Spinning Black Holes

On November 22, 2014, a burst of x-rays was detected by ASASSN—that's the All Sky Automated Survey for Super Novae. But this was no supernova. The signal came from the center of a galaxy around 290 million light-years away, and what we now believe happened was a star came too close to a supermassive black hole with a mass millions of times that of our Sun, and it was eaten. The black hole fed on the star, and yes, this is the actual terminology astrophysicists use to describe it.

Events like these are thought to be rare, occurring maybe once every 10,000 to 100,000 years in a galaxy. They're called Tidal Disruption Events, or Tidal Disruption Flares. As the star approached, the side closest to the black hole experienced a much greater gravitational pull than the other side, ripping the star to shreds. Matter spiraling into the black hole formed an accretion disk—an annular ring of gas and dust that's accelerating and heating up, emitting visible light, UV, and X-rays observable from Earth.

Now, what's remarkable about this event is that it transformed a dormant or quiescent black hole—one that wasn't really feeding—into one that we can observe, thanks to the matter falling in from that star. And this is what it looked like. Okay, if you're disappointed, check out these artists' renditions of the same event. But if you're cynical, you might say, "Well, how do we know that's what really happened? What if the scientists are just making this up to get more grant funding or to inspire people to go into science?" Well, I'll explain how we know this is actually what went down.

But first, things got weirder. Scientists trained three X-ray telescopes to observe this part of the sky for years after the event, and what they found was a strong and regular pulse of X-rays, brightening and dimming every 131 seconds. It shows up in the data from all three telescopes they observed periodically over 450 days. But the pulse maintained this rhythm and didn't get weaker. In fact, as time went on, the relative strength of the pulse got stronger, modulating the X-ray signal by around 40%.

So, what was causing these periodic flashes of X-rays, and what could it tell us about the black hole? Well, let's back up, because black holes are some of the simplest objects in the Universe. By that, I just mean that they are characterized by only two attributes: mass and spin. Okay, there's also charge, but since black holes should essentially be neutral, mass and spin are the two that count.

Mass is relatively easy to determine. Far away from a black hole, you can even use Newtonian physics. By measuring the gravitational effects of the black hole on other bodies, you can estimate the mass of the black hole. This has been done, and black holes have been found with masses ranging from just a few times our Sun—stellar-mass black holes—up to billions of solar masses—supermassive black holes. It's generally accepted that there is a supermassive black hole at the centers of most galaxies, including our own.

But what about spin? Since black holes form from collapsing stars and all known stars rotate, all black holes should also be rotating. I mean, what are the chances that a bunch of matter just collapses into a point perfectly with no rotation? It's just not going to happen. And then additional matter falling into the black hole contributes its angular momentum. So, like a figure skater pulling their arms into a point object, you can imagine black holes get spinning pretty fast.

But spin is harder to measure because, unlike mass, it only affects objects relatively close to the black hole. But there is a way to do it—actually, three ways. To understand all of them, you have to understand ISCO. In Newtonian physics, around a compact mass, you can place an object in a circular orbit at any radius, and it will be stable. It doesn't matter how close you get. This is not the case according to general relativity.

Here, there is an innermost stable circular orbit, with a radius known as r_ISCO. Closer than this, and no orbits are stable: they all fall into the black hole. So, when you're looking at a black hole that is feeding, the innermost edge of the accretion disk is at r_ISCO. What's useful for our purposes is that r_ISCO depends on the spin of the black hole. The faster it's spinning, the smaller r_ISCO becomes, assuming it's spinning in the same direction as the matter in the accretion disk.

The rotation enables particles to orbit closer to the black hole than they'd be able to for a non-spinning black hole. So you can kind of think of it as though the spin is supporting the particles against the relentless pull of gravity. Now, spin is normally discussed in terms of a dimensionless parameter that ranges from 0—no spin—to 1—maximum spin. Though I guess you could also have spins down to -1 if the black hole is spinning in the opposite direction from the accretion disk.

