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Why are accretion disks flat?

Why are accretion disks around black holes flat?

There are two basic reasons that accretion disks can be flat:

  1. The material that is feeding the accretion disk usually comes from gas that is orbiting the black hole and therefore already in a flat plane, and
  2. The accretion disk is able to cool down efficiently, so it doesn't have a lot of excess heat that can cause the gas to expand out of the flat plane that it starts in.

These two points are discussed further below.

Regarding (1), in the case of stellar mass black holes (i.e. a black hole that evolved from a normal star), the material that enters the accretion disk usually comes from a companion star which is in orbit around the black hole. In the case of supermassive black holes in the centers of galaxies, on the other hand, the material usually comes from gas that is in orbit around the center of galaxy. So in both cases the matter has angular momentum -- that is, it is moving around the central black hole in a particular direction, and the force of gravity swings it around in a circle in a particular plane. Gravity will tend to pull any material "above" or "below" this plane down into the plane, and once it is in the plane, gravity cannot easily pull it into the black hole because most of the gravitational force is used up swinging the material around in a circle. Thus the end result is a flat accretion disk extending to large distances from the black hole.

However, that is not the whole story. Even if material in an accretion disk starts off in a flat plane, it can expand out of that plane if it is hot enough. This is due to the simple fact that a hot gas has more pressure than a cold one, so as it heats up, it will counteract the force of gravity pulling it down to the flat plane and therefore expand. A disk that can cool efficiently (through radiating away a lot of its energy in the form of light) will therefore remain thin, and this is true for some of the accretion disks we see in nature. However, it's also worth pointing out that some accretion disks actually are relatively thick, because they are not able to cool efficiently. This can happen when most of the energy in the accretion disk is held by protons rather than electrons, since protons have a harder time emitting light than electrons. It can also happen when there is a large amount of material flowing into the disk. This material carries a lot of energy with it, and that energy causes the disk to heat up and expand.

April 2005, Dave Rothstein (more by Dave Rothstein) (Like this Answer)

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