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Non-radial instabilities in collapsing galaxies: an analytically solvable model


 This study examines the stability of a family of simplified, collisionless models of galaxy collapse, to fluid-like perturbations that leave the radial density profile unaltered, but distort the galaxy’s shape. The unperturbed models have constant density, and exhibit fully non-linear oscillations around an equilibrium radius in physical space. The equations that determine the time-development of perturbations in the linear regime are derived, and are shown to be of the Mathieu type; they are solved in the special case of the quadrupole mode. The ranges of values of the usual parameter 2T/|W| for which instability exists, leading inevitably to triaxial solutions, are determined. It is shown that, for 2T/|W|<0.1541, the initial configurations are unstable and the growth time of the instability is sufficiently short to lead to flattened final configurations. It is suggested that all of these results apply to realistic models of galaxy collapse.