The Local Void: for or against ΛCDM?

The emptiness of the Local Void has been put forward as a serious challenge to the current standard paradigm of structure formation in I > cold dark matter (CDM). We use a high-resolution cosmological N-body simulation, the Millennium-II run, combined with a sophisticated semi-analytic galaxy formation model, to explore statistically whether the Local Void is allowed within our current knowledge of galaxy formation in I > CDM. We find that about 14 per cent of the Local Group analogue systems (11 of 77) in our simulation are associated with nearby low-density regions having size and 'emptiness' similar to those of the observed Local Void. This suggests that, rather than a crisis of the I > CDM, the emptiness of the Local Void is indeed a success of the standard I > CDM theory. The paucity of faint galaxies in such voids results from a combination of two factors: a lower amplitude of the halo mass function in the voids than in the field, and a lower galaxy formation efficiency in the void haloes due to halo assembly bias effects. While the former is the dominated factor, the later also plays a sizeable role. The halo assembly bias effect results in a stellar mass fraction 25 per cent lower for void galaxies when compared to field galaxies with the same halo mass.