Statistics – Computation
Scientific paper
May 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990mnras.244..111e&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 244, May 1, 1990, p. 111-129. Research supported by SER
Statistics
Computation
20
Astronomical Models, Computational Astrophysics, Stellar Systems, Angular Momentum, Distribution Functions, Equations Of Motion, Hydrodynamics, Isophotes, Kinematics, Orbital Mechanics
Scientific paper
The family of flattened isochrones is introduced. This comprises a one-parameter sequence of oblate or prolate mass models whose gravitational potential is of Staeckel form in spheroidal coordinates. Properties of the mass model and its projection on the plane of the sky are derived. In the equatorial plane, the potential is exactly that of the isochrone and the orbits are expressible as elementary functions. This is the simplest possible behavior for spheroidal Eddington systems. For the most elementary flattened isochrone, two distinct distribution functions are found. The thin shell model, in which all orbits are infinitesimally thin short-axis tubes, has a distribution function that is an elementary function of the turning points. The Jeans model, in which the distribution function depends only on the classical isolating integrals, the energy and component of angular momentum parallel to the symmetry axis, can be found using integral transform methods. For both models, the equations of stellar hydrodynamics can be simply solved and analytic expressions deduced for the velocity dispersions.
de Zeeuw Tim P.
Evans Wyn N.
Lynden-Bell Donald
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