Statistics – Computation
Scientific paper
Feb 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988mnras.230..597b&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 230, Feb. 15, 1988, p. 597-627.
Statistics
Computation
71
Diffusion, Euclidean Geometry, Fokker-Planck Equation, Orbits, Stellar Motions, Entropy, Hamiltonian Functions, Maxwell-Boltzmann Density Function, Perturbation Theory, Secular Variations, Solar Neighborhood
Scientific paper
Deviations of the potentials of stellar systems from integrability cause stars to diffuse through three-dimensional orbit space. The Fokker-Planck equation that describes this diffusion takes a particularly simple form when actions are used as orbit-space coordinates. The rate of diffusion is governed by a vector Δ and a tensor Δ2, which according to the circumstances of a particular problem should be calculated either from kinetic theory or from Hamiltonian perturbation theory. In many astrophysically interesting circumstances Δ is related to the divergence of the more readily calculated tensor Δ2. In addition to being computationally handy, this relationship ensures that the orbital diffusion described by the Fokker-Planck equation causes the system's entropy, derived from any H-function, to increase whenever the system is interacting with a hotter system of scatterers. An investigation of the heating of stellar discs in the light of these general results is discussed in detail.
Binney James
Lacey Cedric
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