Mass deficit

{{short description|Lack of stellar mass in the centers of galaxies}}

{{About|mass deficits in galaxies|mass deficits in general|Binding energy#Mass-energy relation|mass deficits in atomic nuclei|Nuclear binding energy#Mass defect}}

In astronomy, 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.

File:mdef.jpg

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.{{cite book |last=Ferrarese |first=Laura |display-authors=etal |editor-first=Vladimir|editor-last=Karas |editor2-first=Giorgio |editor2-last=Matt |title=Black Holes: from Stars to Galaxies|publisher=Cambridge University Press |date=2007 |pages= 261–268|chapter=The Inner Workings of Early-Type Galaxies: Cores, Nuclei and Supermassive Black Holes |isbn=978-0-521-86347-6 |chapter-url=http://www.cambridge.org/gb/knowledge/isbn/item1173713/?site_locale=en_GB}}Dullo, Bililign T.; Graham, Alister W. (2014) [http://adsabs.harvard.edu/abs/2014MNRAS.444.2700D Depleted cores, multicomponent fits, and structural parameter relations for luminous early-type galaxies]

The greatest observed stellar cores reach 3.2 to 5.7 kiloparsecs in radius.

{{cite journal

| last1= Postman |first1= M.

| last2= Lauer |first2= T. R.

| last3= Donahue |first3= M. |author3-link= Megan Donahue

| last4= Graves |first4= G.

| last5= Coe |first5= D.

| last6= Moustakas |first6= J.

| last7= Koekemoer |first7= A.

| last8= Bradley |first8= L.

| last9= Ford |first9= H. C.

| last10= Grillo |first10= C.

| last11= Zitrin |first11= A.

| last12= Lemze |first12= D.

| last13= Broadhurst |first13= T.

| last14= Moustakas |first14= L.

| last15= Ascaso |first15= B.

| last16= Medezinski |first16= E.

| last17= Kelson |first17= D.

| title= A Brightest Cluster Galaxy with an Extremely Large Flat Core

| year= 2012

| journal= The Astrophysical Journal

| volume= 756

|issue= 2

| pages= 159

| doi= 10.1088/0004-637X/756/2/159

| arxiv= 1205.3839

| bibcode= 2012ApJ...756..159P

|s2cid= 54547473

}}

{{cite journal

| last1= Bonfini |first1= P.

| last2= Graham |first2= A. W.

| title= The Quest for the Largest Depleted Galaxy Core: Supermassive Black Hole Binaries and Stalled Infalling Satellites

| year= 2016

| journal= The Astrophysical Journal

| volume= 829

|issue= 2

| pages= 81

| doi= 10.3847/0004-637X/829/2/81

| arxiv= 1610.00801

| bibcode= 2016ApJ...829...81B

|s2cid= 119284190

|doi-access= free

}}

{{cite journal

| last1= López-Cruz |first1= O.

| last2= Añorve |first2= C.

| last3= Birkinshaw |first3= M.

| last4= Worrall |first4= D. M.

| last5= Ibarra-Medel |first5= H. J.

| last6= Barkhouse |first6= W. A.

| last7= Torres-Papaqui |first7= J. P.

| last8= Motta |first8= V.

| title= The Brightest Cluster Galaxy in A85: The Largest Core Known So Far

| year= 2014

| journal= The Astrophysical Journal Letters

| volume= 795

|issue= 2

| pages= L31

| doi= 10.1088/2041-8205/795/2/L31

| arxiv= 1405.7758

| bibcode= 2014ApJ...795L..31L

|s2cid= 1140857

}}

It is believed that cores are produced by binary supermassive black holes (SMBHs). Binary SMBHs form during the merger of two galaxies.{{Citation |last= Begelman |first= M. C. |title= Massive black hole binaries in active galactic nuclei |journal= Nature |volume= 287 |issue= 5780|pages= 307–309 |date= 1980 |doi= 10.1038/287307a0|bibcode= 1980Natur.287..307B |s2cid= 4331042 |display-authors=etal}} 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{{Citation |last1= Milosavljevic |first1= Milos |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= 2002 |doi= 10.1046/j.1365-8711.2002.05436.x|doi-access= free |arxiv= astro-ph/0110185 |bibcode= 2002MNRAS.331L..51M|s2cid= 15426918 }} as the amount of mass that was removed in creating the core. Mathematically, the mass deficit is defined as

$$M\_\backslash mathrm\{def\}\; =\; 4\; \backslash pi\; \backslash int\_0^\{R\_c\}\; \backslash left[\backslash rho\_i(r)\; -\; \backslash rho(r)\; \backslash right]r^2\; dr,$$

where {{mvar|ρ_i}} is the original density, {{mvar|ρ}} is the observed density, and {{mvar|R_c}} is the core radius. In practice, the core-Sersic model can be used to help quantify the deficits.{{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= 2004 |doi= 10.1086/424928 |bibcode=2004ApJ...613L..33G|arxiv= astro-ph/0503177|s2cid= 15548647 }}

Observed mass deficits are typically in the range of one to a few times the mass of the central SMBH,{{cite book|last=Merritt|first=David|author-link=David Merritt|title=Dynamics and Evolution of Galactic Nuclei|date=2013|publisher=Princeton University Press|location=Princeton, NJ|isbn=9781400846122|url=https://openlibrary.org/works/OL16802359W/Dynamics_and_Evolution_of_Galactic_Nuclei}} 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 {{Citation |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= 2|pages= 976–986 |date= 2006 |doi= 10.1086/506139 |bibcode=2006ApJ...648..976M|arxiv= astro-ph/0603439|s2cid= 6207227 }} 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.