Fractal distributions of dark matter and gas in the MareNostrum Universe

Context. Large simulations of dark matter and gas structure formation allow us to separate the pure gravitational dynamics from other processes and, hence, to better compare them with observations. Aims. Our objective is to analyse the recent MareNostrum simulation from a new perspective, regarding the geometry of the dark matter and gas distributions in it. We intend to find the fractal geometry of the dark matter and to determine if the gas distribution is fractal as well. If it is, the question is whether or not the gas distribution is nonetheless biased with respect to the dark matter. Methods. We use the methods of multifractal geometry, in particular, an improved method of coarse multifractal analysis based on counts in cells. To detemine the gas biasing, we use statistical methods: we use the cross-correlation coefficient and we develop a Bayesian analysis connected with information theory. We also employ entropic measures to characterize both distributions further than the multifractal analysis. Results. Both distributions are multifractals, with equal spectra. The analysis of cross-correlations is inconclusive, but the Bayesian analysis clearly demonstrates gas biasing. The main feature of the distribution of gas is that it is less concentrated in the high density regions (massive halos). The entropic measures show that this gas bias is small, such that both distributions have the same singularities. Conclusions. Gravity determines a unique distribution of singularities in the gas and the dark matter and, therefore, determines a universal multifractal spectrum. Nevertheless, gas biasing exists and, in general, should be model dependent.