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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 " influence radius".
There are two definitions in common use for the radius of the sphere of influence. The first is given by
r h = G M B H σ 2 {\displaystyle r_{h}={\frac {GM_{\rm {BH}}}{\sigma ^{2}}}}
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.