Dark matter haloes: an additional criterion for the choice of fitting density profiles

Simulated dark matter haloes are fitted by self-similar, universal density profiles, where the scaled parameters depend only on a scaled (truncation) radius, Ξ = R/r0, which, in turn, is supposed to be independent on the mass and the formation redshift. The further assumption of a lognormal distribution (for a selected mass bin) of the scaled radius, or concentration, in agreement with the data from a large statistical sample of simulated haloes (Bullock et al. 2001), allows (at least to a first extent) a normal or lognormal distribution for other scaled parameters, via the same procedure which leads to the propagation of the errors. A criterion for the choice of the best fitting density profile is proposed, with regard to a set of high-resolution simulations, where some averaging procedure on scaled density profiles has been performed, in connection with a number of fitting density profiles. To this aim, a minimum value of the ratio, |xη|/σs η = |η − η|/σs η, is required to yield the best fit, where η is the arithmetic mean over the whole set; η∗ is its counterpart related to the fitting density profile; σs η is the standard deviation from the mean; and η is a selected, ∗Astronomy Department, Padua Univ., Vicolo Osservatorio 2, I-35122 Padova, Italy email: [email protected]