Dynamics of the Milky Way: tidal streams and extended distribution functions for the galactic disc

One of the key goals of Milky Way science is measuring the distribution of dark matter in the Galaxy. Through the study of Galactic dynamics, inferences can be made about the structure of the Galaxy, and hence the dark matter distribution. To this end, we present a study of methods useful for modelling and understanding dynamical systems in the Galaxy. A natural choice of coordinate system when studying dynamical systems is the canonical system of angle-action coordinates. We present methods for estimating the angle-actions in both axisymmetric and triaxial potentials. These fall into two categories: non-convergent and convergent. The non-convergent methods are fast approaches, mostly based on approximations to Stäckel potentials. We investigate the accuracy of these methods for realistic Galactic potentials. The slower convergent methods operate by constructing generating functions to take us from simple analytically-tractable potentials to our target potential. Tidal streams should prove useful for constraining the large-scale dark matter distribution in the Galaxy. Armed with our new angle-action tools, we investigate the properties of known streams in a realistic Galactic potential. We present a simple algorithm for constraining the Galactic potential using a tidal stream, which exploits the expected structure of a stream in the angle-frequency space of the true potential. We expand this approach into a fully probabilistic scheme that allows for handling of large errors, missing data and outliers. We close by discussing another tool useful for modelling the dynamics of the Galaxy: extended distribution functions for the Galactic disc. We present a simple extension of an action-based distribution function from Binney (2010) that includes metallicity information, and compare the model predictions with current data. These models are essential for incorporating the selection effects of any survey, and reveal the important chemo-dynamic correlations that expose the history and evolution of the Galaxy.