A FAMILY OF TRIAXIAL MASS MODELS WITH CENTRAL CUSPS

A simple family of triaxial mass models with a central density cusp is described, for which the projected surface density can be calculated easily. It can show ellipticity variations and isophote twists. These models are flattened versions of the popular spherical gamma-models wi th density profile rho(r)proportional to r(-gamma)(r(0)+r)(gamma-4). T hey are constructed by the addition of two spherical harmonic terms to the potential of the spherical model. The convolution of the surface brightness with a given point spread function is given. The intrinsic shape of the mass density, as a function of the viewing angles, can be derived from the observed ellipticities and the major axis position a ngles at small and large radii. This allows a convenient comparison wi th observations of real galaxies. For a large range of flattenings and cusp slopes, the simple closed orbits in these potentials are accurat ely described by first-order epicyclic theory. This formalism is there fore well-suited for modelling, for example, the velocities of the ion ized gas discs detected in the nuclei of many elliptical galaxies, the mass distributions of which are well-represented by the triaxial gamm a-models.