On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

Abstract

This paper studies the scale and redshift variation of density and velocity distributions in self-gravitating collisionless dark matter flow by a halo-based non-projection approach. All particles are divided into halo and out-of-halo particles for redshift variation of distributions. Without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade at a constant rate ${\epsilon }_u$; iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto {(-{\epsilon }_{u}r)}^{2/3}$, while the odd order moments follow a linear scaling $⟨(\Delta u_L{)}^{2n+1}⟩=(2n+1)⟨(\Delta u_L{)}^{2n}⟩⟨\Delta u_L⟩\propto r$; iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{{}^{\prime }}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{{}^{\prime }}$-$u_L$ and velocity sum $\Sigma u_L$=$u_L^{{}^{\prime }}$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the system entropy; vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution; vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha (z)$ decreasing with time.

Reformatted with data source provided

References in corpus (36)

• 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
• Ellipsoidal collapse and an improved model for the number and spatial distribution of dark matter haloes
• Evolution of structure in cold dark matter universes
• Scaling relations for galaxy clusters in the Millennium-XXL simulation
• Generating Equilibrium Dark Matter Halos: Inadequacies of the Local Maxwellian Approximation
• Dark Matter Direct Detection with Non-Maxwellian Velocity Structure
• Generation of Vorticity and Velocity Dispersion by Orbit Crossing
• A new method for accurate velocity statistics estimation
• Properties of the Cosmological Density Distribution Function
• Modelling redshift space distortions in hierarchical cosmologies
• The Properties of Cosmic Velocity Fields
• Linear and nonlinear contributions to pairwise peculiar velocities
• A comparison of the evolution of the density field in perturbation theory and numerical simulations - II Counts in cells analysis
• Velocity distributions and annual-modulation signatures of weakly-interacting massive particles
• The distribution function of dark matter in massive haloes
• Streaming velocities as a dynamical estimator of Omega
• The distribution of pairwise peculiar velocities in the nonlinear regime
• Evidence for a low-density Universe from the relative velocities of galaxies
• Analytical Approximations to the Low-Order Statistics of Dark Matter Distribution
• The Generation of Vorticity in Cosmological N-body Simulations
• Skewed exponential pairwise velocities from Gaussian initial conditions
• Density distribution of the cosmological matter field
• Gravity in the Local Universe : density and velocity fields using CosmicFlows-4
• On velocity-dependent dark matter annihilations in dwarf satellites
• Constraint on the velocity dependent dark matter annihilation cross section from gamma-ray and kinematic observations of ultrafaint dwarf galaxies
• Constraining cosmology with pairwise velocity estimator
• Universal scaling laws and density slope for dark matter haloes
• Dark matter halo mass functions and density profiles from mass and energy cascade
• Maximum entropy distributions of dark matter in $\Lambda$CDM cosmology
• On the statistical theory of self-gravitating collisionless dark matter flow
• On the statistical theory of self-gravitating collisionless dark matter flow: high order kinematic and dynamic relations
• Two-body collapse model for self-gravitating flow of dark matter and generalized stable clustering hypothesis for pairwise velocity
• The mean flow, velocity dispersion, energy transfer and evolution of rotating and growing dark matter halos
• Evolution of energy, momentum, and spin parameter in dark matter flow and integral constants of motion

Cited by in corpus (2)

• 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