The fractal distribution of haloes

– We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power-law profile, as opposed to a fractal model, can account for the observed power-law galaxy-galaxy correlations. We conclude that such model, which can actually be considered as a degenerate multifractal model, is not realistic but suggests a new picture of multifractal models, namely, as sets of fractal distributions of haloes. We analyse, according to this picture, the properties of the matter distribution produced in cosmological N-body simulations, with affirmative results; namely, haloes of similar mass have a fractal distribution with a given dimension, which grows as the mass diminishes. Introduction. – The model of the large-scale matter distribution consisting of haloes with power-law profile and with centers distributed randomly can be traced back to Peebles [1]. McClelland & Silk [2] and later Sheth & Jain [3] and Murante et al [4] studied the effect on correlation functions of a spectrum of halo masses. The latter authors claimed that this model provides a good description of the observed galaxy correlations, at least on small scales. In particular, their analysis of generalized correlation integrals shows non-trivial scaling, which they consider indistinguishable from the scaling in fractal models. Recently, this conclusion has led Botaccio, Montuori and Pietronero [5] to construct new statistical functions to distinguish both types of models. Motivated by the mentioned preceding works, here we critically examine the model of randomly distributed haloes with power-law profile. We instead propose a model consisting of a set of fractal distributions of haloes, that is, combining both the fractal and the halo models. Actually, Murante et al already considered to place the haloes “more deliberately, for instance in the sheet-like structures produced by large-scale pancake formation” but deferred it to future work. Here, we constructively proceed from the case of a single halo, understood as a degenerate multifractal model, to a general multifractal, considered as a set of fractal distributions of haloes. We argue that this model is plausible in regard to models of structure formation and provides a better description, especially, of void regions. Furthermore, we show that it is supported by the multifractal analysis of N -body simulations. We also discuss the rôle of the two-point correlation function in this context.