Fermat's Last Theorem: Difference between revisions

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He did more than conjecturing it.
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Undid revision 641906465 by Camboxer (talk) gratuitous change of reference format loses the link to the Diamond 1996 paper
 
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{{for|the [[astrodynamics]] term|sphere of influence (astrodynamics)}}
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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 "(gravitational) influence radius".
 
There are two definitions in common use for the radius of the sphere of influence. The first<ref name=Peebles>{{cite journal|last=Peebles|first=J.|title=Star Distribution Near a Collapsed Object|journal=The Astrophysical Journal |date=December 1972 | volume=178 | pages=371-376 | doi=10.1086/151797|url=http://adsabs.harvard.edu/abs/1972ApJ...178..371P|bibcode = 1972ApJ...178..371P }}</ref> is given by
 
<math>r_h = \frac{GM_{\rm BH}}{\sigma^2}</math>
 
where M<sub>BH</sub> 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<ref>{{cite book |last=Merritt | first=David | authorlink=David Merritt |editor-first=Luis |editor-last=Ho |title=Coevolution of Black Holes and Galaxies |publisher=Cambridge University Press |date=2004 |pages=263-275 |chapter=Single and Binary Black Holes and their Influence on Nuclear Structure | series=Carnegie Observatories Astrophysics Series, Vol. 1 | chapterurl=http://adsabs.harvard.edu/abs/2004cbhg.symp..263M | url=http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=0521824494#contributors|isbn=}}</ref> is the radius at which the enclosed mass in stars equals twice M<sub>BH</sub>, i.e.
 
<math>M_\star(r<r_h) = 2 M_{\rm BH} </math>.
 
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 <math>\sigma</math> 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.
 
It is a minimum requirement that the sphere of influence be well [[Angular resolution|resolved]] in order that the mass of the black hole be determined dynamically.<ref>{{cite journal | last = Ferrarese | first = Laura | last2 = Ford | first2 = Holland
| title = Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research
| journal = Space Science Reviews | volume = 116 | issue = 3-4 | pages = 523-624
| publisher = Springer | date = 2005
| url = http://adsabs.harvard.edu/abs/2005SSRv..116..523F
| doi = 10.1007/s11214-005-3947-6|arxiv = astro-ph/0411247 |bibcode = 2005SSRv..116..523F }}
</ref>
 
==Rotational influence sphere==
If the black hole is rotating, there is a second radius of influence associated with the rotation. <ref name=DEGN>{{cite book|last=Merritt|first=D.|authorlink=David Merritt |title=Dynamics and Evolution of Galactic Nuclei|year=2013|page=284|publisher=Princeton University Press|location=Princeton, NJ|isbn=9781400846122|url=http://openlibrary.org/works/OL16802359W/Dynamics_and_Evolution_of_Galactic_Nuclei}}</ref> This is the radius inside of which the [[Lense-Thirring precession|Lense-Thirring torques]] from the black hole are larger than the Newtonian torques between stars. Inside the rotational influence sphere, stellar orbits [[precession|precess]] 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 [[Sagittarius A*|Milky Way black hole]] is maximally rotating, its rotational influence radius is about 0.001 parsec,<ref>{{cite journal |last=Merritt |first=David | authorlink=David Merritt |last2=Alexander |first2=Tal |last3=Mikkola | first3 = Seppo | last4=Will | first4=Clifford |date= 2010|title=Testing properties of the Galactic center black hole using stellar orbits |url=http://adsabs.harvard.edu/abs/2010PhRvD..81f2002M |journal=Physical Review D |volume=81 |issue= |pages=062002 |doi=10.1103/PhysRevD.81.062002| authorformat = vanc | author-separator=, | author-name-separator = &#32; }}</ref> while its radius of gravitational influence is about 3 parsecs.
 
== References ==
 
{{reflist}}
 
{{DEFAULTSORT:Sphere Of Influence}}
[[Category:Galaxies]]
[[Category:Stellar astronomy]]
[[Category:Supermassive black holes]]

Latest revision as of 23:33, 10 January 2015

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