Structure of box-shaped bulges and other spheroidal components

We use a systematic approach to the choice of distribution functions to construct models of box-shaped spheroidal components. We argue that box-shaped bulges differ from elliptical spheroidal components in that in box-shaped systems, only a particular two-dimensional subset of the full three-dimensional continuum of possible orbits is heavily populated. This conjecture is tested by means of two families of distribution functions tailored to yield models with the same radial density profile as Henon's isochrone model. In a given spherical potential, the members of one family generate elliptical models while members of the second family generate models with rectangular isophotes. The rotation properties of models of the two families differ principally in that box-shaped models ‘rotate on cylinders’, in contrast to the more nearly spheroidal rotation characteristic of the elliptical models. This distinction is expected on general grounds and is in agreement with observation. It is argued that distribution functions of the type that generate box-shaped systems can arise either through the cannibalism of small galaxies by large, or through mergers of favourably inclined pairs of galaxies.