Mass-sigma Correlation

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The "Mass Sigma" relation is also sometimes called the "Black hole and velocity dispersion relationship" and was first described in a paper by Ferrarese and Merritt[1] which says:

The masses of supermassive black holes correlate almost perfectly with the velocity dispersions of their host bulges.

Karl Gebhart from the University of Texas, [2], mass sigma is spelled out:

  • Sigma is a measure of how fast the stars are moving in the galaxy (also called the velocity dispersion).
  • The sigma is measured far away from the black hole where it doesn't have any influence. For example, in our galaxy if we magically took the black hole out of the center, our Sun (and us) wouldn't care at all. We are too far away from it and it has too small a mass.
  • We have found that the black hole mass is about 0.1% of the galaxy bulge mass - a very small quantity.
  • Thus, how does such a small thing in the middle of the galaxy end up correlating so well with the rest of the galaxy.
  • a tight correlation

The great thing is that current physics cannot explain why the correlation exists[3]:

While the ability of the M-sigma relation to clarify the data has been an enormous boon, the existence of such a tight correlation must also be telling us something fundamental about the way in which black holes form and about the connection between black holes and bulges. Unfortunately, the theoretical understanding of this connection has lagged behind the phenomenology.

Curvity can explain the relationship because the same "push" that is driving the stars to rotate faster then expected, i.e. flat rotation curves, is responsible for the evidence used to support the existence of a black hole, aka the "null balance". There exists a relationship between the motion of the stars around the center of the galaxy and the stars in the bulge because both are affected by negative gravity of surrounding galaxies.


  1. "A Fundamental Relation Between Supermassive Black Holes and Their Host Galaxies", Laura Ferrarese (UCLA), David Merritt (Rutgers), The Astrophysical Journal, S39:L9-L12, August 10th, 2000
  2. "Lecture notes from A309 Class" link, Dr. Gebhart, University of Texas, lect3bh.html lecture note
  3. "Relationship of Black Holes to Bulges", Merritt and Ferrarese, The Central kpc of Starbursts and AGN, ASP Conference Series, Vol. zzz, 2001