Figure: The black-hole mass versus velocity dispersion correlation: a common history of the galaxy bulge and its black hole?
Observations of nearby galaxies reveal a strong correlation between the mass of the central black hole (MBH)
and the velocity dispersion σ of the host galaxy, of the form log(MBH/MSun) = a + b·log(σ/σ0). In the figure, mass measurements based on stellar kinematics are denoted by circles, on
gas kinematics by triangles, and on maser kinematics by asterisks; Nuker
measurments are denoted by filled circles. The dashed lines show the
1-sigma limits on the best-fit correlation.
A new determination of the slope by Tremaine et al. (see below) using 31 galaxies yields b = 4.02 +/- 0.32, a = 8.13 +/- 0.06, for σ0 = 200 km/s. The MBH-σ relation has a small intrinsic dispersion (in log MBH, no larger than 0.3 dex).
The MBH-σ relation is of interest not only for its strong predictive power (only by measuring the dispersion, one could predict the BH mass using the correlation) but also because it implies that central black hole mass is constrained by and closely related to properties of the host galaxy's bulge. As Gebhardt et al. (2000) write, "The tight correlation between BH mass and velocity dispersion strongly suggets a causal connection between the formation and evolution of the BH and the bulge...It is natural to assume
that bulges, BHs and quasars formed, grew, or turned on as parts of the same process, in part because the collapse of merger of bulges might provide a rich fuel supply to a centrally located BH."
According to the Nukers, the key results of this kind of study are:
- Supermassive black holes are so common, nearly every large galaxy has one.
- A black hole's mass is proportional to the mass of the host galaxy, so that, for example, a galaxy twice as massive as another would have a black hole that is also twice as massive. This discovery suggests that the growth of the black hole is linked to the formation of the galaxy in which it is located.
- The number and masses of the black holes found are consistent with what would have been required to power the quasars.
"We believe we are looking at "fossil quasars" and that most galaxies at one time burned brightly as a quasar," says team leader Doug Richstone of the University of Michigan, Ann Arbor, Michigan. These conclusions are consistent with previous Hubble Space Telescope observations showing quasars dwelling in a variety of galaxies, from isolated normal-looking galaxies to colliding pairs.
Though several groups have previously found massive black holes dwelling in galaxies the size of our Milky Way or larger, these new results suggest smaller galaxies have lower-mass black holes, below Hubble's detection limit. The survey shows the black hole's mass is proportional to the host galaxy's mass. Like shoe sizes on adults, the bigger the galaxy, the larger the black hole.
It remains a challenging puzzle as to why black holes are so abundant, or why they should be proportional to a galaxy's mass. One idea, supported by previous Hubble observations, is that galaxies formed out of smaller "building blocks" consisting of star clusters. A massive "seed" black hole may have been present in each of these protogalaxies. The larger number of building blocks needed to merge and form very luminous galaxies would naturally have provided more seed black holes to coalesce into a single, massive black hole residing in a galaxy's nucleus.
An alternative model is that galaxies start at some early epoch with a modest black hole (not necessarily approaching the masses discussed here), but that the black hole consumes some fixed fraction of the total gas shed by the stars in the galaxy during their normal evolution. If that fraction is around 1 percent, the black holes could easily weigh as much as they do now, and would naturally track the current luminosity of the galaxy.
Hubble's high resolution then allowed the team to peer deep into the cores of the galaxies with extraordinary resolution unavailable from ground-based telescopes, and measure velocities of stars orbiting the black hole. A sharp rise in velocity means that a great deal of matter is locked away in the galaxy's core, creating a powerful gravitational field that accelerates nearby stars.
Credit: Figure 7 from the paper "The slope of the black-hole mass versus velocity dispersion correlation" by: Tremaine, Scott; Gebhardt, Karl; Bender, Ralf; Bower, Gary; Dressler, Alan; Faber, S. M.; Filippenko, Alexei V.; Green, Richard; Grillmair, Carl; Ho, Luis C.; Kormendy, John; Lauer, Tod R.; Magorrian, John; Pinkney, Jason; Richstone, Douglas (the "Nukers").
Astrophysical Journal 574, (2002), 740-753. This paper is available here.
The Nukers team members are Douglas Richstone (team leader), Karl Gebhardt (University of Michigan), Scott Tremaine and John Magorrian (University of Toronto, Canadian Institute for Advanced Research), John Kormendy (University of Hawaii), Tod Lauer (National Optical Astronomy Observatories), Alan Dressler (Carnegie Observatories), Sandra Faber (University of California), Ralf Bender (Ludwig Maximilian University, Munich), Ed Ajhar (National Optical Astronomy Observatories), and Carl Grillmair (Jet Propulsion Laboratory).