Dynamical traction and black hole orbital migration
We investigate the circumstances which allow a black hole to remain put at the galactic centre when the stellar core is anisotropic. We use N-body calculations to study the response of stellar orbit families embedded in a larger, isotropic isochrone (Hénon) background potential. When the BH orbits in an odd f[E,Lz] velocity distribution function, they transfer angular momentum to it. We call this dynamical traction: it takes place whenever the kinetic energy drawn from f[E,Lz] has an excess of streaming motion over its (isotropic) v-dispersion. For a dynamically cold disc, the outcome depends on both the orbit of the BH and that of a Jeans-unstable stellar sub-structures. When the stellar clumps have much binding energy, a BH may scatter off of them after they formed. In the process the BH may be dislodged from the centre and migrate outward due to dynamical traction. When the stellar clumps are less bound, they may still migrate to the centre where they either dissolve or merge with the BH. The final configuration is similar to a nuclear star cluster which may yet be moving at ~10 km/s wrt the barycentre. The angular momentum transferred to a BH by dynamical traction delays the migration to the galactic centre by several hundred million years. The efficiency of angular momentum transfer is a strong function of the fragmented (cold) state of the stellar space density. In a dynamically cold environment, a BH is removed from the central region through a two-stage orbital migration instability. A criterion against this instability is proposed in the form of a threshold in isotropic velocity dispersion compared to streaming motion. For a BH to settle at the heart of a galaxy on time-scales of ~ 300 Myr or less requires that a large fraction of Lz be dissipated, or, alternatively, that the BH grows in situ in an isotropic environment devoid of sub-structures.