Was the Gravitational Wave Background Finally Discovered?!? (script) (Patreon)

A few weeks ago a large team of gravitational wave astronomers announced something pretty wild. The moderately confident detection of pervasive ripples in the fabric of space time that presumably fills the cosmos, detected by watching for subtle connections between the signals from rapidly spinning cores of dead stars in our galactic neighbourhood. In other words, the gravitational wave background has probably been detected using a pulsar timing array.

The likely detection of the gravitational wave background is huge. Several channels have gotten to this news item before us, but, in our defence, we did an episode on the slightly more tentative detection  two years ago. Now the detection is on firmer footing and the basics have been thoroughly covered by ourselves and others, we can dig a little deeper. So today I want to talk a bit about what it took to spot the gravitational wave background, and then more about what it tells us about our universe.

First up, let’s take a moment to appreciate the awesomeness of this achievement.

We started with a deceptively simple idea. And by we I mean humanity, but specifically the incidence of humanity named Albert Einstein. The following thought popped into his head:

“For a man falling from the roof of a house, there is no gravitational field.” This became the equivalence principle, which basically states that the feeling of weightlessness you have while falling is *the same* as weightlessness in the absence of gravity. And the feeling of heaviness when accelerating is the same as that when stationary in a gravitational field. At least as far as the laws of physics are concerned. From the equivalence principle and one more axiom that the speed of light is constant for all observers, an inevitable chain of reasoning led Einstein to the general theory of relativity, which explains gravity as being due to the warping of space and time.

The equations of GR give us so much more than gravity—they predict that gravitational fields slow clocks and deflect light, reveal the inevitability of black holes, and also predict that the fabric of spacetime should carry waves.

Gravitational waves were the last great prediction of general relativity to be experimentally verified, and this happened only in 2016 when LIGO spotted the spacetime ripples caused when a pair of black holes spiraled together and merged over a billion light years away. They do this by measuring the literal stretching and squishing of space, using what amount to a pair of ultra-precise rulers a few kilometers in length, set at right angles to each other.

In the 8 years we’ve been doing this, we’ve observed the gravitational waves resulting from the final inspiral of pairs of black holes and/or neutron stars. These have mass from a few to a few tens of times the mass of the Sun. Our Earth-based facilities were built to be sensitive to these, because we knew there should be lots of them. As waves, gravitational waves have wavelengths. An observatory will be sensitive to wavelengths that have a similar size to the detector arm—to its rulers. And inspiralling stellar corpses generate wavelengths roughly equal to their orbital period times the speed of light—which is a few kilometers in the last seconds of that inspiral.

The larger the orbit the longer the wavelength. The gravitational waves produced by binary stellar mass black holes when they’re further apart should be visible to the Laser Interferometer Space Antenna—LISA—with the 2.5 million km long arms of its laser-connected spacecraft.

But there are also gravitational waves that stretch for light years—waves that no human-built device could hope to detect because we can’t build galactic-scale rulers. But by happy chance the galaxy has obliged and provided us with a network of natural rulers—the pulsars. Well, more clocks than rulers. Pulsars are rapidly rotating and precessing neutron stars whose jets sweep past the Earth, resulting in blips of electromagnetic radiation that repeat with extreme regularity, sometimes several hundred times a second. Those ridiculously fast ones are called millisecond pulsars, and they are the most precise clocks in the universe, natural or unnatural.

But we wanted a ruler, not a clock. But with the conveniently constant speed of light, a clock becomes a ruler if we just measure the travel time of light.  If a gravitational wave passes by the stream of incoming signals from a pulsar, it will stretch and compact the space between those pulses. Measuring the change in pulse arrival time measures the gravitational wave. This can, in principle, be used to spot individual gravitational waves.

But that’s not what this new result is. Several international collaborations have now been watching dozens of pulsars for over 15 years using many of the largest radio telescopes on Earth. These pulsar timing arrays don’t yet have a sure signal from a single gravitational wave, but essentially all these teams agree that their data reveal something that’s arguably even cooler. All of spacetime across the pulsar network, and probably across the universe, is a bit wibbly wobbly. They claim detection of the stochastic gravitational wave background—the jumbled overlap of many many very weak but very long wavelength gravitational waves that must originate from across the known universe.

We don’t know what causes it yet—it could be echoes from the inflationary epoch which kickstarted the Big Bang, or universe-wide phase transitions right after that. It could be cosmic string collisions in which fissures in spacetime tangle and split, or the frolicking of galactic gigawhales in galaxies far far away. Probably not that, but we can hope. Most likely, this gravitational wave background results from binary black holes. Although in this case, it’s not from the individual 10s-of-solar-mass black holes seen by LIGO. We’re probably seeing the reverberating tremors caused by binary pairs of behemoth supermassive black holes in the hearts of galaxies.

These SMBHs are close to my own heart as a researcher, so I’m more than a little excited about what we can learn about them, and I’m going to spend some time on that today.

But first, let’s start with an analogy to get a better picture of all this craziness.

Take the surface of a still lake and very rapidly stir it at one point with a pin point. The expanding ripples are like the gravitational radiation detected by LIGO. Now, instead of one pin-point spiral, stir the surface of the lake with many many … I dunno, tree trunks or something, but much more slowly. The entire lake is now covered in a jumble of very low-frequency ripples that aren’t distinguishable from each other.

This is similar to what the stochastic gravitational wave background should look like if it's caused by binary supermassive black holes. LIGO is tiny compared to the resulting spacetime ripples. Both of its arms are affected to the same degree by lightyears-long oscillation, and so it doesn’t notice their passage. But the relative distances to pulsars ARE affected by these enormous waves, and so they should cause observable shifts in the timing of their pulses as we observe them.

