An Iterative Method for the Construction of Equilibrium N-Body Models for Stellar Disks

Abstract

One widely used technique for the construction of equilibrium models of stellar disks is based on the Jeans equations and the moments of velocity distribution functions derived using these equations. Stellar disks constructed using this technique are shown to be "not entirely" in equilibrium. Our attempt to abandon the epicyclic approximation and the approximation of infinite isothermal layers, which are commonly adopted in this technique, failed to improve the situation substantially. We conclude that the main drawback of techniques based on the Jeans equations is that the system of equations employed is not closed, and therefore requires adopting an essentially ad hoc additional closure condition. A new iterative approach to constructing equilibrium N-body models with a given density distribution is proposed. The main idea behind this approach is that a model is first constructed using some approximation method, and is then allowed to adjust to an equilibrium state with the specified density and the required parameters of the velocity distribution remaining fixed in the process. This iterative approach was used to construct isotropic, spherically symmetric models and models of stellar disks embedded in an external potential. The numerical models constructed prove to be close to equilibrium. It is shown that the commonly adopted assumption that the profile of the radial velocity dispersion is exponential may be wrong. The technique proposed can be applied to a wide range of problems involving the construction of models of stellar systems with various geometries.