Evolution of axis ratios from phase space dynamics of triaxial collapse

Abstract

We investigate the evolution of axis ratios of triaxial haloes using the phase space description of triaxial collapse. In this formulation, the evolution of the triaxial ellipsoid is described in terms of the dynamics of eigenvalues of three important tensors: the Hessian of the gravitational potential, the tensor of velocity derivatives and the deformation tensor. The eigenvalues of the deformation tensor are directly related to the parameters that describe triaxiality, namely, the minor to major and intermediate to major axes ratios ($s$ and $q$) and the triaxiality parameter $T$. Using the phase space equations, we evolve the eigenvalues and examine the evolution of the PDF (probability distribution function) of the axes ratios as a function of mass scale and redshift for Gaussian initial conditions. We find that the ellipticity and prolateness increase with decreasing mass scale and decreasing redshift. These trends agree with previous analytic studies but differ from numerical simulations. However, the PDF of the scaled parameter $\tilde{q}=(q-s)/(1-s)$ follows a universal distribution over two decades in mass range and redshifts which is in qualitative agreement with the universality for conditional PDF reported in simulations. We further show using the phase space dynamics that, in fact, $\tilde{q}$ is a phase space invariant and is conserved individually for each halo. These results, demonstrate that the phase space analysis is a useful tool that provides a different perspective on the evolution of perturbations and can be applied to more sophisticated models in the future.

10 pages, 5 figures, accepted in MNRAS

References in corpus (15)

• The universality of the virial halo mass function and models for non-universality of other halo definitions
• Some like it triaxial: the universality of dark matter halo shapes and their evolution along the cosmic time
• Environmental dependence in the ellipsoidal collapse model
• Void Ellipticity Distribution as a Probe of Cosmology
• Universality of dark matter haloes shape over six decades in mass: Insights from the Millennium XXL and SBARBINE simulations
• Self-Similar Solutions of Triaxial Dark Matter Halos
• On the shape of dark matter halos from MultiDark Planck simulations
• Ellipsoidal halo finders and implications for models of triaxial halo formation
• Why does the clustering of haloes depend on their formation history
• Evolution and Statistics of Non-Sphericity of Dark Matter Halos from Cosmological N-Body Simulation
• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• Systematic Errors in the Hubble Constant Measurement from the Sunyaev-Zel'dovich effect
• Systematic errors in the determination of Hubble constant due to the asphericity and non-isothermality of clusters of galaxies
• Non-linear density-velocity divergence relation from phase space dynamics
• The Einstein-Boltzmann equations revisited