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

Abstract

Simulated dark matter haloes are fitted by self-similar, universal density profiles, where the scaled parameters depend only on a scaled (truncation) radius, ? = R/r0, which, in turn, is supposed to be independent of 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 approximation) a normal or lognormal distribution for other scaled parameters, via the same procedure which leads to the propagation of the errors. A criterion is proposed for the choice of the best fitting density profile, 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, |x?|/?s? = |?-?*|/?s?, is required to yield the best fit, where ? is the arithmetic mean over the whole set; ?*is its counterpart related to the fitting density profile; ?s? is the standard deviation from the mean; and ? is a selected, scaled i.e. dimensionless parameter. The above criterion is applied to a pair of sets each made of a dozen of high-resolution simulations, FM01 (Fukushige and Makino 2001) and KLA01 (Klypin et al. 2001), in connection with two currently used fitting density profiles, NFW (e.g. Navarro et al. 1997) and MOA (e.g. Moore et al. 1999), where the dependence of the scaled radius on the mass and the formation redshift may be neglected to a first extent. With regard to FM01 and KLA01 samples, the best fits turn out to be MOA and NFW, respectively. In addition, the above results also hold in dealing with rms errors derived via the propagation of the errors, with regard to the distributions of scaled parameters. The sensitivity error of simulations is also estimated and shown to be less than the related, standard deviation, that is a necessary condition for detectability of accidental errors. Some features of the early evolution of dark matter haloes, represented by fitting density profiles, are discussed in the limit of the spherical top-hat model. Although the related matter distributions appear to be poorly representative of simulated haloes, unless the (mean) peak height is an increasing function of the mass, the results are shown to be consistent, provided considerable acquisition of angular momentum takes place during the expansion phase.