Pedagoguery

Black holes, despite their mystery, are actually fairly simple objects. They can be described by only three quantities: mass, spin, and electrical charge. In practice, if a back hole gained a significant electrical charge, both the gravitational and elctromagnetic fields would tend to attract matter to counter it, so only mass and spin will typically be sufficient.

What can the spin of a black hole tell us? For galactic black holes, those produced through supernova explosions, it can tell us something of the dynamics of the supernova itself. More interesting, however, are the super massive black holes at the center of galaxies. The spins of those black holes can tell us a number of things. First of all, it can give us an idea of the history of the black hole, since the two ways in which black holes grow affect their spins. The first way is through accretion of matter. Accretion will tend to spin up a black hole in the direction that the accreting matter is rotating. The second way is through mergers. Since mergers can happen at any angle, the spin axis of the resultant black hole will thus depend on the angles of spins and masses of the two progenitor black holes.

Super massive black holes are also believed to profoundly impact the evolution of the galaxies in which they reside. It is believed that the power of the jets that black holes emit depends on the spin of the black hole. These jets heat the surrounding intergalactic matter, causing less of it to fall into the galaxy and thus restricting the galaxy's size.

How, then do we determine the spin of a black hole? Part of it has to do with something called the innermost stable circular orbit. This is the minimum distance from a black hold that an object can have a stable orbit. Inside of this orbit, you are on a ballistic trajectory into the black hole. The size of this orbit depends on the spin of the black hole because of a phenomenon called frame dragging. In general relativity, any spinning mass drags space around it, but for most masses the effect is too small to notice. For a black hole, however, the effect is significant, and the faster the spin of the black hole, the greater the effect. Frame dragging adds angular momentum to orbiting matter in the direction of the black hole's orbit. Thus, if the black hole orbits in the same direction as the accretion disc (prograde), the innermost stable circular orbit is smaller, while if the black hole orbits opposite the accretion disc (retrograde), it is pushed outward. Thus, determining the inner edge of the accretion disc will tell us how fast the black hole is rotating.

That leaves us with the problem of figuring out what how far the inner edge of the accretion disc is from the black hole. Since most black holes are too far away for us to be able to image the accretion discs, some other way must be found. Fortunately, the innermost edge of the accretion disc also happens to be the hottest, so observing the black hole in x-rays can give us an idea of the dynamics of the system.

There are two techniques that can be used to estimate the spin of the black hole. The first is spectral-line modeling. Spectral-line modeling requires the detection of an iron emission line called Fe Kα. This strong emission line is typically emitted throughout the disc, but when observed from the inner disc, the line is stretched and skewed because of the extreme environment from which it is emitted. The precise amount of skewing and stretching tells us how close to the black hole the radiation is emitted.

The second method is called thermal modeling. Since we need to accurately know the distance and mass of the black hole to use this method, it cannot be used on super massive black holes. In this, we measure the x-ray flux of the accretion disc, and based on the distance and mass, we can compute the inner edge of the black hole.

Using these observations on black holes, we have found that the majority of those we have been able to measure are spinning quite fast, usually over 75% of the speed of light. They almost always spin prograde, and galactic black holes tend to spin slightly faster than super massive black holes. However, that latter observation is countered by the fact that we have so far been able to measure only a few super massive black holes.

Next time, macro scale quantum physics.