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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
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at approximately the Lense-Thirring rate; while outside this sphere, orbits evolve predominantly in response to perturbations from stars on other orbits. Assuming that the
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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.
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is maximally rotating, its rotational influence radius is about 0.001 parsec, while its radius of gravitational influence is about 3 parsecs.
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If the black hole is rotating, there is a second radius of influence associated with the rotation. This is the radius inside of which the
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from the black hole are larger than the
Newtonian torques between stars. Inside the rotational influence sphere, stellar orbits
377:
Ferrarese, Laura; Ford, Holland (2005). "Supermassive Black Holes in
Galactic Nuclei: Past, Present and Future Research".
467:, Alexander T, Mikkola S, Will C (2010). "Testing properties of the Galactic center black hole using stellar orbits".
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There are two definitions in common use for the radius of the sphere of influence. The first is given by
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42:. The radius of the sphere of influence is called the "(gravitational) influence radius".
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The second definition is the radius at which the enclosed mass in stars equals twice
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Region where a supermassive black hole gravitationally dominates its galaxy
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338:"Single and Binary Black Holes and their Influence on Nuclear Structure"
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in order that the mass of the black hole be determined dynamically.
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of the black hole dominates the gravitational potential of the host
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It is a minimum requirement that the sphere of influence be well
344:. Carnegie Observatories Astrophysics Series. Vol. 1.
97:{\displaystyle r_{h}={\frac {GM_{\text{BH}}}{\sigma ^{2}}}}
202:{\displaystyle M_{\star }(r<r_{h})=2M_{\text{BH}}.}
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Tidal disruption event ยง Tidal-disruption radius
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294:"Star Distribution Near a Collapsed Object"
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436:Dynamics and Evolution of Galactic Nuclei
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19:For the general astrodynamics term, see
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21:sphere of influence (astrodynamics)
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111:is the mass of the black hole,
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292:Peebles, J. (December 1972).
242:Rotational influence sphere
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499:10.1103/PhysRevD.81.062002
441:Princeton University Press
346:Cambridge University Press
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409:10.1007/s11214-005-3947-6
298:The Astrophysical Journal
537:Supermassive black holes
224:{\displaystyle \sigma }
36:gravitational potential
32:supermassive black hole
248:Lense-Thirring torques
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129:gravitational constant
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379:Space Science Reviews
340:. In Ho, Luis (ed.).
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30:is a region around a
348:. pp. 263โ275.
256:Milky Way black hole
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491:2010PhRvD..81f2002M
401:2005SSRv..116..523F
364:2004cbhg.symp..263M
310:1972ApJ...178..371P
117:velocity dispersion
28:sphere of influence
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532:Stellar astronomy
469:Physical Review D
439:. Princeton, NJ:
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431:Merritt, D.
304:: 371โ376.
268:Roche limit
521:Categories
279:References
507:118646069
482:0911.4718
465:Merritt D
417:119091861
219:σ
154:⋆
84:σ
527:Galaxies
433:(2013).
336:(2004).
262:See also
236:resolved
487:Bibcode
397:Bibcode
360:Bibcode
306:Bibcode
252:precess
141:, i.e.
127:is the
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123:, and
104:where
40:galaxy
503:S2CID
477:arXiv
413:S2CID
387:arXiv
350:arXiv
121:bulge
445:ISBN
165:<
26:The
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63:=
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