Cold dark matter subhaloes at arbitrarily low masses

A defining prediction of the cold dark matter (CDM) cosmological model is the existence of a very large population of low mass haloes, down to planet-size masses. However, their fate as they are accreted onto haloes many orders of magnitude more massive remains fundamentally uncertain. A number of numerical explorations have found subhaloes to be very resilient to tides, but resolution limits make it difficult to explore tidal evolution at arbitrarily low masses. What are the structural properties of heavily stripped subhaloes? Do tidal effects destroy low-mass CDM subhaloes? Here we focus on cosmologically motivated subhaloes orbiting CDM hosts, and show that subhaloes of any initial mass can be stripped to arbitrarily small mass fractions. We show that previous numerical results can be reproduced by a simple model that describes tidal evolution as a progressive `peeling' in energy space and subsequent re-virialization. Tidal heating can effectively be neglected at all masses, because its importance i) does not increase for subhaloes of decreasing mass at accretion, and ii) it decreases as stripping proceeds. This allows us to predict analytically the structural properties of subhaloes with any initial mass and arbitrary degrees of mass loss. Under the hypotheses that CDM haloes have centrally divergent density profiles and approximately isotropic phase space distributions, our results prove that subhaloes of very low masses are a robust prediction of the CDM model: as for haloes, CDM subhalo populations extend and are abundant down to very low masses.