The loss cone problem in axisymmetric nuclei

Understand

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.