These ripples are messy—apparently random, or “stochastic”. So how can we be sure we’re even seeing gravitational waves? After all, there are various reasons why the rate of a pulsar’s signal may change. Pulsar rotations rates can slow down or speed up, and the travel time of their signals to us can be affected by more than gravitational waves. For example, passing through a region of ionized gas slows the radio light. But all of these things should affect each pulsar individually, or at worst affect groups of pulsars in one particular direction.

However, gravitational waves cause the pulse rates of pulsars across the galaxy to change in ways that are correlated with each other. Imagine signals traveling to us from different pairs of pulsars. Those signals could be traveling together if the pulsars are near each other on the sky. They could be traveling to us from opposite directions on the sky. Or the signals could be traveling at right angles to each other. Or they could be situated in between those extreme cases.

Any given gravitational wave that makes up part of the background will also be traveling through the galaxy in some direction relative to both of the pulsar signals. In some cases, that relative direction will cause both pulse rates to be affected in the same way—correlated, and in some cases they’ll be affected in opposite ways—anticorrelated.

For example, you would get a correlated pulsar timing shift if both pulsar signals are surfing the same gravitational wave, or if a 180-degree-separated pulsar pair encounters a gravitational wave moving at right angles to both signals. And you’d get an anti-correlated shift if the pulsar signals are traveling at right angles to each other because of the way gravitational waves alternatively stretch and squish space at 90 degrees as they pass.

The correlation or anticorrelation due to a single gravitational wave is extremely difficult to pick out from all the sources of noise. However, if you look at enough pairs of pulsars for enough time, you expect to see a statistical correlation in what we call the pulsar timing residual—the amount of deviation from the very precise expected arrival time of these pulses.

This is the Hellings-Downs curve. It’s the theoretical correlation between pulsar timing residuals for pairs of pulsars as a function of their separation on the sky. Pulsars with little separation should be highly correlated. Pulsars with 180 degree separation should be somewhat correlated. Pulsars with 90 degree separation should be anticorrelated.

OK, so how are the real pulsars behaving? This is the result published by the NANOgrav collaboration. That’s for every combination of pairs for 67 pulsars observed over 15 years. It’s very consistent with our Hellings-Downs curve, and NANOgrav claims that this is from 3.5 to 4 sigma depending on the statistical analysis used. That means it’s not quite a slam-dunk detection, in that this apparent correlation could still have popped out of random noise by a 1 in thousands chance. But it’s looking increasingly likely that the correlations are real. The same results have been observed by other pulsar timing array experiments, including with varying degrees of confidence.

Now we can start digging into what we learn about the universe from this observation. But before we do that, let’s pause for a moment to appreciate how crazy this achievement really is. Remember we started with a simple thought experiment about the experience of someone falling off a roof. That “what if” scenario led us all the way to an actual observation of galactic-scale spacetime ripples.

But spacetime ripples from what? I’ve been talking about binary supermassive black holes, because that’s what the NANOgrav team thinks this is. The type of timing correlation that was observed is what you’d expect from many, many sources of gravitational waves that are a) powerful and low frequency, b) randomly distributed across the cosmos, and c) randomly polarized - so no preferred direction for the stretching and squishing of space from any given wave. Any such population of sources should give you this characteristic curve.

So why binary SMBHs? Well they do potentially fit the requirements, but just as importantly, we know they should exist. We know that every galaxy contains a huge black hole at its center. And we know that bigger galaxies are made from smaller galaxies combining, and that bigger galaxies have bigger black holes. It only stands to reason that there are a good number of binary supermassive black holes out there, even if we haven’t seen them directly. Any other source for a gravitational wave background like this is much more speculative—and we talk about those in our previous episode.

OK, so what does this signal tell us about giant black holes, assuming they’re the cause? The pulsar timing data contains more information than the Hellings-Downs correlation. We also learn about the frequencies of the underlying waves. For binary black holes, the frequency of the outgoing gravitational wave is basically the rate at which the monsters orbit each other. If we can see what different frequencies make up the jumbled mess of the gravitational wave background we can learn something about those black hole orbits. In particular, we can learn about how they spiral together and eventually merge. For example, if those binaries spend a lot of time orbiting each other at a great distance, then there should be a very strong low frequency signal.

This is the NANOgrav frequency spectrum. The grey … funny shapes represent the strength of each frequency observed in the gravitational wave background. The dashed line is what we expect from a simple model of how supermassive black holes grew and formed binary pairs over cosmic history. It’s not inconsistent with the data, but there’s a hint of difference compared to the simple model prediction. Perhaps too much high frequency signal, or too little low frequency signal. The NANOgrav collaboration speculate that the latter could be due to the binary supermassive black holes interacting with the stars of their surrounding galaxies, causing them to spiral together quicker than without that interaction.

There’s also hint that the gravitational wave background is a bit stronger than expected from the simple binary black hole model, which means the SMBH pairs may be more massive than expected or there are more of them. But this is all very loose, and there isn’t enough data yet to make any conclusive statements.

But that data is coming. With this spectacular result you can be sure our pulsar timing array projects will continue. The longer we watch, the larger these arrays get. That’s because gravitational waves will have time to traverse larger distances and affect the timing of more distant pulsars. For example, in NANOgrav’s 12.5 year data release they included 47 pulsars, while at 15 years they could include 67. As the pulsar timing array gets larger, and as we track the correlations between pulsar pairs for longer, we hope this detection of the gravitational wave background becomes rock solid. Then we can really start to pin down its origin, and use our new galaxy-scale observatory to study those mysterious cosmic cataclysms that are sending tremors through the fabric of all of spacetime.