Distribution functions for a family of axially symmetric galaxy models

TL;DR

This paper derives distribution functions for a family of axially symmetric galaxy models with finite radius, using potential-density pairs, Kalnajs' method, and maximum entropy principles, providing new equilibrium state models.

Contribution

It introduces a novel approach to derive distribution functions for the first four members of a galaxy disk family, combining multiple methods including maximum entropy.

Findings

Derived distribution functions depending on the Jacobi integral.

Obtained new equilibrium models for finite flat galaxy disks.

Extended the methods to include odd parts of distribution functions.

Abstract

We present the derivation of distribution functions for the first four members of a family of disks, previously obtained in (MNRAS, 371, 1873, 2006), which represent a family of axially symmetric galaxy models with finite radius and well behaved surface mass density. In order to do this we employ several approaches that have been developed starting from the potential-density pair and, essentially using the method introduced by Kalnajs (Ap. J., 205, 751, 1976) we obtain some distribution functions that depend on the Jacobi integral. Now, as this method demands that the mass density can be properly expressed as a function of the gravitational potential, we can do this only for the first four discs of the family. We also find another kind of distribution functions by starting with the even part of the previous distribution functions and using the maximum entropy principle in order to find the odd part and so a new distribution function, as it was pointed out by Dejonghe (Phys. Rep., 133, 217, 1986). The result is a wide variety of equilibrium states corresponding to several self-consistent finite flat galaxy models.