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

## TL;DR

This paper introduces a new axisymmetric Jeans modeling method aligned with spherical coordinates, enabling detailed galaxy kinematic analysis with variable anisotropy and dark matter, validated on a large galaxy sample.

## Contribution

The paper presents JAM_sph, a novel, efficient algorithm for axisymmetric Jeans equations with spherical alignment, expanding galaxy dynamical modeling capabilities.

## Key findings

- JAM_sph accurately models galaxy kinematics and photometry.
- Results from JAM_sph and JAM_cyl are statistically consistent.
- The method is validated on the Atlas3D galaxy sample.

## Abstract

I present a flexible solution for the axisymmetric Jeans equations of stellar hydrodynamics under the assumption of an anisotropic (three-integral) 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 JAM_cyl and spherical Jeans solutions, which I also summarize in this paper. Comparisons between results obtained with either JAM_sph or JAM_cyl can be used to asses the robustness of inferred dynamical quantities. As an illustration, I modelled the Atlas3D sample of 260 early-type galaxies with high-quality integral-field spectroscopy, using both methods. I found that they provide statistically indistinguishable total-density logarithmic slopes. This may explain the previously-reported success of the JAM method in recovering density profiles of real or simulated galaxies. A reference software implementation of JAM_sph is included in the publicly-available JAM software package.

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Source: https://tomesphere.com/paper/1907.09894