Abstract

The dynamical systems approach to galactic dynamics relies on a Hamiltonian formulation, modeling the components of a galaxy (disc, bar, and halo) via analytical gravitational potentials to study spiral arm formation. In this context, the invariant manifolds emanating from Lyapunov periodic orbits around the unstable equilibrium points at the ends of the bar delineate the arms of barred galaxies. This talk extends this classical autonomous framework to address two realistic challenges: spatial asymmetries and time-varying bar angular velocities.

First, to analyze the influence of observed mass inhomogeneities and bar-disc offsets, we study the numerical continuation of equilibrium points. We show that minor bar offsets or internal bar mass inhomogeneities distort the invariant manifolds into asymmetric two-armed structures. Severe offsets, however, trigger a pitchfork bifurcation that collapses the traditional collinear equilibria into a single unstable point, naturally generating a one-armed galaxy.

Second, to account for the secular slowing of the bar, we transition to a non-autonomous regime and adapt Lagrangian Coherent Structures (LCS). We demonstrate that LCS strainlines effectively identify regions of maximal repulsion in the time-dependent regime, proving that the global autonomous predictions remain robust. Finally, we present a data-driven methodology to extract key galactic features from a single time snapshot. We will discuss how integrating these inputs into our dynamical models paves the way for studying complex, asymmetrical systems like the Large Magellanic Cloud.

Mathematical Physics and Dynamical Systems Seminar