3-INTEGRAL OBLATE GALAXY MODELS

A simple numerical scheme is presented for the construction of three-i ntegral phase-space distribution functions for oblate galaxy models wi th a gravitational potential of Stackel form, and an arbitrary axisymm etric luminous density distribution. The intrinsic velocity moments ca n be obtained simultaneously with little extra effort. The distributio n of the inner and outer turning points of the short-axis tube orbits that are populated can be specified freely, and is chosen in advance. The entire distribution function is then derived from the density by a n iterative scheme that starts from the explicitly known distribution function of the thin-orbit (maximum streaming) model, in which only th e tubes with equal inner and outer turning points are populated. The v ersatility and limitations of this scheme are illustrated by the const ruction of a number of self-consistent three-integral flattened isochr one models of Kuzmin-Kutuzov type, and by investigation of special cas es where the scheme is tractable analytically. This includes the behav iour of the distribution functions in the outer regions of the models. The scheme converges rapidly for models containing orbits with ratios of the outer to inner turning point as large as ten, and is particula rly suited for the construction of tangentially anisotropic flattened models, self-consistent as well as non-consistent. The algorithm simpl ifies in the disc and spherical limits, and can be generalized to tria xial models.