Extended stellar hydrodynamics for galactic discs. II
Abstract
A highermoment 3D model for axisymmetric threeintegral disc galaxies is reexamined and modified slightly in order to take proper account of the possibly nonellipsoidal 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 nonisothermality to the third isolating integral, and none to the deviations of the vertical and verticalradial kurtoses from their Maxwellian values. It is argued that such a model is also appropriate for comparison with observations. The simple `modelfree' 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.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 December 1991
 DOI:
 10.1093/mnras/253.3.427
 Bibcode:
 1991MNRAS.253..427C
 Keywords:

 Galactic Structure;
 Hydrodynamic Equations;
 Three Dimensional Models;
 Astronomical Models;
 Distribution Functions;
 Elliptical Galaxies;
 HamiltonJacobi Equation;
 Milky Way Galaxy;
 Velocity Distribution;
 Astrophysics