## Phase Space Structure of Disequilibrium in the Milky Way

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##### Date

##### Authors

Darling, Keir

##### Keyword

Galaxy , Galactic Dynamics , Milky Way , Dynamics , Dynamic Mode Decomposition , Bending waves , Simulation , Phase space , Distribution function

##### Abstract

Following Gaia Data Release 2, observations of spiral structure in the vertical phase space of the Milky Way have been made. In this thesis we set out to explain these structures, using a combination of analytic modeling, simulations, and Dynamic Mode Decomposition to study explicitly their formation and evolution in the presence of self gravity. In doing so, we have demonstrated the first application of DMD to collisionless, self-gravitating systems.
We show by comparison of self-gravitating and independent-particle simulations in a realistic Milky Way model, that the timescale of phase space spiral formation is drastically dependent on whether or not stars mutually interact. This is followed by the proposition that mutually interacting stars in a background potential conducive to oscillations can produce a persisting spiral in their phase space distribution, existing on much longer time scales than predicted by traditional kinematic phase mixing arguments.
Our proposition is investigated with use of Dynamic Mode Decomposition, which facilitates determining eigenfunctions of the time evolution operator of a system from data snapshots. We apply this to two one-dimensional models for the vertical structure of the Milky Way: the homogeneous slab, and the isothermal plane. We found that the eigenfunctions, or modes, determined for a self-gravitating system undergoing phase mixing comprise a set of modes similar to what is expected from linear perturbation theory. Particularly, the disequilibrium distribution function can be modeled as the superposition of an equilibrium mode and a combination of perturbative modes, all computed directly from snapshots of the system.
DMD solutions are determined for the isothermal plane model with a variable relative dominance of self-gravity and background potential. We find that there is a regime of relative dominance where modes of the distribution function containing pronounced spiral structure can persist on extremely long time scales. This implies that a single snapshot of a phase space spiral could belong to an evolution where the distribution function remains in a spiral for long times, driven by mutual interactions, as opposed to the spiral being a short lived transient response as in kinematic phase mixing.