Coupling Basis Function Expansion with Multi-Channel Singular Spectrum Analysis: a Powerful Toolkit for Dynamical Systems

Dynamical evolution of astronomical systems is driven by a complex interplay of features on many scales, both in simulations and in nature. Until now, there have been few tools that enable discovery of the underlying dynamical processes. We develop the combination of basis function expansions (BFEs) with multi-channel singular spectrum analysis (M-SSA) to address this challenge for the case of self-gravitating systems described by phase-space distribution functions. When applied to a simulation of an isolated Milky-Way-like galaxy the BFE/M-SSA combination is able to cleanly separate three low level features in this near-equilibrium, multi-component system: particle noise; phase-mixing from an initially mild disequilibrium; and structures forming due to a dynamical coupling of the disk and halo components. These successes demonstrate the power of this technique as a toolkit for dynamical analysis more generally.