Wednesday 19 January 2022

You'll shoot your eye out: the shock of the recoil

The latest data dump from gravitational-wave detectors turns out to be full of juicy science, just waiting to be scooped out. 

Last month it was the first measurement of black holes enacting one of the most gorgeous quirks of Einstein's famously peculiar theory of gravity. Two black holes were spiralling into each other and one of them was spinning almost as fast as physically possible and that, through a process with no analogue in our daily experience, caused the entire orbit to affect a gentle sway. The effect was ten billion times stronger than previous measurements, which were from much less extreme events, by which I mean two stars that have been squashed to only ten kilometres across and are orbiting each other ten times closer than Mercury orbits our sun, and are therefore rather pedestrian compared to black holes colliding.

This month came a new wonder from the same event: after the two black holes merged into one, the final massive black hole -- over sixty times more massive than the sun -- received a huge kick from the gravitational waves it gave off and shot away across space at over 700km per second. At least! It was more likely 1500km per second, and could have been as high as 2500. Ok, these are all extreme crazy astronomical things, everything goes fast. Is that really such a big deal? Yes! If this merger happened deep in the obscure innards of some galaxy, the final black hole would be hurtling fast enough to escape the galaxy and zoom off into empty space. 

The first result, the long-awaited first measurement of precession, emerged from a month of careful detective work by my group in Cardiff, and came out just before Christmas. The new recoil result is from a group of nine people working at eight institutions across the US and Germany. They put their paper up on the arxiv in the first week of January. So really all this poring over the new data was going on at the same time. 

As I wrote in the last post, I have been working on precession since around 2010 and gravitational-wave astronomers have been eagerly looking out for it since the first detections in 2015. My emotional attachment to recoil goes back further. I first met recoil as a postdoc in 2004 at a journal club, where I learned a tantalising fact. And since it was the only interesting thing I had ever learned in a journal club, I never forgot it! 

In classic clickbait fashion, I couldn't possibly have guessed what would happen next. Prepare for swashbuckling science adventures and serious cursing-and-spitting drama!


Flashback: science and gossip

The recoil happens because the gravitational waves from a binary carry off linear momentum and according to good old Newton's "every action..." third law, the binary recoils in the opposite direction. When the black holes are in orbit most of the recoil is "sideways" to the orbit, and the direction changes as the black holes go around. The usual analogy is to one of those spinning lawn sprinklers: as the little arms spin around, the water shoots out in different directions, and so instead of the sprinkler being pushed backwards it gets pushed in a circle. The same thing happens with the binary. 

This is not much of an "analogy": they're just two illustrations of the same physical effect. One fires off jets of water and the other undulations in the geometry of space and time. Except that only one of them will get you drenched in your back yard.

The exciting part of the recoil effect is the last bit. The two black holes are spiralling towards their centre of mass, which is itself moving in a circle due to the recoil effect. As the black holes get closer they go faster, and the gravitational-wave emission gets increasingly intense, and so the recoil gets stronger and the centre of mass circles faster and faster. Then POW! the black holes collide, and the emission shuts off -- and the final black hole just keeps going. It's like when your child is in the living room swinging a toaster by its electrical cord, faster and faster, and you know that at any moment their grip will slip and the toaster will fly off in some random direction. You have no idea what the direction will be, except that it will cause maximum damage.

The tantalising bit about this, back in 2004, was that in the black-hole case no-one knew how fast the final black hole would move. Remember that this is an effect that emerges from deep in the mathematical murk of Einstein's theory. To calculate it people had to resort to simplifying approximations, and all of these broke down at the point of collision. The crucial final recoil was out of reach. All people could do was make estimates. Since the 1970s there had been ever more sophisticated attempts to get a reliable value for the recoil. After all, this effect could be big enough to kick black holes out of their home galaxies, so it could be a significant astrophysical phenomenon. Was it "only" 50km/s? Was it 500km/s? Was it even higher?

For me the exciting clincher of the story was: obviously we will be able to work out the recoil, once and for all, when we are finally able to produce computer solutions of Einstein's equations for black holes merging. Which was exactly what I worked on! So I was extremely pleased to be given another good reason to get out of bed in the morning. 

Fast forward two years, and suddenly those numerical solutions were possible. In principle the elusive recoil was just a number you could read off when the code was finished. And so the handful of groups around the world that had black-hole codes were in a rush to snatch this juicy piece of low-hanging fruit. 

I was lucky enough to be in the group that got it first. In October 2006 we worked out what the largest recoil could be from two black holes colliding. I still remember the exact number: 172.5km/s. Job done. 

