Gravitational loss-cone instability

Abstract

We study physical corollaries of the existing analogy between the simplest plasma traps (mirror traps) and star clusters surrounding massive black holes or dense galactic nuclei. There is a loss cone in the system through which plasma particles with low velocities transverse to the trap axis or, similarly, stars with low angular momenta (destroyed or absorbed by the central body) escape. The consequences of the “beam-like” deformation of the plasma distribution function in a trap are well known: a peculiar loss-cone instability producing a plasma flow into the loss cone develops as a result. We show that a similar gravitational loss-cone instability can also arise under certain conditions in the galactic case of interest to us. This instability is related to the slow precessional motions of highly elongated (nearly radial) stellar orbits and the main condition for its growth is that the precession of such orbits be retrograde (in the direction opposite to the orbital rotation of stars). Only under this condition do oscillations that can become unstable in the presence of a loss cone arise instead of the radial orbit instability (a variety of the Jeans instability in systems with highly elongated orbits) that takes place in the case of prograde precession. The instability produces a stream of stars onto the galactic center, i.e., serves as a mechanism of fueling the nuclear activity of galaxies. For a mathematical analysis, we have obtained relatively simple characteristic equations that describe small perturbations in a sphere of radially highly elongated stellar orbits. These characteristic equations are derived through a number of successive simplifications from a general linearized system of equations, including the collisionless Boltzmann kinetic equation and the Poisson equation (in action-angle variables). The central point of our analysis of the characteristic equations is preliminary detection of neutral modes (or proof of their absence in the case of stability).