M–sigma relation

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 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.

[10] 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 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.

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.

Two other techniques—reverberation mapping in active galactic nuclei, and the Sołtan argument, which computes the cosmological density in black holes needed to explain the quasar light—both gave a mean value of M/Mbulge that was a factor ≈10 smaller than implied by the Magorrian relation.

A common use of the M–σ relation is to estimate black hole masses in distant galaxies using the easily measured quantity σ.

[17] No clear evidence has been found for ultra-massive black holes with masses above 1010 M☉, although this may be an expected consequence of the observed upper limit to σ.