When Black Holes Collide (Script) (Patreon)

When physicists talk about black holes they’re usually referring to highly theoretical objects – static, unchanging black holes viewed from “infinitely” far away. This makes everything clean and simple enough to attempt the already notoriously complex calculations of black hole physics. But real black holes are created in the violent deaths of massive stars, and there’s nothing clean about that. And we now know that black holes merge – and in the process produce gravitational radiation that we’ve only just managed to detect with the miraculous work of the LIGO and VIRGO gravitational wave observatories. In the instant after its merger, the new, joined black hole looks nothing like the idealized theoretical black hole.

Imagine it: two event horizons – two roughly spherical black surfaces that are literal boundaries to our universe. They spiral together and touch – instantly becoming a single surface. Technically, in that instant we go from two black holes to one. But in the beginning this new black hole looks nothing like its progenitors. It’s not even close to spherical – it’s dumbbell-shaped, then it’s an elongated blob, and then it’s an oscillating spheroid – like a ball of water wriggling in space. But what exactly is oscillating here? The event horizon seems to define the surface of the black hole, but really it’s the fabric of spacetime itself that’s vibrating.

The two inspiralling black holes make powerful spacetime ripples – gravitational waves – which intensify as the black holes approach merger, only becoming observable in the last fraction of a second. And then the merged black hole continues to radiate these spacetime ripples as it oscillates, but these quickly die away as the black hole settles into its final static form. This final phase is called the ring-down – an expression comes from the analogy with a bell. When struck, a bell vibrates with many different frequencies – many overlapping harmonics. As those vibrations give up their energy – in this case to sound waves – the vibrations fade. The bell rings down.

A “struck” black hole also vibrates with many different harmonic frequencies. The harmonics of a vibrating sphere – be it a blob of water in zero-g or a black hole – are analogous to the harmonics on a vibrating guitar string or piano wire. In the latter cases we can describe the vibrating string as a series of standing sine waves of different frequencies, all happening at the same time. The lowest frequency the string can support is called the fundamental mode – it’s usually the strongest or loudest, and defines the note – middle-c, f-sharp, whatever - played by that string. Higher frequency modes are called overtones, and they provide richness and texture to the sound. The full set of possible frequencies a string can support are called its harmonics.

The harmonic oscillations of 2-D surfaces – like drum skins, bells, or the event horizons of black holes – are a good bit more complex than in 1-D. In the case of the event horizon, or any spherical-ish surface, we break down the oscillations not into sine waves but into spherical harmonics. These are a set of functions pretty analogous to 2-D sine waves on the surface of a sphere, and each spherical harmonic can represent a single, pure oscillation on that spherical surface with a set frequency.

A harmonic oscillation that decays over time is called a quasinormal mode. For a black hole, another way to think of its quasinormal modes is as a set of gravitational waves trapped in orbit around the black hole. They leak away over time, but while present they warp the shape of the event horizon.

OK, so a black hole can ring like a bell – then a black hole merger is the biggest hammer strike of all. But what does the ring-down of a black hole really look like? We can answer that be asking what harmonics are present in that oscillation, and how quickly to each of those harmonics fade away.

Many scientists had assumed that in order to see the overtones you’d need to look at the tail end of the ring-down, when the black hole was approaching a more spherical shape. 

They thought that right after merger the black hole would be too chaotic – that the oscillations should be “non-linear”, or in other words not well represented by adding together a simple set of spherical harmonics. The problem is, at the tail-end of the ring-down the LIGO signals are probably too weak to detect overtones.

Matthew Giesler, Max Isi, Mark Scheel and Saul Teukolsky of CalTech and MIT went against this these prior assumptions in their recent paper. They looked for overtones in the ring-down from right at the point of merger. Now this wasn’t a real black hole merger – we’ll get to that shortly. Giesler and team first they found the harmonics in a fake black hole merger. Specifically, a simulated merger by the SXS – Simulating Extreme Spacetimes – project – basically the result of teaching a supercomputer general relativity and, among other things, telling it to collide thousands of black holes. The advantage of first trying it with a simulation is 1) you don’t have to use a signal degraded by a billion years of travel, and 2) you know exactly what parameters went into the signal – in particular black hole mass and spin, so you know if you got the right answer when you try to predict these values.

The researchers found a few very surprising things. First, the waveform was nicely simulated by spherical harmonic oscillations right from the point of merger, so it was not the chaotic mess previously assumed. Second, when the ringdown begins some of the overtones are actually stronger than the fundamental mode, even though they do die out more quickly. This means that these overtones are potentially detectable in the real merger signals from LIGO and VIRGO. And THAT has some very exciting implications.

