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We present the analytical solution of the two-integrals Jeans equations forMiyamoto-Nagai discs embedded in Binney logarithmic dark matter haloes. Theequations can be solved (both with standard methods and with the ResidueTheorem) for arbitrary choices of the parameters, thus providing a veryflexible two-component galaxy model, ranging from flattened discs to sphericalsystems. A particularly interesting case is obtained when the dark matter haloreduces to the Singular Isothermal Sphere. Azimuthal motions are separated inthe ordered and velocity dispersion components by using the Satohdecomposition. The obtained formulae can be used in numerical simulations ofgalactic gas flows, for testing codes of stellar dynamics, and to study thedependence of the stellar velocity dispersion and of the asymmetric drift inthe equatorial plane as a function of disc and halo flattenings. Here, weestimate the inflow radial velocities of the interstellar medium, expected bythe mixing of the stellar mass losses of the lagging stars in the disc with apre-existing gas in circular orbit.

Miyamoto-Nagai discs embedded in the Binney logarithmic potential: analytical solution of the two-integrals Jeans equations