Astronomy and Astrophysics – Astronomy
Scientific paper
May 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010dda....41.0506v&link_type=abstract
American Astronomical Society, DDA meeting #41, #5.06; Bulletin of the American Astronomical Society, Vol. 41, p.930
Astronomy and Astrophysics
Astronomy
Scientific paper
This paper describes a low-dimensional model of the dynamics of a galaxy that possesses triplanar symmetry with planes of symmetry that are fixed in an inertial frame of reference. The governing equations are the complete set of moment equations of the second order associated with the collisionless Boltzmann equation. A subset of the moment equations reduces to the tensor virial equations. The remaining moment equations govern the evolution of the kinetic energy tensor of the system. Closure of the moment equations requires a specification of the density distribution in the galaxy and the velocity field describing the mean motions of the stars. In the closure of the equations for the present model, the galaxy is represented as a heterogeneous ellipsoid with an arbitrary stratification of the density, and the adopted velocity field sustains that density distribution consistently with the equation of continuity. The virial equations reduce in that case to a system of ordinary differential equations governing the semi-axes of an ellipsoid that characterizes the size and shape of the galaxy. The evolution of the model is quasi-homologous in the sense that the semi-axes are functions of time, whereas the stratification of the density does not change. The equations governing the kinetic energy tensor are solved with the aid of non-classical integrals of the motion, which were discovered by G. Som Sunder and R. K. Kochhar. With the resulting elimination of the kinetic energy tensor in the virial equations, the dynamics of the galaxy is reduced to the dynamics of an oscillator in three degrees of freedom. An application of this model to a study of chaos in the oscillations of galaxies is described in a poster paper to be presented at this meeting.
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