But it wasn't over. We hadn't looked at whether the recoil could be larger if the black holes were spinning. And this was where the race really heated up. 

In early 2007 -- January 26th, in fact -- a paper appeared that showed that spinning black holes could produce a recoil of almost 500km/s. Bloody hell! That blew our measly 172.5 out of the water!

But save your surprise, because only three days later yet another paper appeared: if the spins are tipped over, you could get an even larger recoil. Maybe as high as 1300km/s!

Now we step out of this rarefied talk of numbers and into the real world of ambitious human beings in desperate search of a prize. The latest paper looked like a panic reaction. They had not done the computer calculations to find the 1300km/s; they had done a pen-and-paper estimate of how much bigger the new spin effect could be, and were postulating the large recoil. Why didn't they just do the calculation?  

The nerve-racking reality of some research is that as soon as you spot a result it's like walking past a gem in the gutter across the street. It's a miracle you noticed it, but now that you've seen it, you're sure that it must be blindingly obvious to everyone else, especially all those people walking RIGHT PAST IT. You'd better dash across the street RIGHT NOW and grab it! Even if you have to risk getting run over to do it!

In our group we guessed that these people had been working on their "1300" computer calculations, then the "500" paper came out, and they decided they'd better get their clever insight out quick. (For reasons that may become clear, I have never verified this guess.)

Risky move. Now we were asking ourselves, could we do it first? Some of us thought not: there were several subtleties to this effect, and it could take ages, and surely this other group was far ahead. But one of the other postdocs thought, to hell with it, let's just try. He started off the code, and a day or so later the result was in... not 1300, but 2500! This was well beyond anything anyone had ever dreamed of. We immediately started to write it up. 

You might read this and think: that's a bit underhanded. Those other people had realised this cool effect, and they were clearly working on it. It's their thing. Let them do it. 

As a young fellow still new to the niceties of scientific etiquette, I raised this very question with our supervisor, who I should say was at all times an extremely scrupulous and courteous person. He had an unexpected take. "They pointed out a possible effect, and we have found it. This is science at its best." His conclusion was especially memorable: "They will be happy that we have followed up their suggestion."

What a fascinating prediction! Fortunately, I was able to be a good scientist and experimentally test it. We were all about to leave for a conference and our competitors would also be in attendance. If all went according to plan, our paper would likely appear on the second day of the conference. I could see for myself how happy they would be!

I could string out the suspense with all of the antics of the next few days, but we should get straight to the experimental results. I won't go into my altercation with a German train ticket collector that almost lead to me missing my flight to the US. Or how all the conference participants viewed us as a bunch of losers for huddling in a corner during the conference's first day coffee breaks, tapping on our laptops. Or the discombobulated plenary speaker who was struggling to review the current state of the field, hours after our paper appeared. 

I will just report immediately that our competitors were not happy. 

On the other hand, let me reassure you that no scientists were permanently harmed by the events in this story. It was an exciting time, packed with big results. Some people called it a "gold rush", and that's pretty much what it was. Everyone in our two groups went on to successful scientific careers.


The flashback ends

So: back to the new result. One of the cute subtleties of these large recoils is that they depend on the direction of the black hole's spin axis relative to the orbit. If the biggest recoil happens when, for example, one black hole's spin is pointing at the other black hole, then the recoil will be zero when the spin is at right angles to the other black hole. The spin's direction stays roughly fixed in space while the black holes zip around in their orbit. So the direction of spin relative to the other black hole changes very rapidly during the last furious orbits before merger. You cannot tell whether the final recoil will be huge or whether it will be zero, unless you nail down a measurement of the spin's direction. Sadly, the spin's direction has a very weak effect on the gravitational-wave signal, so it is extremely difficult to measure. 

(For nonspinning black holes, our old 172.5km/s result appears when one black hole is roughly three times as massive as the other, and so a small-ish recoil was already inferred from an earlier gravitational-wave detection, GW190412. It's the huge spin-induced galaxy-escaping recoils that are hard to measure.)

But not for this new signal, GW200129! The signal is strong enough that you can measure the spin's direction just before the black holes collide, and so you can measure the recoil! This is what was reported in the most recent paper. We have now entered an era where gravitational-wave detections are strong enough to pull out these subtle but powerful effects. 

Is this another gold rush? Not quite yet. It's still the occasional gem in the gutter. Beware of scientists dashing madly through traffic.


Previously: the first precession measurement

More on gravitational waves 

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