The sphere of influence is a region around a supermassive black hole in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy.
where MBH is the mass of the black hole, σ is the stellar velocity dispersion of the host bulge, and G is the gravitational constant.
The second definition[2] is the radius at which the enclosed mass in stars equals twice MBH, i.e.
The first definition takes into account the bulge's overall effect on the motion of a star, since
It is a minimum requirement that the sphere of influence be well resolved in order that the mass of the black hole be determined dynamically.
Assuming that the Milky Way black hole is maximally rotating, its rotational influence radius is about 0.001 parsec,[5] while its radius of gravitational influence is about 3 parsecs.