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A mass deficit is the amount of mass that has been removed from the center of a galaxy, presumably by the action of a binary supermassive black hole.
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.The greatest observed stellar cores reach 3.2 to 5.7 kiloparsecs in radius.
It is believed that cores are produced by binary supermassive black holes. Binary SMBHs form during the merger of two galaxies. 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 as the amount of mass that was removed in creating the core. Mathematically, the mass deficit is defined as