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| {{About|mass deficits in galaxies|mass deficits in atomic nuclei|Binding energy}}
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| A '''mass deficit''' is the amount of mass (in stars) that has been removed from the center of a [[galaxy]], presumably by the action of a [[binary star|binary]] [[supermassive black hole]].
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| [[File:mdef.jpg|thumb|left|Mass deficit.]]
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| The density of stars increases toward the center in most galaxies. In small galaxies, this increase continues into the very center. In large galaxies, there is usually a "core", a region near the center where the density is constant or slowly rising. The size of the core – the "core radius" – can be as great as a few hundred [[parsec]]s in the largest [[elliptical galaxy|elliptical galaxies]].<ref>{{cite book |last=Ferrarese |first=Laura et al. |editor-first=Vladimir|editor-last=Karas | editor2-first=Giorgio | editor2-last=Matt |title=Black Holes: from Stars to Galaxies|publisher=Cambridge University Press |year=2007 |pages= 261–268|chapter=The Inner Workings of Early-Type Galaxies: Cores, Nuclei and Supermassive Black Holes |isbn=978-0-521-86347-6
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| | url=http://www.cambridge.org/gb/knowledge/isbn/item1173713/?site_locale=en_GB}}</ref>
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| It is believed that cores are produced by binary supermassive black holes (SMBHs). Binary SMBHs form during the [[galaxy merger|merger]] of two galaxies.<ref>{{Citation | last = Begelman | first = M. C.| last2 = et al. | title = Massive black hole binaries in active galactic nuclei| journal = Nature| volume = 287| issue = | pages = 307–309| date = | year = 1980| month = | url = http://adsabs.harvard.edu/abs/1980Natur.287..307B| doi = 10.1038/287307a0|bibcode = 1980Natur.287..307B }}</ref> If a star passes near the massive binary, it will be ejected, by a process called the [[gravitational slingshot]]. This ejection continues until most of the stars near the center of the galaxy have been removed. The result is a low-density core. Such cores are ubiquitous in giant elliptical galaxies.<ref>{{cite book |last=Graham |first=Alister |editor-first=I. S. ''et al.''|editor-last=McLean |title=Planets, Stars and Stellar Systems |publisher=Springer |year=2012 |pages= |chapter=A review of elliptical and disc galaxy structure, and modern scaling laws |isbn=978-90-481-8817-8}}</ref>
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| The mass deficit is defined<ref>{{Citation | last = Milosavljevic| first = Milos| author-link = | last2 = Merritt | first2 = David| author2-link = David Merritt | last3 = Rest | first3 = Armin | last4 = van den Bosch | first4 = Frank | title = Galaxy cores as relics of black hole mergers| journal = Monthly Notices of the Royal Astronomical Society| volume = 331| issue = 4| pages = L51-L55| date = | year = 2002| month = | url = http://onlinelibrary.wiley.com/doi/10.1046/j.1365-8711.2002.05436.x/full | doi = 10.1046/j.1365-8711.2002.05436.x|arxiv = astro-ph/0110185 |bibcode = 2002MNRAS.331L..51M }}</ref> as the amount of mass that was removed in creating the core. The figure illustrates how mass deficits are measured, using the observed brightness profile of a galaxy.<ref>{{Citation | last = Graham| first = Alister | title = Core Depletion from Coalescing Supermassive Black Holes | journal = The Astrophysical Journal Letters| volume = 613 | issue = 1| pages = L33-L36| date = | year = 2004| month = | url = http://iopscience.iop.org/1538-4357/613/1/L33/| doi = 10.1086/424928 | bibcode=2004ApJ...613L..33G|arxiv = astro-ph/0503177 }}</ref> Mathematically, the mass deficit is defined as
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| <math>
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| M_\mathrm{def} = 4\pi\int_0^{R_c} \left[\rho_i(r) - \rho(r) \right]r^2 dr
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| </math>
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| where ''ρ''<sub>i</sub> is the original density, ''ρ'' is the observed density, and ''R''<sub>c</sub> is the core radius.
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| Observed mass deficits are typically in the range of one to a few times the mass of the central SMBH,<ref name=DEGN>{{cite book|last=Merritt|first=David|author-link=David Merritt|title=Dynamics and Evolution of Galactic Nuclei|year=2013|publisher=Princeton University Press|location=Princeton, NJ|isbn=9781400846122|url=http://openlibrary.org/works/OL16802359W/Dynamics_and_Evolution_of_Galactic_Nuclei}}</ref> and observed core radii are comparable to the [[sphere of influence (astronomy)|influence radii]] of the central SMBH. These properties are consistent with what is predicted in theoretical models of core formation <ref>{{Citation
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| | last = Merritt | first = David | author-link = David Merritt | title = Mass Deficits, Stalling Radii, and the Merger Histories of Elliptical Galaxies| journal = The Astrophysical Journal| volume = 648 | issue = | pages = 976–986| date = | year = 2006| month = | url = http://iopscience.iop.org/0004-637X/648/2/976/
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| | doi = 10.1086/506139 | bibcode=2006ApJ...648..976M|arxiv = astro-ph/0603439 }}</ref> and lend support to the hypothesis that all bright galaxies once contained binary SMBHs at their centers.
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| It is not known whether most galaxies still contain massive binaries, or whether the two black holes have coalesced. Both possibilities are consistent with the presence of mass deficits.
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| == References ==
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| {{reflist|colwidth=30em}}
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| == External links ==
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| *Ferrarese, L. and [[David Merritt|Merritt, D.]] (2002). [http://arxiv.org/abs/astro-ph/0206222 Supermassive Black Holes]. ''Physics World'', June 2002, p. 41.
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| [[Category:Astrophysics]]
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| [[Category:Supermassive black holes]]
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