Numerical linear stability analysis of round galactic disks

The method originally developed by Kalnajs for the numerical linear stability analysis of round galactic disks is implemented in the regimes of non-analytic transformations between position space and angle-action space, and of vanishing growth rates. This allows effectively any physically plausible disk to be studied, rather than only those having analytic transformations into angle-action space which have formed the primary focus of attention to date. The transformations are constructed numerically using orbit integrations in real space, and the projections of orbit radial actions on a given potential density basis are Fourier transformed to obtain a dispersion relation in matrix form. Nyquist diagrams are used to isolate modes growing faster than a given fraction of the typical orbital period and to assess how much extra mass would be required to reduce the growth rate of the fastest mode below this value. To verify the implementation, the fastest m = 2 growth rates of the isochrone and the Kuzmin-Toomre disks are recovered, and the weaker m = 2 modes are computed. The evolution of those growth rates as a function of the halo mass is also calculated, and some m = 1 modes are derived as illustration. Algorithmic constraints on the method’s scope are assessed and its application to observed disks is discussed. keywords: Galaxies – methods: analytical, numerical – stability, dynamics, disks – bars. To appear in Monthly Notices of the Royal Astronomical Society