Distribution functions for a family of axially symmetric galaxy models

Understand

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.