An accurate comprehensive approach to substructure – I. Accreted subhaloes

This is the first of a series three Papers devoted to study halo substructure in hierarchical cosmologies by means CUSP formalism. In present Paper we derive properties subhaloes and diffuse dark matter (dDM) accreted onto haloes their progenitors. Specifically, relate dDM at any time inter-halo medium real Universe or cosmological simulation with corresponding free-streaming mass resolution mass, respectively, establish link between seeds initial density field. By monitoring collapse virialisation haloes, from principles no single free parameter abundance radial distribution them. Our predictions are excellent agreement results simulations, but for predicted fraction dDM, which larger than reported previous works as they only count final halo, not its The derivation pursued here clarifies origin some key features substructure. Overall, our demonstrate that powerful tool understanding extending simulations arbitrary masses, redshifts formation times cosmology endowed random Gaussian perturbations.