The flattening of the concentration-mass relation towards low halo masses and its implications for the annihilation signal boost

In the standard cold dark matter (CDM) theory for understanding the formation of structure in the Universe, there exists a tight connection between the properties of dark matter (DM) haloes, and their formation epochs. Such relation can be expressed in terms of a single key parameter, namely the halo concentration. In this work, we examine the median concentration-mass relation, c(M), at present time, over more than 20 orders of magnitude in halo mass, i.e. from tiny Earth-mass microhaloes up to galaxy clusters. The c(M) model proposed by Prada et al. (2012), which links the halo concentration with the rms amplitude of matter linear fluctuations, describes remarkably well all the available N-body simulation data down to similar to 10(-6) h(-1) M-aS (TM) microhaloes. A clear fattening of the halo concentration-mass relation towards smaller masses is observed, that excludes the commonly adopted power-law c(M) models, and stands as a natural prediction for the CDM paradigm. We provide a parametrization for the c(M) relation that works accurately for all halo masses. This feature in the c(M) relation at low masses has decisive consequences e.g. for gamma-ray DM searches, as it implies more modest boosts of the DM annihilation flux due to substructure, i.e. similar to 35 for galaxy clusters and similar to 15 for galaxies like our own, as compared to those huge values adopted in the literature that rely on such power-law c(M) extrapolations. We provide a parametrization of the boosts that can be safely used for dwarfs to galaxy cluster-size haloes.