Black Hole Merger at LIGO

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A comic about the black hole merger at LIGO

The black hole merger at LIGO

You’ve probably read it in the news: this Thursday, LIGO is going to announce it has detected a black hole merger. What is it exactly and how is it detected?

A black hole merger happens when two black holes start spinning around each other, eventually smashing together and making a bigger black hole. The reason they spin is, of course, because of their gravitational attraction. However, unlike the Earth, which seems pretty happy in its orbit, black holes have a tendency to get closer and closer. This should come as a surprise: in space there is very little friction, so the black holes should not be losing any energy, which means they should stay in their orbits. But they don’t: instead, they spiral into each other until they merge.

Gravitational waves

The key is something called “gravitational waves.” In General Relativity, space and time are not passive spectators, but the source of what we called the gravitational “force.” Matter bends space and time around it, which causes trajectories that were initially straight to curve, giving rise to the familiar orbits around the Sun, for example. There is no force: particles just move in a “straight” line, it’s just that this straight line is in a curved space. This is similar to being on Earth and starting to walk forward: even though our path feels “straight”, we will eventually arrive at the same point because the space we live in is curved.

The moment you accept that matter bends space, you realise that the curvature should be able to travel around. If I move my rubber duck back and forth in my bath, it will create ripples moving through the water; in the same way, fast-moving, massive objects will create ripples that move through space. We call these ripples “gravitational waves.”

Everything creates gravitational waves. However, since gravity is such a weak force, they are really hard to detect. Only massive objects like black holes will emit waves powerful enough to be felt on Earth, at least with current technology. That’s why people at LIGO expected to see only events such as the merger of two black holes, which are massive enough and move fast enough to create a noticeable effect.

Waves carry energy, it’s kind of their thing. The energy carried by a wave is proportional to its frequency (think about it: would you rather be hit in the head 2 or 20 times per second?). When two black holes spin around each other, the frequency of the waves they give off is the same as the frequency of their spin. As they get closer, the black holes spin faster, which means they give off higher energy waves, which means they lose energy faster and get even closer. Therefore, if we ever saw the gravitational waves given off by two black holes merging, we should see waves of a frequency that is increasing faster and faster. This is exactly what LIGO has seen, which is the graph on the last frame of the comic strip.

Detecting gravitational waves

The tricky part in all of this is, of course, seeing the gravitational waves. We know they are a ripple in space and time, but what does that translate to? A ripple in space and time should mean that space contracts and expands periodically between two points. That is, if a gravitational wave goes through you right now, your head will get a bit smaller, then a bit bigger, then back to normal. The problem is that rulers will also shrink and expand, so you can’t use them to figure out whether a wave just passed you!

A gravitational wave between two electrons and a photon
Even though the ruler changes size, the photon always travels the same distance after the same time.

Thankfully, there’s a way around. What you can do is send a photon between the two points and see how long it takes. Since the speed of light has to be the same for everyone, you should see a difference in the time and use that to detect the wave.

But measuring the time it takes for a photon to do anything is not easy, because photons take almost no time to travel between places. What LIGO does is use a phenomenon called interference: it sends two photons against each other and sees if they disappear. This is based on the idea of quantum clocks that I talked about here: every particle has a little timer attached to it, which spins faster or slower depending on the energy of the particle. If two identical particles (like two photons) meet at the same place and their clocks are pointing in opposite directions, they will annihilate: they’ll both disappear. I can use this to figure out if a gravitational wave has gone through. To do that, I need an L-shaped device, where I send photons which are perpendicular to each other to a certain point. I make certain that, under normal conditions, the photons disappear: we call this destructive interference. Now, what happens if a gravitational wave goes through my L-shaped device? Then, the length of one of the arms will change. This means that those photons will take longer to reach the same point, which in turn means their quantum clocks will have run for longer than those in the other arm. Therefore, now the quantum clocks of the photons coming from both sides are not exactly opposite any more, which means I should see some photons where there were none. Therefore, every time I detect a photon, it means a gravitational wave went through my device. Clever!


The problem, of course, is getting a device that is sensitive enough to detect these differences. In LIGO, the arms are roughly 4 km in length and there are two L-shaped devices, which allows them to pinpoint the location of the source of waves. In general, the bigger the arms, the easier it is to detect the waves, since the change in length is proportional to the length of the arm. In fact, there is already a project under way to build a gravitational wave detector in space! It will be called LISA and made up of satellites beaming lasers at each other.

LIGO’s announcement this Thursday

Now you’re in a position to understand what LIGO will announce this Thursday: they have seen the merger of two black holes with masses equal to 36 and 29 Suns into a bigger black hole with 62 masses. Now, a some quick math will show you that the total mass of the two black holes is 36 + 29 = 65, whereas the resulting black hole only has 62 solar masses. Where did the 3 missing solar masses go? They were converted into the energy of the gravitational waves. Yes, that’s right: just the waves carry the equivalent of 3 solar masses worth of energy. Mind-boggling stuff.

Apparently, LIGO have seen the exact frequency increase predicted by Einstein’s relativity, which is yet another confirmation of his theory. The merger has been seen by both their devices, with the correct delay between them, showing that gravitational waves travel at the speed of light. Exciting times to be a physicist!

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