LOWERED EVANS MODELS - ANALYTIC DISTRIBUTION-FUNCTIONS OF OBLATE HALOPOTENTIALS

We describe an analytic distribution function of a finite, oblate stel lar system, which is useful for the practical modelling of dark haloes . The function is determined by lowering Evans's distribution function of a flattened, cored isothermal system in analogy with the lowering of the singular, isothermal sphere in the definition of the King model s. We derive analytic expressions for the density, maximal streaming v elocity and velocity dispersion profiles as functions 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 lambda = 0.0, 0.05 and 0.18 using N-body simulatio ns with 50 000 particles. The lambda = 0.18 model is unstable to the f ormation of a triaxial bar within approximately 5 King radii, while th e other models appear stable. We conclude that the slowly rotating sys tems are useful for modelling flattened dark haloes.