An Infinite Family of Self-consistent Models for Axisymmetric Flat Galaxies

TL;DR

This paper introduces a new infinite family of self-consistent, axisymmetric flat galaxy models with analytical distribution functions, demonstrating their realistic kinematic behavior and stability without requiring dark matter halos.

Contribution

It presents a novel class of analytical galaxy models based on superpositions of Kalnajs family members, with explicit distribution functions and stability analysis.

Findings

Models exhibit well-behaved surface density profiles.

Rotational curves show satisfactory behavior without dark matter.

Orbit stability and phase space structures are analyzed.

Abstract

We present the formulation of a new infinite family of self-consistent stellar models, designed to describe axisymmetric flat galaxies. The corresponding density-potential pair is obtained as a superposition of members belonging to the generalized Kalnajs family, by imposing the condition that the density can be expressed as a regular function of the gravitational potential, in order to derive analytically the corresponding equilibrium distribution functions (DF). The resulting models are characterized by a well-behaved surface density, as in the case of generalized Kalnajs discs. Then, we present a study of the kinematical behavior which reveals, in some particular cases, a very satisfactory behavior of the rotational curves (without the assumption of a dark matter halo). We also analyze the equatorial orbit's stability and Poincare surfaces of section are performed for the 3-dimensional orbits. Finally, we obtain the corresponding equilibrium DFs, using the approaches introduced by Kalnajs (Ap. J., 205, 751, 1976) and Dejonghe (Phys. Rep., 133 (3-4), 217, 1986).