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

**Authors:** Michele Cappellari  
**arXiv:** [1907.09894](https://arxiv.org/abs/1907.09894)  
**Date:** 2019-07-23  
**Summary page:** https://www.summarizepaper.com/en/paper/1907.09894v2/

## Key points

- Michele Cappellari presents a new method called the spherically-aligned Jeans Anisotropic Modelling (JAM_sph) for solving the axisymmetric Jeans equations of stellar hydrodynamics
- JAM_sph assumes an anisotropic (three-integral) velocity ellipsoid aligned with the spherical polar coordinate system and allows for spatially-varying anisotropy or stellar mass-to-light ratio gradients as well as general dark matter distributions and supermassive black holes
- Cappellari outlines a robust and efficient algorithm for numerical computation and describes how to evaluate intrinsic velocity moments and project all first and second velocity moments including both line-of-sight velocities and proper motions
- The JAM_sph method can accurately describe photometry and kinematics of real galaxies, complementing previously derived cylindrically-aligned JAM_cyl and spherical Jeans solutions
- To assess its robustness in inferring dynamical quantities, Cappellari models the Atlas3D sample of 260 early-type galaxies with high-quality integral field spectroscopy using both methods
- He finds that they provide statistically indistinguishable total density logarithmic slopes which may explain why previous studies have reported success in recovering density profiles of real or simulated galaxies using JAM methods
- A reference software implementation of JAM_sph is included in the publicly available JAM software package
- Overall, this new method provides a flexible solution to better understand galactic dynamics by accurately modeling photometry and kinematics while allowing for complex astrophysical phenomena such as dark matter distributions and supermassive black holes.

## Summary

In the paper "Efficient solution of the anisotropic spherically-aligned axisymmetric Jeans equations of stellar hydrodynamics for galactic dynamics," Michele Cappellari presents a new method, called the spherically-aligned Jeans Anisotropic Modelling (JAM_sph), for solving the axisymmetric Jeans equations of stellar hydrodynamics. The JAM_sph method assumes an anisotropic (three-integral) velocity ellipsoid aligned with the spherical polar coordinate system and allows for a spatially-varying anisotropy or stellar mass-to-light ratio gradients as well as for the inclusion of general dark matter distributions and supermassive black holes. Cappellari outlines a robust and efficient algorithm for numerical computation and describes how to evaluate intrinsic velocity moments and project all first and second velocity moments including both line-of-sight velocities and proper motions. The JAM_sph method can accurately describe photometry and kinematics of real galaxies, complementing previously derived cylindrically-aligned JAM_cyl and spherical Jeans solutions. To assess its robustness in inferring dynamical quantities, Cappellari models the Atlas3D sample of 260 early-type galaxies with high-quality integral field spectroscopy using both methods. He finds that they provide statistically indistinguishable total density logarithmic slopes which may explain why previous studies have reported success in recovering density profiles of real or simulated galaxies using JAM methods. A reference software implementation of JAM_sph is included in the publicly available JAM software package. Overall, this new method provides a flexible solution to better understand galactic dynamics by accurately modeling photometry and kinematics while allowing for complex astrophysical phenomena such as dark matter distributions and supermassive black holes.