The loss cone problem in axisymmetric nuclei

TL;DR

This paper analyzes how stars are captured by supermassive black holes in axisymmetric galaxies, using analytical models and N-body simulations to estimate capture rates and orbit types involved.

Contribution

It provides a detailed analytical and numerical study of stellar diffusion and capture rates in axisymmetric galactic nuclei, extending previous spherical models.

Findings

Capture rates are modestly higher than in spherical models, up to a factor of a few.

Most captures originate from saucer orbits in the low-angular-momentum phase space.

Analytical diffusion coefficients agree with N-body simulation results.

Abstract

We consider the problem of consumption of stars by a supermassive black hole (SBH) at the center of an axisymmetric galaxy. Inside the SBH sphere of influence, motion of stars in the mean field is regular and can be described analytically in terms of three integrals of motion: the energy E, the z-component of angular momentum L_z, and the secular Hamiltonian H. There exist two classes of orbits, tubes and saucers; saucers occupy the low-angular-momentum parts of phase space and their fraction is proportional to the degree of flattening of the nucleus. Perturbations due to gravitational encounters lead to diffusion of stars in integral space, which can be described using the Fokker-Planck equation. We calculate the diffusion coefficients and solve this equation in the two-dimensional phase space (L_z, H), for various values of the capture radius and the degree of flattening. Capture rates are found to be modestly higher than in the spherical case, up to a factor of a few, and most captures take place from saucer orbits. We also carry out a set of collisional N-body simulations to confirm the predictions of the Fokker-Planck models. We discuss the implications of our results for rates of tidal disruption and capture in the Milky Way and external galaxies.