By Jason Sanders
This paintings provides a research of tools beneficial for modeling and realizing dynamical structures within the Galaxy. A usual coordinate procedure for the examine of dynamical platforms is the angle-action coordinate process. New tools for the approximation of the action-angle variables in most cases potentials are provided and mentioned. those new instruments are utilized to the development of dynamical versions for 2 of the Galaxy’s parts: tidal streams and the Galactic disc. Tidal streams are remnants of tidally stripped satellites within the Milky method that have the results of the big scale constitution of the Galactic gravitational strength, whereas the Galactic disc offers insights into the character of the Galaxy close to the sunlight. acceptable action-based types are offered and mentioned for those elements, and prolonged to incorporate additional details reminiscent of the metallicity of stars.
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Extra resources for Dynamics of the Milky Way: Tidal Streams and Extended Distribution Functions for the Galactic Disc
Therefore, given a point (x, v), we follow this procedure: 1. We begin by calculating the z-component of the angular momentum, L z , and the energy, E, in the ‘true’ potential. 2. We then integrate the orbit in the ‘true’ potential. We use the initial time-steps of the orbit integration to find the best-fitting coordinate system: at several points along the orbit we evaluate Eq. 15) and average to find a sufficiently accurate value for a. With the coordinate system found, we continue integrating to find the edges of the orbit, λ+ , λ− and ν+ , that define the fitting region.
For the radial and vertical angle, the largest error occurs at apoapsis. In a Stäckel potential, the momenta, pτ , depend on τ and the isolating integrals, which, once determined, are taken to be constant. Therefore, at a given location in the orbit, the angle is solely a function of the position coordinates and the velocity information is essentially ignored. Around turning points in the orbit, the velocity coordinates contain the majority of the information, whilst the position coordinates are changing very slowly.
7 Overview of Thesis 15 presence of selection effects. Surveys naturally select in the colour and magnitude of the stars, which in turn affects the observed metallicity distribution. Metallicity and age are believed to be correlated with velocity as, for instance, older metal-poor stars are members of hotter populations. Therefore, inclusion of metallicity in a distribution function is necessary for modelling the dynamics of a survey. Additionally, it provides a probe of the formation and history of the Galaxy, and useful leverage on constraining the Galactic potential.