The Dynamical Inverse Problem for Axisymmetric Stellar Systems

The standard method of modelling axisymmetric stellar systems begins from the assumption that mass follows light. The gravitational potential is then derived from the luminosity distribution, and a unique two-integral distribution function f(E,Lz) that generates the stellar density in this potential is found. We show that the gravitational potential can instead be generated directly from the velocity data in a two-integral galaxy, thus allowing one to drop the assumption that mass follows light. The rotational velocity field can also be recovered in a model-independent way. We present regularized algorithms for carrying out the inversions and test them by application to pseudo-data from a family of oblate models.Comment: 23 LATEX pages, 5 Postscript figures, uses AASTEX, epsf.sty. To appear in The Astronomical Journal, Vol. 112, September 199

Optimal Smoothing for N-Body Codes

In any collisionless N-body code, there is an optimal choice for the smoothing parameter that minimizes the average error in the force evaluations. We show how to compute the optimal softening length in a direct-summation code and demonstrate that it varies roughly as 1/N^(1/3).Comment: 6 TEX pages, 3 PostScript figures, uses AASTEX, epsf.sty. Submitted to The Astronomical Journal, November 1995; revised January 199