Sphere of influence (astronomy)

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 bulge.

There are two definitions in common use for the radius of the sphere of influence.The first [Peebles, J. (1972), [http://adsabs.harvard.edu/abs/1972ApJ...178..371P| Star Distribution Near a Collapsed Object] ] is given by

$r\_h\; =\; frac\{GM\}\{sigma^2\}$

where M is the mass of the black hole, $sigma$ is the stellar velocity dispersion of the host bulge, and $G$ is the gravitational constant. The second definition [Merritt, D. (2004), [http://adsabs.harvard.edu/abs/2004cbhg.symp..263M| Single and Binary Black Holes and their Influence on Nuclear Structure] ] is the radius at which the enclosed mass in stars equals twice M, 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 $sigma$ 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. The two definitions are equivalent in the case of the so-called singular isothermal sphere, in which the stellar density falls as the inverse square of the distance from the bulge center.

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 [Marconi, A. and Hunt, D. (2003), [http://adsabs.harvard.edu/abs/2003ApJ...589L..21M| The Relation between Black Hole Mass, Bulge Mass, and Near-Infrared Luminosity] ] [Valluri, M. et al. (2004), [http://adsabs.harvard.edu/abs/2004ApJ...602...66V| Difficulties with Recovering the Masses of Supermassive Black Holes from Stellar Kinematical Data] ]

References