Astronomy and Astrophysics – Astrophysics
Scientific paper
2008-06-26
Astronomy and Astrophysics
Astrophysics
Submitted to MNRAS
Scientific paper
We present the derivation of two-integral distribution functions for the first four members of the family of generalized Kalnajs discs, recently obtained by Gonzalez and Reina (MNRAS, 371, 1873, 2006), and 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's 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.
Gonzalez Guillermo A.
Pedraza Juan F.
Ramos-Caro Javier
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