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We present the formulation of a new infinite family of self‐consistent stellar models, designed to describe axisymmetric flat galaxies. The corresponding density–potential pair is obtained as a superposition of members belonging to the generalized Kalnajs family, by imposing the condition that the density can be expressed as a regular function of the gravitational potential, in order to derive analytically the corresponding equilibrium distribution functions (DFs). The resulting models are characterized by a well‐behaved surface density, as in the case of generalized Kalnajs discs. Then, we present a study of the kinematical behaviour which reveals, in some particular cases, a very satisfactory behaviour of the rotational curves (without the assumption of a dark matter halo). We also analyse the equatorial orbit's stability, and Poincaré surfaces of section are performed for the three‐dimensional orbits. Finally, we obtain the corresponding equilibrium DFs, using the approaches introduced by Kalnajs and Dejonghe.

An infinite family of self‐consistent models for axisymmetric flat galaxies