Professor James Binney FRS

Abstract:

We analyse the heating of stellar discs by non axisymmetric structures and giant molecular clouds (GMCs) in N-body simulations of growing disc galaxies. The analysis resolves long-standing discrepancies between models and data by demonstrating the importance of distinguishing between measured age-velocity dispersion relations (AVRs) and the heating histories of the stars that make up the AVR. We fit both AVRs and heating histories with formulae ∝ tβ and determine the exponents β bar R and β bar z derived from in-plane and vertical AVRs and βR and βz from heating histories. Values of βz are in almost all simulations larger than values of βbarz , wheras values of βR are similar to or mildly larger than values of β bar R. Moreover, values of βz (β bar z) are generally larger than values of βR (β bar R). The dominant cause of these relations is the decline over the life of the disc in importance of GMCs as heating agents relative to spiral structure and the bar. We examine how age errors and biases in solar neighbourhood surveys in uence the measured AVR: they tend to decrease β values by smearing out ages and thus measured dispersions. We compare AVRs and velocity ellipsoid shapes σz/σR from simulations to Solar-neighbourhood data. We conclude that for the expected disc mass and dark halo structure, combined GMC and spiral/bar heating can explain the AVR of the Galactic thin disc. Strong departures of the disc mass or the dark halo structure from expectation spoil fits to the data.

Abstract:

We review the available methods for estimating actions, angles and frequencies of orbits in both axisymmetric and triaxial potentials. The methods are separated into two classes. Unless an orbit has been trapped by a resonance, convergent, or iterative, methods are able to recover the actions to arbitrarily high accuracy given sufficient computing time. Faster non-convergent methods rely on the potential being sufficiently close to a separable potential, and the accuracy of the action estimate cannot be improved through further computation. We critically compare the accuracy of the methods and the required computation time for a range of orbits in an axisymmetric multicomponent Galactic potential. We introduce a new method for estimating actions that builds on the adiabatic approximation of Schönrich and Binney and discuss the accuracy required for the actions, angles and frequencies using suitable distribution functions for the thin and thick discs, the stellar halo and a star stream. We conclude that for studies of the disc and smooth halo component of the Milky Way, the most suitable compromise between speed and accuracy is the Stäckel Fudge, whilst when studying streams the non-convergent methods do not offer sufficient accuracy and the most suitable method is computing the actions from an orbit integration via a generating function. All the software used in this study can be downloaded from https://github.com/jls713/tact.