Mass deficit

This article is about mass deficits in galaxies. For mass deficits in general, see Binding energy § Mass-energy relation. For mass deficits in atomic nuclei, see Nuclear binding energy § Mass defect.

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 supermassive black hole.

The figure illustrates how mass deficits are measured, using the observed brightness profile of a galaxy

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 a few hundred parsecs in large elliptical galaxies. ^{[1] [2]} The greatest observed stellar cores reach 3.2 to 5.7 kiloparsecs in radius. ^{[3] [4] [5]}

It is believed that cores are produced by binary supermassive black holes (SMBHs). Binary SMBHs form during the merger of two galaxies. ^[6] 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.

The mass deficit is defined ^[7] as the amount of mass that was removed in creating the core. Mathematically, the mass deficit is defined as$${\displaystyle M_{\mathrm {def} }=4\pi \int _{0}^{R_{c}}\left[\rho _{i}(r)-\rho (r)\right]r^{2}dr,}$$

where ρ_i is the original density, ρ is the observed density, and R_c is the core radius. In practice, the core-Sersic model can be used to help quantify the deficits. ^[8]

Observed mass deficits are typically in the range of one to a few times the mass of the central SMBH, ^[9] and observed core radii are comparable to the influence radii of the central SMBH. These properties are consistent with what is predicted in theoretical models of core formation ^[10] and lend support to the hypothesis that all bright galaxies once contained binary SMBHs at their centers.

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.

References

1. Ferrarese, Laura; et al. (2007). "The Inner Workings of Early-Type Galaxies: Cores, Nuclei and Supermassive Black Holes". In Karas, Vladimir; Matt, Giorgio (eds.). Black Holes: from Stars to Galaxies. Cambridge University Press. pp. 261–268. ISBN   978-0-521-86347-6.
2. Dullo, Bililign T.; Graham, Alister W. (2014) Depleted cores, multicomponent fits, and structural parameter relations for luminous early-type galaxies
3. Postman, M.; Lauer, T. R.; Donahue, M.; Graves, G.; Coe, D.; Moustakas, J.; Koekemoer, A.; Bradley, L.; Ford, H. C.; Grillo, C.; Zitrin, A.; Lemze, D.; Broadhurst, T.; Moustakas, L.; Ascaso, B.; Medezinski, E.; Kelson, D. (2012). "A Brightest Cluster Galaxy with an Extremely Large Flat Core". The Astrophysical Journal . 756 (2): 159. arXiv: 1205.3839 . Bibcode:2012ApJ...756..159P. doi:10.1088/0004-637X/756/2/159. S2CID   54547473.
4. Bonfini, P.; Graham, A. W. (2016). "The Quest for the Largest Depleted Galaxy Core: Supermassive Black Hole Binaries and Stalled Infalling Satellites". The Astrophysical Journal . 829 (2): 81. arXiv: 1610.00801 . Bibcode:2016ApJ...829...81B. doi: 10.3847/0004-637X/829/2/81 . S2CID   119284190.
5. López-Cruz, O.; Añorve, C.; Birkinshaw, M.; Worrall, D. M.; Ibarra-Medel, H. J.; Barkhouse, W. A.; Torres-Papaqui, J. P.; Motta, V. (2014). "The Brightest Cluster Galaxy in A85: The Largest Core Known So Far". The Astrophysical Journal Letters. 795 (2): L31. arXiv: 1405.7758 . Bibcode:2014ApJ...795L..31L. doi:10.1088/2041-8205/795/2/L31. S2CID   1140857.
6. Begelman, M. C.; et al. (1980), "Massive black hole binaries in active galactic nuclei", Nature, 287 (5780): 307–309, Bibcode:1980Natur.287..307B, doi:10.1038/287307a0, S2CID   4331042
7. Milosavljevic, Milos; Merritt, David; Rest, Armin; van den Bosch, Frank (2002), "Galaxy cores as relics of black hole mergers", Monthly Notices of the Royal Astronomical Society , 331 (4): L51–L55, arXiv: astro-ph/0110185 , Bibcode:2002MNRAS.331L..51M, doi: 10.1046/j.1365-8711.2002.05436.x , S2CID   15426918
8. Graham, Alister (2004), "Core Depletion from Coalescing Supermassive Black Holes", The Astrophysical Journal Letters, 613 (1): L33–L36, arXiv: astro-ph/0503177 , Bibcode:2004ApJ...613L..33G, doi:10.1086/424928, S2CID   15548647
9. Merritt, David (2013). Dynamics and Evolution of Galactic Nuclei. Princeton, NJ: Princeton University Press. ISBN   9781400846122.
10. Merritt, David (2006), "Mass Deficits, Stalling Radii, and the Merger Histories of Elliptical Galaxies", The Astrophysical Journal, 648 (2): 976–986, arXiv: astro-ph/0603439 , Bibcode:2006ApJ...648..976M, doi:10.1086/506139, S2CID   6207227

External links

• Ferrarese, L. and Merritt, D. (2002). Supermassive Black Holes. Physics World, June 2002, p. 41.