In a separate paper (Bertin & Varri) we have described a general method for the construction of self-consistent non-spherical models of quasi-relaxed stellar systems, and, in particular, of those that extend the spherical King models to the case in which an external tidal field is taken into account explicitly. Here we describe the resulting two parameter family of physically justified triaxial models, characterized by a concentration parameter (as for the spherical case) and by a second parameter, the tidal strength, defined as the square of the ratio of the orbital revolution frequency to the central dynamical frequency of the stellar system. The most significant departures from spherical symmetry occur when the truncation radius is of the order of the tidal radius, which, for a given concentration, sets a maximum value to the allowed tidal strength. We illustrate several properties that characterize the intrinsic and the projected structure of the models. Under the guidance of this analytical framework, by means of N-body simulations we also show that, as a result of the presence of a tidal field, an initially spherical configuration tends to evolve into configurations similar to those predicted by our analytical equilibrium models.
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