Now, as spin increases, r_ISCO decreases by a factor of 6, shrinking down to the size of the event horizon. And this sets what many scientists think is the maximum spin a black hole can have. Because if the minimum stable orbit were the size of the event horizon, then light could escape from the black hole, allowing us to see into the singularity. This is called a naked singularity, and it makes a lot of scientists uncomfortable. As yet, there isn't a strong theoretical reason why a black hole can't exceed this maximum spin; it's just that we haven't seen one, and the thought of an exposed singularity just kind of feels wrong. Most suspect the maximum real-world spin parameter is around 0.998.

So how can you use r_ISCO to measure the spin of a black hole? Well, first, let's think of how we measure the size of anything far away from us in deep space, like the radius of a star. Most stars are so far away that they're simply point objects in our telescopes. So how can you figure out their radii? Well, first, look at the spectrum of their light. By seeing how red-shifted absorption lines are, you can determine how far away the star is.

The spectrum also tells you the temperature of the star—because it should approximate a black-body curve. And now, the power radiated per unit area is strongly dependent on its temperature. So, if you know how bright the star appears from Earth, how far away it is, and how much power it's radiating per unit area, well, then you could work out its area and hence its radius.

You can actually do something very similar for a black hole's accretion disk. Just instead of estimating the radius of a glowing sphere, you're estimating the radius of the dark circle, r_ISCO, in the middle of the glowing accretion disk. Then you can use r_ISCO to find the spin parameter. This has been done for a number of black holes, revealing spin parameters from around 0.1 up to close to the maximum. But this method only works if the radiation from the black hole is dominated by black-body radiation from the accretion disk, which, often, it's not.

Another approach involves looking at X-rays emitted by iron around a black hole. Some black holes show a distinct iron emission line. But instead of the single frequency you'd expect, the line is broadened by factors like the Doppler shift due to the high velocity of the iron in the accretion disk and gravitational redshift due to the extreme gravitational fields close to the black hole. By looking at the low-energy limit of the iron emission line, you can determine how close the iron was emitted, and hence, r_ISCO.

But what if there is no bright iron emission line? Well, luckily, there is a third way, and that is to look for periodic oscillations in the data. Like the repeated X-rays observed every 131 seconds. The thinking is these cycles must be caused by clumps of matter orbiting the black hole. And at frequencies that high, they must be orbiting very close in, probably near r_ISCO. Even that close, they'd be going half the speed of light.

But what kind of clumps or objects would these be? Well, the study's authors argue that the best candidate involves an unlikely scenario: years before the tidal disruption event, they propose that there was a white dwarf star in orbit around this black hole. Now, it might be stable, orbiting in this way, for perhaps one or two hundred years. By itself, it wouldn't be visible from Earth. But then the other star wandered by and was ripped apart in the tidal disruption event. Its mass fell in towards the black hole, forming an accretion disk.

With the addition of this stellar debris, the white dwarf was cloaked in glowing matter, creating an X-ray hotspot orbiting the black hole. Its period would directly relate to the spin of the black hole. In this case, the measured spin parameter turned out to be at least 0.7 and possibly as high as the theoretical maximum of 0.998, meaning objects in the accretion disk were going at least half the speed of light. This is the first measurement of spin made possible by a tidal disruption event.

The implication is that this could provide a method for determining the spin of black holes—particularly ones that have been dormant, which is about 95% of supermassive black holes. If they shred a star, we get insight into their spin. Now, why is this important? Well, because it helps us understand the origins of black holes. If supermassive black holes grow in size mainly by feeding on a steady stream of matter from within their own galaxy, you'd expect their spins to be very large because the angular momentum of that matter would be more or less aligned, so it would add up over time.

But if instead, supermassive black holes grow predominantly by merging with other black holes, you might expect their spins to be lower because the spins of two black holes are likely to be randomly oriented rather than aligned. As we are able to measure the spins of more black holes in different ways, further out and therefore further back in time, we should be able to better understand their growth.

And since supermassive black holes lie at the center of most galaxies, they also lie at the center of an understanding of how those galaxies have formed and evolved over billions of years.