EXTENDED STELLAR HYDRODYNAMICS FOR GALACTIC DISKS .2.

A higher-moment 3D model for axisymmetric three-integral disc galaxies is re-examined examined and modified slightly in order to take proper account of the possibly non-ellipsoidal character of the velocity distribution. General recurrence relations are found, relating certain successive even moments of arbitrary order, which are seen as generalizations of the original closure assumptions. Therefore the closure assumptions can be taken at any moment order, since the model equations generated by the generalized closure relations are valid at all levels of the infinite hierarchy of moment equations. By virtue of the formal equivalence between the infinite set of moments and the distribution function, this strongly suggests that the distribution function which underlies the model is a solution of the collisionless Boltzmann equation within the approximations of the model. The physical significance of the model is seen as attributing all of the vertical non-isothermality to the third isolating integral, and none to the deviations of the vertical and vertical-radial kurtoses from their Maxwellian values. It is argued that such a model is also appropriate for comparison with observations. The simple 'model-free' analytic expression derived in the previous paper (valid for all kinds of potential) for the orientation of the velocity ellipsoid at points near the plane is shown to yield the correct orientation exactly for any system in which the potential is Stackel separable in general spheroidal coordinates. A possible functional form for the distribution function corresponding to the model is also discussed.