The sphere of influence is a region around a

supermassive black hole A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions of times the mass of the Sun (). Black holes are a class of astronomical ob ...

in which the

gravitational potential In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric ...

of the black hole dominates the gravitational potential of the host galaxy. The radius of the sphere of influence is called the "(gravitational) influence radius". There are two definitions in common use for the radius of the sphere of influence. The first is given by

r_h = \frac

where M_BH is the mass of the black hole, ''σ'' is the stellar

velocity dispersion In astronomy, the velocity dispersion (''σ'') is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or supercluster. By measurin ...

of the host

bulge __NOTOC__ Bulge may refer to: Astronomy and geography *Bulge (astronomy), a tightly packed group of stars at the center of a spiral galaxy *Equatorial bulge, a bulge around the equator of a planet due to rotation * Tharsis bulge, vast volcanic pl ...

, and ''G'' is the gravitational constant. The second definition is the radius at which the enclosed mass in stars equals twice M_BH, i.e.

M_\star(r .

Which definition is most appropriate depends on the physical question that is being addressed. The first definition takes into account the bulge's overall effect on the motion of a star, since \sigma is determined in part by stars that have moved far from the black hole. The second definition compares the force from the black hole to the local force from the stars.

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.

Rotational influence sphere

If the black hole is rotating, there is a second radius of influence associated with the rotation. This is the radius inside of which the Lense-Thirring torques from the black hole are larger than the Newtonian torques between stars. Inside the rotational influence sphere, stellar orbits

precess Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...

at approximately the Lense-Thirring rate; while outside this sphere, orbits evolve predominantly in response to perturbations from stars on other orbits. Assuming that the Milky Way black hole is maximally rotating, its rotational influence radius is about 0.001 parsec, while its radius of gravitational influence is about 3 parsecs.

References

{{DEFAULTSORT:Sphere Of Influence Galaxies Stellar astronomy Supermassive black holes