Jeans modelling of axisymmetric galaxies with multiple stellar populations

We present the theoretical framework to efficiently solve the Jeans equations for multicomponent axisymmetric stellar systems, focusing on the scaling of all quantities entering them. The models may include an arbitrary number of stellar distributions, a dark matter halo, and a central supermassive black hole; each stellar distribution is implicitly described by a two- or three-integral distribution function, and the stellar components can have different structural (density profile, flattening, mass, scale length), dynamical (rotation, velocity dispersion anisotropy), and population (age, metallicity, initial mass function, mass-to-light ratio) properties. In order to determine the ordered rotational velocity and the azimuthal velocity dispersion fields of each component, we introduce a decomposition that can be used when the commonly adopted Satoh decomposition cannot be applied. The scheme developed is particularly suitable for a numerical implementation; we describe its realization within our code JASMINE2, optimized to maximally exploit the scalings allowed by the Poisson and the Jeans equations, also in the post-processing procedures. As applications, we illustrate the building of three multicomponent galaxy models with two distinct stellar populations, a central black hole, and a dark matter halo; we also study the solution of the Jeans equations for an exponential thick disc, and for its multicomponent representation as the superposition of three Miyamoto-Nagai discs. A useful general formula for the numerical evaluation of the gravitational potential of factorized thick discs is finally given.