Presentation #106.03 in the session Advances in Theory and Numerics for Galactic Dynamics.
Isotropic dark-matter (DM) halos have weakly damped point modes. The l=1 mode is a seiche mode and the l=2 is the precursor to the radial-orbit instability (ROI). I will show that small deviations in the distribution function (DF) can destabilize these modes and leads to a newly identified instability for NFW-like DM halos. These modes have been corroborated using linear-response theory and identified in simulations using singular spectrum analysis. The non-linear development of the new mode correlates the radial angle of eccentric orbits and leads to a density enhancement that swings from one side of the halo to another along a diameter. This mode is the l=1 analog of the ROI. The density amplitude reaches 10% at saturation in n-body simulations. The l=1 growth rate increases with increasing extent and the amplitude of excursions in the outer distribution. Since the DF is unlikely to be smooth, these modes may be ubiquitous in physical systems. Halos that are less extended than NFW, such as the Hernquist model, do not have unstable l=1 but are susceptible to unstable l=2. For outer slopes with exponents between Hernquist and NFW: both instabilities can coexist. These instabilities illustrate a more general property of DM halos: the overall DM response depends sensitively on the outer density profile. In particular, the halo response to satellites will depend on the outer halo profile as well as the inner profile.