The sizes of mini-voids in the local universe: an argument in favor of a warm dark matter model?

Using high-resolution simulations within the Cold and Warm Dark Matter models we study the evolution of small scale structure in the Local Volume, a sphere of 8 Mpc radius around the Local Group. We compare the observed spectrum of mini-voids in the Local Volume with the spectrum of mini-voids determined from the simulations. We show that the \LWDM model can easily explain both the observed spectrum of mini-voids and the presence of low-mass galaxies observed in the Local Volume, provided that all haloes with circular velocities greater than 20 km/s host galaxies. On the contrary within the LCDM model the distribution of the simulated mini-voids reflects the observed one if haloes with maximal circular velocities larger than 35 km/s host galaxies. This assumption is in contradiction with observations of galaxies with circular velocities as low as 20 km/s in our Local Universe. A potential problem of the LWDM model could be the late formation of the haloes in which the gas can be efficiently photo-evaporated. Thus star formation is suppressed and low-mass haloes might not host any galaxy at all.