Friday, October 10, 2014

Astro Notations: The M-σ Relation

This week I thought I would discuss the M-σ relation.

The M-σ relation is a puzzle of modern astronomy. You see, it shouldn’t exist, or rather - we don’t understand why it exists. The M-σ relation is a correlation between the mass of supermassive black holes (M) and the velocity dispersion of the stars in the host galaxy (σ).

What the heck does that mean? I hear you asking. Well I’ll tell you.

First, the stellar velocity dispersion. This is a measurement of the range of velocities that stars have while flying around the galaxy. An observer from Earth sees some of the stars flying toward her, while others are flying away, and many are traveling with velocities somewhere in-between directly toward and directly away. The range of those velocities is what we call the dispersion, and it is directly determined by the amount of mass within the orbits of the stars.

Now what about the mass of the black holes? Well, black holes are really, really massive. Some are so massive, they are dubbed supermassive, and those supermassive black holes rest at the center of nearly every galaxy in the universe. The supermassive ones have more mass than a million of our Suns, and some have more mass than a billion. A billion. And that means that they have a lot of gravity. Mass leads to gravity, and gravity binds galaxies together.

But as big as supermassive black holes are, they are nothing compared to the galaxies in which they reside. And all the stars and all the gas and dust in the galaxy (what we call baryonic matter) is still small compared to the dark matter in the halos of the galaxies.

But before this turns into a discussion about the largest structures of the universe, let’s scale back to the supermassive black holes. While those black holes are massive enough to influence the orbits of the stars that are very nearby, they are not massive enough to influence the orbits of stars that are further away in the bulge of the host galaxy. The galaxy is so much bigger than the black hole, that the black hole can only influence - can only pull on - the stars closest to it. And that is precisely why the M-σ relation should not exist.

We measure the velocity dispersion of the galaxy, which should not be influenced by the black hole, and we measure the mass of the black hole. When we examine the measurements from many different galaxies, we find that the more massive the black hole is, the bigger the velocity dispersion is in the host galaxies. But the galaxies are so much bigger than the black holes - how do they "know" about the mass of the black hole at the center? Why does that relationship even exist?

There are a couple explanations that might connect the supermassive black holes to the host galaxies. One involves smashing galaxies together and merging the black holes within them. The other adds a layer of feedback from black hole growth into the host galaxy. Neither of these ideas are definitively confirmed yet, but there is evidence for both. I’ll leave that for another day.

For now, check out this cool artwork of an active galactic nucleus. What is it? Where did it come from? What is it doing? Although, I have discussed the Teacup AGN in a previous post, I'll keep discussing AGN in the future. I'll even discuss how we can use AGN to study the M-σ relation.


  1. How is it that (what appears to be) light energy is directed only along (for lack of a better metaphor) the north and south poles? Is the influence of a black hole - perhaps - aligned in such a way, that the other galactic objects not along that "line of influence" are not affected so much by the pull of a black hole?

    Secondly, why does the energy resemble a DNA helix, and what might that have to do with anything?

  2. The artist has attempted to visualize a couple of physical components of the AGN. I'll post a tour of AGN next. But generally, the light here is oriented along the poles in part because there is a a dusty ring surrounding the nucleus, blocking the light from passing through. Another part is that often AGN exhibit jets, which are polar-aligned. I don't study jets, so I don't know much about them.