The rich structure of overtones in a musical instrument can tell you what instrument you’re listening to. Similarly, the overtone structure of a black hole ringdown can identify the fundamental properties of the black hole – namely its mass and spin. The researchers found that they could pinpoint the mass and spin of the simulated black hole with much greater precision than if they’d just used the gravitational wave signal from the lead-up to the merger.

In astronomy, the analysis of the different frequencies of light is called spectroscopy. So this sort of frequency analysis of gravitational waves is being called gravitational wave spectroscopy.

Now for this to be useful probably we’d want to look at some real black hole mergers. The team totally did this – and reported the results in a follow-up paper, adding Will Farr to the team for this one. Isi et al. looked at the merger and ring-down signal from the largest black hole merger we’ve seen. Which, in fact, was also the first one LIGO reported: GW150914 – a pair of black holes, each 30 or so times the mass of the sun, spiraling into each other one and a half billion light years away.

The team analyzed the harmonics in the gravitational wave ring-down from this event and claim a likely detection of at least one overtone – detected with a confidence of 3.6 sigma. That means it seems very likely they really detected the overtone, but to effectively eliminate doubt we’d want more observations. By analyzing the harmonics, the team calculates the mass of the final black hole as 68.5 solar. They also get a spin for the final black hole – a so-called dimensionless spin magnitude of .69 – where the spin magnitude can vary between 0 – not spinning – or 1 – spinning as fast as possible. .69 means this is a rapidly rotating black hole, which is unsurprising seeing as it just absorbed the orbital angular momentum of two black holes.

Both the mass and spin derived from the ringdown are consistent with the estimate that was previously obtained by analyzing the entire waveform WITHOUT accounting for overtones. This is important, because the overtone analysis ONLY looked at the ringdown, so this tells us that all information on the nature of the final black hole properties is embedded in those final oscillations.

And this brings us to the last, and perhaps coolest application of this technique – testing Einstein. General relativity predicts that black holes should be completely defined by three properties – their mass, spin, and electric charge. 

It doesn’t matter what fell in to make the black hole – atoms, photons, dark matter, monkeys – all that information should be lost, leaving only 3 properties. This is the no-hair theorem – black holes have no hair. Well, at most 3 hairs. And astrophysical black holes are also expected to have no electric charge, so mass and spin should define everything – including the nature of the oscillations during ring-down.

The researchers test the no-hair theorem by checking whether the frequency of oscillations and the time for the decay of those oscillations agree perfectly with Einstein’s predictions. They do – at least within the uncertainties of the experiment. The oscillations are consistent with a black hole purely defined by its mass and spin. The authors claim this as tentative support for the no-hair theorem. It’s a long way from a confirmation of the theorem – but with the analysis of more black hole mergers, any deviations from the pure-general relativity, hairless black hole will either appear or become less and less likely to exist. For now, Einstein reigns supreme.

And what about those new mergers? It’s been a while since we saw a big press release from LIGO. The last was the incredible binary neutron star merger that was also detected across the electromagnetic spectrum as a giant explosion. Well, rest assured that detections have continued. LIGO and VIRGO have been in their 3rd observing run since April 1st after massive upgrades to its sensitivity, and this run will last one year. 

The team typically waits until the run is complete to announce findings because it takes a while to fully confirm each signal. But the team isn’t nearly as secret as they once were. LIGO has a publicly available alert system so that astronomers can follow up gravitational wave detections with other telescopes. LIGO’s gravitational-wave candidate event database reveals many, many candidate detections – many of which will prove to be real.

So far the list of high-confidence events included around 20 new black hole-black hole mergers, a few black hole-neutron star, and neutron star-neutron star mergers. The observatories are seeing a new event roughly every 5 days on average, but sometimes on multiple days in a row. On August 28th, two black hole mergers were seen separated by only 20 minutes, and potentially in the same part of the sky. This is currently looking like just a coincidence, but if not it’ll be hard to come up with a plausible explanation for why two pairs of binary black holes should merge near each other at the same time.

So, long story short – the initial promise of LIGO and the first detection of gravitational waves really seems to be panning out. Gravitational wave astronomy is now really a thing. We’re seeing many, many mergers of black holes and neutron stars, and we’re learning an awful lot about these objects. And with the new subfield of gravitational wave spectroscopy, we can now listen to the harmonics of ringing black holes, and through them better understand the fundamental nature of extreme spacetime.