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The M–sigma (or ''M''–''σ'') relation is an empirical correlation between the stellar velocity dispersion ''σ'' of a galaxy bulge and the mass M of the supermassive black hole at its center. The M–σ relation was first presented in 1999 during a conference at the Institut d'astrophysique de Paris in France. The proposed form of the relation, which was called the "Faber–Jackson law for black holes", was : where is the solar mass. Publication of the relation in a refereed journal, by two groups, took place the following year.〔Ferrarese, F. and Merritt, D. (2000), (A Fundamental Relation between Supermassive Black Holes and Their Host Galaxies ), ''The Astrophysical Journal'', 539, L9-L12〕 〔Gebhardt, K. et al. (2000), (A Relationship between Nuclear Black Hole Mass and Galaxy Velocity Dispersion ), ''The Astrophysical Journal'', 539, L13–L16〕 One recent study, based on a complete sample of published black hole masses in nearby galaxies, 〔McConnell, N. J. et al. (2011), ( Two ten-billion-solar-mass black holes at the centres of giant elliptical galaxies ), ''Nature'', 480, 215–218〕 gives : Earlier work had demonstrated a possible relationship between galaxy luminosity and black hole mass,〔Magorrian, J. et al. (1998), ( The Demography of Massive Dark Objects in Galaxy Centers ), ''The Astronomical Journal'', 115, 2285–2305〕 but that relationship had a large scatter. The much smaller scatter of the ''M''–''σ'' relation is generally interpreted to imply some source of mechanical feedback between the growth of supermassive black holes and the growth of galaxy bulges, although the source of this feedback is still uncertain. Discovery of the M–σ relation was taken by many astronomers to imply that supermassive black holes are fundamental components of galaxies. Prior to about 2000, the main concern had been the simple detection of black holes, while afterward the interest changed to understanding the role of supermassive black holes as a critical component of galaxies. This led to the main uses of the relation to estimate black hole masses in galaxies that are too distant for direct mass measurements to be made, and to assay the overall black hole content of the Universe. ==Origin== The tightness of the M–σ relation suggests that some kind of feedback acts to maintain the connection between black hole mass and stellar velocity dispersion, in spite of processes like galaxy mergers and gas accretion that might be expected to increase the scatter over time. One such mechanism was suggested by Joseph Silk and Martin Rees in 1998.〔Silk, J. and Rees, M. (1998), ( Quasars and galaxy formation ), ''Astronomy and Astrophysics'', 331, L1–L4〕 These authors proposed a model in which supermassive black holes first form via collapse of giant gas clouds before most of the bulge mass has turned into stars. The black holes created in this way would then accrete and radiate, driving a wind which acts back on the accretion flow. The flow would stall if the rate of deposition of mechanical energy into the infalling gas was large enough to unbind the protogalaxy in one crossing time. The Silk and Rees model predicts a slope for the M–σ relation of α=5, which is approximately correct. However, the predicted normalization of the relation is too small by about a factor of one thousand. The reason is that there is far more energy released in the formation of a supermassive black hole than is needed to completely unbind the stellar bulge. A more successful feedback model was first presented by Andrew King at the University of Leicester in 2003. In King's model, feedback occurs through momentum transfer, rather than energy transfer as in the case of Silk & Rees's model. A "momentum-driven flow" is one in which the gas cooling time is so short that essentially all the energy in the flow is in the form of bulk motion. In such a flow, most of the energy released by the black hole is lost to radiation, and only a few percent is left to affect the gas mechanically. King's model predicts a slope of α=4 for the M–σ relation, and the normalization is exactly correct; it is roughly a factor c/σ ≈ 103 times larger than in Silk & Rees's relation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「M–sigma relation」の詳細全文を読む スポンサード リンク
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