Halos and voids in a multifractal model of cosmic structure

Abstract

On the one hand, the large scale structure of matter is arguably scale invariant, and, on the other hand, halos and voids are recognized as prominent features of that structure. To unify both approaches, we propose to model the dark matter distribution as a set of fractal distributions of halos of different kinds. This model relies on the concept of multifractal as the most general scaling distribution and on a plausible notion of halo as a singular mass concentration in a multifractal. Voids arise as complementary to halos, namely, as formed by regular mass depletions. To provide halos with definite size and masses, we coarse-grain the dark matter distribution, using the length given by the lower cutoff to scaling. This allows us to relate the halo mass function to the multifractal spectrum. Hence, we find that a log-normal model of the mass distribution nicely fits in this picture and, moreover, the Press-Schechter mass function can be recovered as a bifractal limit. To support our model of fractal distributions of halos, we perform a numerical study of the distribution produced in cosmological N-body simulations. In the Virgo L-CDM GIF2 simulation, we indeed find fractal distributions of halos with various dimensions and a halo mass function of bifractal type. However, this mass function is not of Press-Schechter's type, and we interprete it instead as caused by the undersampling of the distribution at the scale of halos, due to discretization.

22 pages (AASTeX), 9 EPS figure files; general halo definition considered, connection with SDSS results and new references added, accepted in ApJ

References in corpus (22)

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Cited by in corpus (18)

• The Fractal Geometry of the Cosmic Web and its Formation
• Non-linear gravitational clustering of cold matter in an expanding universe: indications from 1D toy models
• Galaxy Distributions as Fractal Systems
• Crystallization of space: Space-time fractals from fractal arithmetic
• Millennium Simulation Dark Matter Haloes: Multi-fractal and Lacunarity Analysis with Homogeneity Transition
• Fractal Analysis of the UltraVISTA Galaxy Survey
• Description of turbulent dynamics in the interstellar medium: multifractal/microcanonical analysis I. Application to Herschel observations of the Musca filament
• Statistics and geometry of cosmic voids
• Fractal analysis of the large-scale stellar mass distribution in the Sloan Digital Sky Survey
• Fractal distributions of dark matter and gas in the MareNostrum Universe
• On de-Sitter Geometry in Cosmic Void Statistics
• Scaling Laws in the Cosmic Structure and Renormalization Group
• Turbulence model of the cosmic structure
• Smooth halos in the cosmic web
• Scaling laws in the stellar mass distribution and the transition to homogeneity
• Scale Symmetry in the Universe
• Halo Models of Large Scale Structure and Reliability of Cosmological N-Body Simulations
• Wavepacket of the Universe and its spreading