Fractal distributions of dark matter and gas in the MareNostrum Universe

TL;DR

This paper introduces a refined multifractal analysis method for cosmological simulations, revealing that dark matter and gas distributions form indistinguishable, self-similar multifractal structures across scales, with minor biasing effects.

Contribution

The authors develop an improved multifractal analysis technique that accounts for discreteness and homogeneity, demonstrating the multifractal nature of dark matter and gas distributions in simulations.

Findings

Dark matter and gas are indistinguishable as multifractals.

The halo mass function follows a Press-Schechter type with a -2 exponent.

Gas biasing is small but present across scales.

Abstract

We develop a method of multifractal analysis of N-body cosmological simulations that improves on the customary counts-in-cells method by taking special care of the effects of discreteness and large scale homogeneity. The analysis of the Mare-Nostrum simulation with our method provides strong evidence of self-similar multifractal distributions of dark matter and gas, with a halo mass function that is of Press-Schechter type but has a power-law exponent -2, as corresponds to a multifractal. Furthermore, our analysis shows that the dark matter and gas distributions are indistinguishable as multifractals. To determine if there is any gas biasing, we calculate the cross-correlation coefficient, with negative but inconclusive results. Hence, we develop an effective Bayesian analysis connected with information theory, which clearly demonstrates that the gas is biased in a long range of scales, up to the scale of homogeneity. However, entropic measures related to the Bayesian analysis show that this gas bias is small (in a precise sense) and is such that the fractal singularities of both distributions coincide and are identical. We conclude that this common multifractal cosmic web structure is determined by the dynamics and is independent of the initial conditions.