Sphere of influence (astronomy)
Encyclopedia
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
.
There are two definitions in common use for the radius of the sphere of influence.
The first is given by
where MBH is the mass of the black hole,
is the stellar velocity dispersion of the host bulge, and 
is the gravitational constant
.
The second definition is the radius at which the enclosed mass in stars equals twice MBH, i.e.
.
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
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.
Supermassive black hole
A supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have...
in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
.
There are two definitions in common use for the radius of the sphere of influence.
The first is given by
where MBH is the mass of the black hole,
is the stellar velocity dispersion of the host bulge, and is the gravitational constantGravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
.
The second definition is the radius at which the enclosed mass in stars equals twice MBH, i.e.
.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
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
Angular resolution
Angular resolution, or spatial resolution, describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object...
in order that the mass of the black hole be determined dynamically.