Lowered Evans Models: Analytic Distribution Functions of Oblate Halo Potentials

Abstract

We describe an analytic distribution function of a finite, oblate stellar system that is useful for the practical modelling of dark halos. The function is determined by lowering Evans's (1993) distribution function of a flattened, cored isothermal system in analogy to the lowering of the singular, isothermal sphere in the definition of the King (1966) models. We derive analytic expressions of the density, maximal streaming velocity and velocity dispersion profiles as a function of the potential. As for the King models, the potential must be calculated numerically. We also present a recipe for generating N-body realizations of this distribution function and examine the stability in three models with dimensionless spins $λ=$0.0, 0.05 and 0.18 using N-body simulations with 50,000 particles. The $λ=0.18$ model is unstable to the formation of a triaxial bar within $\sim 5$ King radii while the other models appear stable. We conclude that the slowly rotating systems are useful for modelling flattened dark halos.