Efficient solution of the anisotropic spherically-aligned axisymmetric Jeans equations of stellar hydrodynamics for galactic dynamics

Abstract: I present a flexible solution for the axisymmetric Jeans equations of stellar hydrodynamics under the assumption of an anisotropic (three-integrals) velocity ellipsoid aligned with the spherical polar coordinate system. I describe and test a robust and efficient algorithm for its numerical computation. I outline the evaluation of the intrinsic velocity moments and the projection of all first and second velocity moments, including both the line-of-sight velocities and the proper motions. This spherically-aligned Jeans Anisotropic Modelling (JAM_sph) method can describe in detail the photometry and kinematics of real galaxies. It allows for a spatially-varying anisotropy, or stellar mass-to-light ratios gradients, as well as for the inclusion of general dark matter distributions and supermassive black holes. The JAM_sph method complements my previously derived cylindrically-aligned and spherical Jeans solutions, which I also summarize in this paper. I will include a reference software implementation of JAM_sph in the publicly-available JAM software package.