New dipole instabilities in spherical stellar systems

TL;DR

This paper identifies new dipole instabilities in spherical stellar systems caused by small wiggles in the distribution function, with implications for dark matter halos and their stability.

Contribution

It demonstrates the destabilization of dipole modes by distribution function wiggles in NFW-like halos using simulations and linear theory, revealing a new instability mechanism.

Findings

New dipole instability modes identified in NFW-like halos.

Instability peaks inside the half-mass radius with outer-halo pattern speed.

Stability depends on the density profile's global shape and power-law exponents.

Abstract

Spherical stellar systems have weakly-damped response modes. The dipole modes are seiche modes. The quadrupole are zero pattern-speed prolate modes, the stable precursors to the radial-orbit instability (ROI). We demonstrate that small wiggles in the distribution function (DF) can destabilise the dipole modes and describe the newly identified instabilities in NFW-like dark-matter (DM) halos and other power-law spherical systems. The modes were identified in N-body simulations using multivariate singular spectrum analysis (MSSA) and corroborated using linear-response theory. The new mode peaks inside the half-mass radius but has a pattern speed typical of an outer-halo orbit. As it grows, the radial angle of the eccentric orbits that make up the mode correlate and lose angular momentum by a resonant couple to outer-halo orbits. This leads to an unsteady pattern with a density enhancement that swings from one side of the halo to another along a diameter, like the orbits that comprise the instability. In this way, the dipole mode is similar to the ROI. Since the DF found in Nature is unlikely to be smooth and isotropic with $df(E)/dE<0$ necessary for Antonov stability, these modes may be ubiquitous albeit slowly growing. Halos that are less extended than NFW, such as the Hernquist model, tend to be stable to this dipole instability. We present the critical stability exponents for one- and two-power models. These different critical outer power-law exponents illustrate that the gravitational coupling between the inner and outer DM halo depends on the global shape of density profile.