On the statistical theory of self-gravitating collisionless dark matter flow

Abstract

Dark matter, if exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e. correlation, structure, dispersion, and spectrum functions are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share same kinematic relations for even order correlations. The limiting correlation of velocity ${\rho }_L=1/2$ on the smallest scale ($r=0$) is a unique feature of collisionless flow (${\rho }_L=1$ for incompressible flow). On large scale, transverse velocity correlation has an exponential form $T_2\propto e^{-r/r_2}$ with a constant comoving scale $r_2$=21.3Mpc/h that maybe related to the horizon size at matter-radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of $S_2^l\propto r^{1/4}$. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale $r$ between 1 and 7Mpc/h. Divergence is negatively correlated for $r$>30Mpc/h that leads to a negative density correlation.

arXiv commentPublished version, 22 pages, 28 figures

References in corpus (20)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The cosmological simulation code GADGET-2
• Baryonic Features in the Matter Transfer Function
• Ellipsoidal collapse and an improved model for the number and spatial distribution of dark matter haloes
• Galaxy Clustering in Early SDSS Redshift Data
• Evolution of structure in cold dark matter universes
• Scaling relations for galaxy clusters in the Millennium-XXL simulation
• Generation of Vorticity and Velocity Dispersion by Orbit Crossing
• Large-scale dark matter simulations
• Modelling redshift space distortions in hierarchical cosmologies
• The Properties of Cosmic Velocity Fields
• A comparison of the evolution of the density field in perturbation theory and numerical simulations - II Counts in cells analysis
• The Generation of Vorticity in Cosmological N-body Simulations
• CUBE: An Information-optimized parallel Cosmological $N$-body Algorithm
• An alternative method to generate pre-initial conditions for cosmological $N$-body simulations
• A Hybrid Fast Multipole Method for Cosmological N-body Simulations
• Bayesian redshift-space distortions correction from galaxy redshift surveys
• Universal scaling laws and density slope for dark matter haloes
• Universal spectrum and scaling laws for halo mass function, structure, and dark matter mass constraints

Cited by in corpus (5)

• Dark matter halo mass functions and density profiles from mass and energy cascade
• On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions
• On the statistical theory of self-gravitating collisionless dark matter flow: high order kinematic and dynamic relations
• Cosmic quenching and scaling laws for the evolution of supermassive black holes and host galaxies
• On a critical acceleration scale of dark matter in Lambda-CDM and dynamical dark energy