How general is the global density slope–anisotropy inequality?

@article{Ciotti2010HowGI,
  title={How general is the global density slope–anisotropy inequality?},
  author={Luca Ciotti and Lucia Morganti},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2010},
  volume={408},
  pages={1070-1074}
}
  • L. Ciotti, L. Morganti
  • Published 11 June 2010
  • Physics, Mathematics
  • Monthly Notices of the Royal Astronomical Society
Following the seminal result of An & Evans, known as the central density slope– anisotropy theorem, successive investigations unexpectedly revealed that the density slope–anisotropy inequality holds not only at the center, but at all radii in a very large class of spherical systems whenever the phase–space distribution function is positive. In this paper we derive a criterion that holds for all spherical systems in which the augmented density is a separable function of radius and potential… Expand
ON THE UNIVERSALITY OF THE GLOBAL DENSITY SLOPE-ANISOTROPY INEQUALITY
Recently, some intriguing results have led to speculations whether the central density slope-velocity dispersion anisotropy inequality (An & Evans) actually holds at all radii for spherical dynamicalExpand
Phase-space consistency of stellar dynamical models determined by separable augmented densities
Assuming the separable augmented density, it is always possible to construct a distribution function of a spherical population with any given density and anisotropy. We consider under what conditionsExpand
The double-power approach to spherically symmetric astrophysical systems
In this paper, we present two simple approaches for deriving anisotropic distribution functions for a wide range of spherical models. The first method involves multiplying and dividing a basicExpand
How to break the density-anisotropy degeneracy in spherical stellar systems
We present a new non-parametric Jeans code, GravSphere, that recovers the density ρ(r) and velocity anisotropy β(r) of spherical stellar systems, assuming only that they are in a steady-state. UsingExpand
A new class of galaxy models with a central BH – I. The spherical case
The dynamical properties of spherically symmetric galaxy models, where a Jaffe stellar density profile is embedded in a total mass density decreasing as r−3 at large radii, are presented. The orbitalExpand
Constraints on Velocity Anisotropy of Spherical Systems with Separable Augmented Densities
  • J. An
  • Physics, Mathematics
  • 2011
If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable into functions of the potential and the radius, the radial function, which can be completelyExpand
Two-component Jaffe models with a central black hole - I. The spherical case
Dynamical properties of spherically symmetric galaxy models where both the stellar and total mass density distributions are described by the Jaffe (1983) profile (with different scale-lenghts andExpand
Analytical solutions to the mass-anisotropy degeneracy with higher order Jeans analysis: a general method
The Jeans analysis is often used to infer the total density of a system by relating the velocity moments of an observable tracer population to the underlying gravitational potential. This techniqueExpand
On radial anisotropy limits in stellar systems
Following earlier authors we re-examine the upper limits on the radial velocity anisotropy of general stellar systems; these constraints coming generically from phase-space density positivity,Expand
Miyamoto–Nagai discs embedded in the Binney logarithmic potential: analytical solution of the two-integrals Jeans equations
We present the analytical solution of the two-integrals Jeans equations for Miyamoto-Nagai discs embedded in Binney logarithmic dark matter haloes. The equations can be solved (both with standardExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 33 REFERENCES
On the global density slope-anisotropy inequality
Starting from the central density slope–anisotropy theorem of An & Evans [1], recent investigations have shown that the involved density slope‐anisotropy inequality holds not only at the center, butExpand
A cusp slope-central anisotropy theorem
For a wide class of self-gravitating systems, we show that if the density is cusped like r-γ near the center, then the limiting value of the anisotropy parameter β = 1 - v/(2v) at the center cannotExpand
Consistency criteria for generalized Cuddeford systems
General criteria to check the positivity of the distributio n function (phase‐space consistency) of stellar systems of assigned density and anisotropy profil e are useful starting points in Jeans‐Expand
A Universal density slope - velocity anisotropy relation for relaxed structures
Abstract We identify a universal relation between the radial density slope α(r) and the velocity anisotropy β(r) for equilibrated structures. This relation holds for a variety of systems, includingExpand
Dynamical models with a general anisotropy profile
Aims. Both numerical simulations and observational evidence indicate that the outer regions of galaxies and dark matter haloes are typically mildly to significantly radially anisotropic. The innerExpand
A simple method to construct exact density-potential pairs from a homeoidal expansion
We start from a study of the density-potential relation for classical homeoids in terms of an asymptotic expansion for small deviations from spherical symmetry. We then show that such expansion is aExpand
Two‐component galaxy models: the effect of density profile at large radii on the phase‐space consistency
It is well known that the density and anisotropy profile in the inner regions of a stellar system with positive phase-space distribution function are not fully independent. Here we study theExpand
Two‐component galaxies with flat rotation curve
Dynamical properties of two-component galaxy models whose stellar density distribution is described by a γ-model while the total density distribution has a pure r 2 profile, are presented. TheExpand
Scale-free dynamical models for galaxies : flattened densities in spherical potentials
This paper presents two families of phase-space distribution functions (DFs) that generate scale-free spheroidal mass densities in scale-free spherical potentials. The `case I' DFs are anisotropicExpand
Spherical stellar systems with spheroidal velocity distributions
A new method is described for deriving families of anisotropic distribution functions consistent with any spherically symmetric density profile. The algorithm is straightforward and sufficientlyExpand
...
1
2
3
4
...