Sphere of influence (black hole)

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. 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

${\displaystyle r_{h}={\frac {GM_{\rm {BH}}}{\sigma ^{2}}}}$

where M_BH 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 is the radius at which the enclosed mass in stars equals twice M_BH, i.e.

${\displaystyle M_{\star }(r<r_{h})=2M_{\rm {BH}}}$.

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