Fractal analysis of the dark matter and gas distributions in the Mare-Nostrum universe

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.

Statistics and geometry of cosmic voids

“…In this regard, we notice that the multifractal analysis of cosmological N -body simulations suggests that the value of D(0) = D b is close to three [15,16,17]. Our recent analysis of simulations of cold dark matter [18] or of cold dark matter plus baryons [19] confirm it. Indeed, the supports of the distributions generated in N -body simulations seem to be their entire regions of definition, that is to say, the distributions appear non lacunar.…”

“…We must reconsider this assumption, in regard to the evidences of a multifractal distribution of (dark) matter with D b = 3 [18,19] and the results of the preceding section. Indeed, a galaxy distribution that closely follows the full matter distribution is probably also non-lacunar.…”

“…Here, we briefly study the statistics of spherical voids in data from cosmological N -body simulations, taking into account the conclusions of multifractal analyses of cosmological simulations [15,16,17,18,19]. We have remarked above that these analyses suggests that the box-counting dimension of the matter distribution is D b = 3, making the fractal nonlacunar.…”

“…Thus, we can reasonably expect that the resulting structure consists in a (multi)fractal attractor of the nonlinear dynamics. Structure formation in CDM models is studied with N -body simulations, which support a multifractal model in a range of scales [15,16,17,18,19]. This range is restricted by the intrinsic limitations of these N -body simulations (even of state-of-the-art simulations).…”

The Fractal Geometry of the Cosmic Web and Its Formation

“…Halo models are also employed for the study of the small scale problems of the Lambda-cold-dark-matter (LCDM) cosmology [26]. Remarkably, the basic halo model, with some modifications, can be combined with fractal models [27][28][29][30][31]. At any rate, halo models have questionable aspects and a careful analysis of the mass distribution within halos shows that it is too influenced by discreteness effects intrinsic to N-body simulations [31,32].We review in this paper a relevant portion of the efforts to understand the cosmic structure, with a bias towards methods of fractal geometry, as regards the description of the structure, and towards nonlinear methods of the theory of turbulence, as regards the formation of the structure.…”