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

TL;DR

This paper derives analytical solutions for the Jeans equations in galaxy models combining Miyamoto-Nagai discs with Binney logarithmic haloes, enabling flexible modeling of galaxy dynamics and gas flows.

Contribution

It provides a general analytical framework for two-integrals Jeans equations in composite galaxy models, including special cases like the Singular Isothermal Sphere.

Findings

Analytical solutions for Jeans equations in composite galaxy models.

Formulas applicable to numerical simulations and stellar dynamics testing.

Estimation of interstellar medium inflow velocities based on stellar mass loss.

Abstract

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.