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 ...
in which the
gravitational potential
In classical mechanics, the gravitational potential is a scalar potential associating with each point in space the work (energy transferred) per unit mass that would be needed to move an object to that point from a fixed reference point in the ...
of the black hole dominates the gravitational potential of the host
galaxy
A galaxy is a Physical system, system of stars, stellar remnants, interstellar medium, interstellar gas, cosmic dust, dust, and dark matter bound together by gravity. The word is derived from the Ancient Greek, Greek ' (), literally 'milky', ...
. 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
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 measu ...
of the host
bulge
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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 pla ...
, and ''G'' is the
gravitational constant
The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It ...
.
The second definition is the radius at which the enclosed mass in stars equals twice ''M''
BH, i.e.