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For refcode 1988MNRAS.233..337L:
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Copyright by Royal Astronomical Society. 1988MNRAS.233..337L Can galaxies oscillate? A self-consistent model of a non- stationary stellar system Peter D. Louis Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild-Str. 1, 8046 Garching, Federal Republic of Germany Ortwin E. Gerhard Institute of Astronomy, Madingley Road, Cambridge CB3 0HA Accepted 1988 January 11. Received 1987 December 21; in original form 1987 October 7 Summary. Observational and theoretical arguments suggest that some galaxies may be in periodically time-dependent dynamical states. For example, if the bar and bulge components of barred galaxies are indeed triaxial as inferred from photometry, and if they rotate through each other, then they cannot do so as rigidly rotating stellar systems. This paper develops the framework for studying such systems via Jeans' theorem in extended phase-space and methods analogous to those used for stationary models of galaxies. As an illustration we construct a self-consistent distribution function for a non-linear spherical mode of the isochrone sphere. This distribution function has pronounced gaps in phase-space at the locations of the resonant orbit families, which appears typical for a large class of spherical oscillations. This property may have interesting connections to the stability of spherical stellar systems, and shows that such spherical oscillations are difficult to set up. Our results show that, in principle, non-linear periodically time-dependent solutions of the combined Poisson and collisionless Boltzmann equations are possible, and indicate that further work along these lines, particularly in view of applications to barred galaxies, might be fruitful.
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