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Dynamics of secular evolution

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Author:  James Binney (Oxford University) 
















Description 
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 stellardynamical 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 angleaction 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 phasespace mixing in slowly evolving potentials. Surfaces of section and frequency analysis are introduced as diagnostics of phasespace structure. Real galactic potentials include a fluctuating part that drives the system towards unattainable thermal equilibrium. Twobody encounters are only one source of fluctuations, and all fluctuations will drive similar evolution. We derive the orbitaveraged FokkerPlanck equation and relations that hold between the secondorder diffusion coefficients and both the power spectrum of the fluctuations and the firstorder diffusion coefficients. From the observed heating of the solar neighbourhood we show that the secondorder 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 tightlywound 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 LinShuKalnajs dispersion relation and even global normalmode calculations provide a very incomplete understanding of the dynamics of stellar discs. 

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