Linear stability and linear response of stellar clusters with the matrix method
Abstract
In the last few decades, observational evidence showed that spheroidal stellar systems of all scales – from the smallest star clusters to the largest galaxies – display significant kinematic diversity: various flavours of anisotropy (preference for more elongated or more circular orbits), and net angular momentum (preferred direction of the azimuthal velocity). Yet, the stability and evolution of anisotropic, rotating spheroidal systems have been scarcely studied. What degree of anisotropy and rotation is expected at the formation of these structures, and at various epochs of their evolution? How does the environment impact their kinematics? In essence, the way in which stellar clusters respond to perturbations is central to their fate, because it allows them to access the free energy reservoir contained in their ordered kinematics. I will describe an analytical method to compute a stellar cluster’s response to an external perturbation, based on linear response theory: the matrix method. I will then illustrate how this theory can be used in two contexts: (i) to evaluate the stability of rotating globular cluster models, and (ii) to compute the way the Milky Way halo responds to the infall of the Large Magellanic Cloud.