The warm dark matter halo mass function below the cut-off scale

Warm dark matter (WDM) cosmologies are a viable alternative to the cold dark matter (CDM) scenario. Unfortunately, an accurate scrutiny of the WDM predictions with N-body simulations has proven difficult due to numerical artefacts. Here, we report on cosmological simulations that, for the first time, are devoid of those problems, and thus are able to accurately resolve the WDM halo mass function well below the cut-off. We discover a complex picture, with perturbations at different evolutionary stages populating different ranges in the halo mass function. On the smallest mass scales we can resolve, identified objects are typically centres of filaments that are starting to collapse. On intermediate mass scales, objects typically correspond to fluctuations that have collapsed and are in the process of relaxation, whereas the high-mass end is dominated by objects similar to haloes identified in CDM simulations. We then explicitly show how the formation of low-mass haloes is suppressed, which translates into a strong cut-off in the halo mass function. This disfavours some analytic formulations that predict a halo mass function that would extend well below the free streaming mass. We argue for a more detailed exploration of the formation of the smallest structures expected to form in a given cosmology, which, we foresee, will advance our overall understanding of structure formation.