Self-consistent dynamical models with a finite extent -- III. Truncated power-law spheres

Abstract

Fully analytical dynamical models usually have an infinite extent, while real star clusters, galaxies, and dark matter haloes have a finite extent. The standard method for generating dynamical models with a finite extent consists of taking a model with an infinite extent and applying a truncation in binding energy. This method, however, cannot be used to generate models with a pre-set analytical mass density profile. We investigate the self-consistency and dynamical properties of a family of power-law spheres with a general tangential Cuddeford (TC) orbital structure. By varying the density power-law slope $\gamma$ and the central anisotropy ${\beta }_0$, these models cover a wide parameter space in density and anisotropy profiles. We explicitly calculate the phase-space distribution function for various parameter combinations, and interpret our results in terms of the energy distribution of bound orbits. We find that truncated power-law spheres can be supported by a TC orbital structure if and only if $\gamma ⩾2{\beta }_0$, which means that the central density slope-anisotropy inequality is both a sufficient and a necessary condition for this family. We provide closed expressions for structural and dynamical properties such as the radial and tangential velocity dispersion profiles, which can be compared against more complex numerical modelling results. This work significantly adds to the available suite of self-consistent dynamical models with a finite extent and an analytical description.

arXiv comment12 pages, 4 figures, accepted for publication in MNRAS

References in corpus (39)

• Empirical models for Dark Matter Halos. I. Nonparametric Construction of Density Profiles and Comparison with Parametric Models
• Density Profiles of Dark Matter Halo are not Universal
• A Family of Models for Spherical Stellar Systems
• A family of lowered isothermal models
• Can tides disrupt cold dark matter subhaloes?
• A Cusp Slope -- Central Anisotropy Theorem
• Statistical mechanics of collisionless orbits. I. Origin of central cusps in dark-matter halos
• Dynamical models with a general anisotropy profile
• The Hernquist model revisited: completely analytical anisotropic dynamical models
• The dynamics of satellite disruption in cold dark matter haloes
• Anisotropic Models for Globular Clusters, Galactic Bulges and Dark Halos
• Testing lowered isothermal models with direct N-body simulations of globular clusters
• Numerical stability of a family of Osipkov-Merrit models
• How general is the global density slope-anisotropy inequality?
• Velocity profiles of Osipkov-Merritt models
• The phase-space structure of tidally stripped halos
• The Radial Orbit Instability in Collisionless N-Body Simulations
• Tidal Stripping in the Adiabatic Limit
• Two-component galaxies with flat rotation curve
• Mass loss in tidally stripped systems; the energy-based truncation method
• The Einasto model for dark matter haloes
• Mapping the stability of stellar rotating spheres via linear response theory
• A completely analytical family of dynamical models for spherical galaxies and bulges with a central black hole
• Special Features of Galactic Dynamics
• Relaxation of N-body systems with additive r^-α interparticle forces
• On the universality of the global slope -- anisotropy inequality
• Two-component galaxy models: the effect of density profile at large radii on the phase-space consistency
• The differential energy distribution and the total integrated binding energy of dynamical models
• Truncated $\gamma$-exponential models for tidal stellar systems
• Notes on the stability threshold for radially anisotropic polytrope
• The double-power approach to spherically symmetric astrophysical systems
• Constraints on velocity anisotropy of spherical systems with separable augmented densities
• On the augmented density of a spherical anisotropic dynamic system
• The differential energy distribution of the universal density profile of dark halo
• Multilayer spherical stellar cluster with uniform density
• The Effective Cross-sections of a Lensing-galaxy: Singular Isothermal Sphere with External Shear
• Self-consistent dynamical models with a finite extent -- II. Radially truncated models
• Investigating Dynamical Properties of Globular Clusters through a Family of Lowered Isothermal Models
• On radial anisotropy limits in stellar systems