Theoretical astrophysics and plasma physics at RPC

Abstract:

The text of lectures to the 2011 Tenerife Winter School. The School's theme was "Secular Evolution of Galaxies" and my task was to present the underlying stellar-dynamical theory. Other lecturers were speaking on the role of bars and chemical evolution, so these topics are avoided here. We start with an account of the connections between isolating integrals, quasiperiodicity and angle-action variables - these variables played a unifying role throughout the lectures. This leads on to the phenomenon of resonant trapping and how this can lead to chaos in cuspy potentials and phase-space mixing in slowly evolving potentials. Surfaces of section and frequency analysis are introduced as diagnostics of phase-space structure. Real galactic potentials include a fluctuating part that drives the system towards unattainable thermal equilibrium. Two-body encounters are only one source of fluctuations, and all fluctuations will drive similar evolution. We derive the orbit-averaged Fokker-Planck equation and relations that hold between the second-order diffusion coefficients and both the power spectrum of the fluctuations and the first-order diffusion coefficients. From the observed heating of the solar neighbourhood we show that the second-order diffusion coefficients must scale as J^{1/2}. We show that periodic spiral structure shifts angular momentum outwards, heating at the Lindblad resonances and mixing at corotation. The equation that would yield the normal modes of a stellar disc is first derived and then used to discuss the propagation of tightly-wound spiral waves. The winding up of such waves is explains why cool stellar discs are responsive systems that amplify ambient noise. An explanation is offered of why the Lin-Shu-Kalnajs dispersion relation and even global normal-mode calculations provide a very incomplete understanding of the dynamics of stellar discs.

Abstract:

We present a new method for detecting and correcting systematic errors in the distances to stars when both proper motions and line-of-sight velocities are available. The method, which is applicable for samples of 200 or more stars that have a significant extension on the sky, exploits correlations between the measured U, V and W velocity components that are introduced by distance errors. We deliver a formalism to describe and interpret the specific imprints of distance errors including spurious velocity correlations and shifts of mean motion in a sample. We take into account correlations introduced by measurement errors, Galactic rotation and changes in the orientation of the velocity ellipsoid with position in the Galaxy. Tests on pseudo-data show that the method is more robust and sensitive than traditional approaches to this problem. We investigate approaches to characterizing the probability distribution of distance errors, in addition to the mean distance error, which is the main theme of the paper. Stars with the most overestimated distances bias our estimate of the overall distance scale, leading to the corrected distances being slightly too small. We give a formula that can be used to correct for this effect. We apply the method to samples of stars from the Sloan Extension for Galactic Understanding and Exploration (SEGUE) survey, exploring optimal gravity cuts, sample contamination, and correcting the used distance relations. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.

Abstract:

In a disc galaxy, the distribution of azimuthal components of velocity is very skew. In the past, this skewness has been modelled by superposed Gaussians. We use dynamical arguments to derive an analytic formula that can be fitted to observed velocity distributions, and validate it by fits to the velocities derived from a dynamically rigorous model, and to a sample of local stars with accurate space velocities. Our formula is much easier to use than a full distribution function. It has fewer parameters than a multi-Gaussian fit, and the best-fitting model parameters give insight into the underlying disc dynamics. In particular, once the azimuthal velocities of a sample have been successfully fitted, the apparatus provides a prediction for the corresponding distribution of radial velocitiesvR. An effective formula like ours is invaluable when fitting to data for stars at some distance from the Sun because it enables one to make proper allowance for the errors in distance and proper motion when determining the underlying disc kinematics. The derivation of our formula elucidates the way the horizontal and vertical motions are closely intertwined, and makes it evident that no stellar population can have a scaleheight and vertical velocity dispersions that are simultaneously independent of radius. We show that the oscillation of a star perpendicular to the Galactic plane modifies the effective potential in which the star moves radially in such a way that the more vertical energy a star has, the larger is the mean radius of its orbit. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.