100. Along the same line, and contrary to existing claims in the literature, instantaneously stripping matter from the outskirts of a DM subhalo also does not result in its complete disruption, even when the instantaneous remnant has positive binding energy. In addition, we show that tidal heating due to high-speed (impulsive) encounters with other subhaloes ('harassment') is negligible compared to the tidal effects due to the host halo. Hence, we conclude that, in the absence of baryonic processes, the complete physical disruption of CDM substructure is extremely rare and that most disruption in numerical simulations therefore must be artificial. We discuss various processes that have been associated with numerical overmerging and conclude that inadequate force softening is the most likely culprit.