# 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} }

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

#### 34 Citations

ON THE UNIVERSALITY OF THE GLOBAL DENSITY SLOPE-ANISOTROPY INEQUALITY

- Physics, Mathematics
- 2011

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 dynamical… Expand

Phase-space consistency of stellar dynamical models determined by separable augmented densities

- Physics
- 2012

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 conditions… Expand

The double-power approach to spherically symmetric astrophysical systems

- Physics
- 2014

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 basic… Expand

How to break the density-anisotropy degeneracy in spherical stellar systems

- Physics
- 2017

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. Using… Expand

A new class of galaxy models with a central BH – I. The spherical case

- Physics
- Monthly Notices of the Royal Astronomical Society
- 2019

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 orbital… Expand

Constraints on Velocity Anisotropy of Spherical Systems with Separable Augmented Densities

- 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 completely… Expand

Two-component Jaffe models with a central black hole - I. The spherical case

- Physics
- 2018

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 and… Expand

Analytical solutions to the mass-anisotropy degeneracy with higher order Jeans analysis: a general method

- Physics
- 2013

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 technique… Expand

On radial anisotropy limits in stellar systems

- Physics
- 2014

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

- Physics
- 2015

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 standard… Expand

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