Miyamoto-Nagai discs embedded in the Binney logarithmic potential:
  analytical solution of the two-integrals Jeans equations
  We present the analytical solution of the two-integrals Jeans equations for
Miyamoto-Nagai discs embedded in Binney logarithmic dark matter haloes. The
equations can be solved (both with standard methods and with the Residue
Theorem) for arbitrary choices of the parameters, thus providing a very
flexible two-component galaxy model, ranging from flattened discs to spherical
systems. A particularly interesting case is obtained when the dark matter halo
reduces to the Singular Isothermal Sphere. Azimuthal motions are separated in
the ordered and velocity dispersion components by using the Satoh
decomposition. The obtained formulae can be used in numerical simulations of
galactic gas flows, for testing codes of stellar dynamics, and to study the
dependence of the stellar velocity dispersion and of the asymmetric drift in
the equatorial plane as a function of disc and halo flattenings. Here, we
estimate the inflow radial velocities of the interstellar medium, expected by
the mixing of the stellar mass losses of the lagging stars in the disc with a
pre-existing gas in circular orbit.
