General spherical anisotropic Jeans models of stellar kinematics: including proper motions and radial velocities

TL;DR

This paper extends the spherical Jeans modeling framework to include all three components of projected stellar kinematics, including proper motions, enabling more comprehensive analysis of stellar systems.

Contribution

It generalizes the spherical Jeans formalism by providing expressions for all projected second moments, including proper motions, with an implementation in the JAM software package.

Findings

Includes proper motion components in the formalism.

Provides explicit expressions for all three projected second moments.

Implementation available in the JAM software package.

Abstract

Cappellari (2008) presented a flexible and efficient method to model the stellar kinematics of anisotropic axisymmetric and spherical stellar systems. The spherical formalism could be used to model the line-of-sight velocity second moments allowing for essentially arbitrary radial variation in the anisotropy and general luminous and total density profiles. Here we generalize the spherical formalism by providing the expressions for all three components of the projected second moments, including the two proper motion components. A reference implementation is now included in the public JAM package available at http://purl.org/cappellari/software