Linear response theory and damped modes of stellar clusters. Issue 2 (21st October 2021) - Fouvry, Jean-Baptiste; Prunet, Simon
ABSTRACT: Because all stars contribute to its gravitational potential, stellar clusters amplify perturbations collectively. In the limit of small fluctuations, this is described through linear response theory, via the so-called response matrix. While the evaluation of this matrix is somewhat straightforward for unstable modes (i.e. with a positive growth rate), it requires a careful analytic continuation for damped modes (i.e. with a negative growth rate). We present a generic method to perform such a calculation in spherically symmetric stellar clusters. When applied to an isotropic isochrone cluster, we recover the presence of a low-frequency weakly damped ℓ = 1 mode. We finally use a set of direct N -body simulations to test explicitly this prediction through the statistics of the correlated random walk undergone by a cluster's density centre.