Using Multichannel Singular Spectrum Analysis to Study Galaxy Dynamics
  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.
