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 microhalos up to galaxy clusters. The c(M) model proposed by Prada et al. (2012), which links the halo concentration with the r.m.s. amplitude of matter linear fluctuations, describes remarkably well all the available N-body simulation data down to ~10^(-6) Msun microhalos. 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., ~35 for galaxy clusters and ~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 halos.

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