On the dynamics of tidal streams in the Milky Way galaxy

We present a brief history of Galactic astrophysics, and explain the origin of halo substructure in the Galaxy. We motivate our study of tidal streams by highlighting the tight constraints that analysis of the trajectories of tidal streams can place on the form of the Galactic potential. We address the reconstruction of orbits from observations of tidal streams. We upgrade the scheme reported by Binney (2008) and Jin & Lynden-Bell (2007), which reconstructs orbits from streams using radial-velocity measurements, to allow it to work with erroneous input data. The upgraded algorithm can correct for both statistical error on observations, and systematic error due to streams not delineating individual orbits, and given high-quality but realistic input data, it can diagnose the potential with considerable accuracy. We complement the work of Binney (2008) by deriving a new algorithm, which reconstructs orbits from streams using proper-motion data rather than radial velocities. We show that the new algorithm has a similar potency for diagnosing the Galactic potential. We explore the concept of Galactic parallax, which arises in connection with our proper-motion study. Galactic parallax allows trigonometric distance calculation to stars at 40 times the range of conventional parallax, although its applicability is limited to only those stars in tidal streams. We examine from first principles the mechanics of tidal stream formation and propagation. We find that the mechanics of tidal streams has a natural expression in terms of action-angle variables. We find that tidal streams in realistic galaxy potentials will generally not delineate orbits, and that attempting to constrain the Galactic potential by assuming that they do can lead to large systematic error. We show that we can accurately predict the real-space trajectories of streams, even when they differ significantly from orbits.