# Sphere of influence (astronomy)

﻿
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

$r_h = frac\left\{GM\right\}\left\{sigma^2\right\}$

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

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Sphere of influence (astrodynamics) — A sphere of influence (SOI) in astrodynamics and astronomy is the spherical region around a celestial body where the primary gravitational influence on an orbiting object is that body. This is usually used to describe the areas in our solar… …   Wikipedia

• Sphere (disambiguation) — A sphere is an object shaped like the surface of a ball, but can be used to refer to a ball shaped object, as well as a sphere like or annular region or shell. Additionally, it has several metaphorical uses.In mathematics: * Sphere, the set of… …   Wikipedia

• sphere — /sfɪə / (say sfear) noun 1. a. a geometrical figure generated by the revolution of a semi circle about its diameter. b. a round body whose surface is at all points equidistant from the centre. 2. any rounded body approximately of this form; a… …   Australian English dictionary

• Sphere — Sphere, n. [OE. spere, OF. espere, F. sph[ e]re, L. sphaera,. Gr. ??? a sphere, a ball.] 1. (Geom.) A body or space contained under a single surface, which in every part is equally distant from a point within called its center. [1913 Webster] 2.… …   The Collaborative International Dictionary of English

• Astronomy — • Divided into two main branches, astrometry and astrophysics; the former concerned with determining the places of the investigation of the heavenly bodies, the latter, with the investigation of their chemical and physical nature Catholic… …   Catholic encyclopedia

• Astronomy — (from the Greek words astron (ἄστρον), star , and nomos (νόμος), law ) is the scientific study of celestial objects (such as stars, planets, comets, and galaxies) and phenomena that originate outside the Earth s atmosphere (such as the cosmic… …   Wikipedia

• sphere — [sfir] n. [ME spere < OFr espere < L sphaera < Gr sphaira] 1. any round body or figure having the surface equally distant from the center at all points; globe; ball 2. a star, planet, etc. 3. the visible heavens; sky 4. short for… …   English World dictionary

• Astronomy in medieval Islam — An 18th century Persian Astrolabe, kept at The Whipple Museum of the History of Science in Cambridge, England. Islamic astronomy or Arabic astronomy comprises the astronomical developments made in the Islamic world, particularly during the… …   Wikipedia

• Sphère de Dyson — Pour les articles homonymes, voir Sphère (homonymie) et Dyson (homonymie). Schéma d’une coquille de Dyson d’une unité astronomique de rayon. Une sphère …   Wikipédia en Français

• ASTRONOMY — In the Bible Although the Bible contains no explicit mention of the science of astronomy, it nevertheless has many references to topics such as the laws of the heavens (Jer. 31:34 (35); 33:25; Job 38:33) and the movements of the sun and the moon… …   Encyclopedia of Judaism