Using Multichannel Singular Spectrum Analysis to Study Galaxy Dynamics

TL;DR

This paper introduces multichannel singular spectrum analysis (M-SSA), a novel method for analyzing galaxy dynamics by extracting dominant spatial and temporal trends from simulation data, revealing insights into bar formation, evolution, and previously unnoticed dynamics.

Contribution

The paper presents M-SSA as a new analytical tool for galaxy simulations, capable of discovering correlated space-time signals and uncovering new dynamical features.

Findings

M-SSA describes bar formation and evolution in galaxy simulations.

It uncovers mode coupling and pattern-speed decay.

It reveals previously unnoticed dynamics in existing simulations.

Abstract

N-body simulations provide most of our insight into the structure and evolution of galaxies, but our analyses of these are often heuristic and from simple statistics. We propose a method that discovers the dynamics in space and time together by finding the most correlated temporal signals in multiple time series of basis function expansion coefficients and any other data fields of interest. The method extracts the dominant trends in the spatial variation of the gravitational field along with any additional data fields through time. The mathematics of this method is known as multichannel singular spectrum analysis (M-SSA). In essence, M-SSA is a principal component analysis of the covariance of time series replicates, each lagged successively by some interval. The dominant principal component represents the trend that contains the largest fraction of the correlated signal. The next principal component is orthogonal to the first and contains the next largest fraction, and so on. Using a suite of previously analysed simulations, we find that M-SSA describes bar formation and evolution, including mode coupling and pattern-speed decay. We also analyse a new simulation tailored to study vertical oscillations of the bar using kinematic data. Additionally, and to our surprise, M-SSA uncovered some new dynamics in previously analysed simulations, underscoring the power of this new approach.