A Supermassive Test for Einstein’s Famous Theory

You’re oscillating. Well, technically, not just you. We are all being stretched and squeezed by an event we can’t see—at least not with the naked eye. Imagine that throughout the day we have imperceivable fluctuations in our height, starting taller in the day, shorter at night, constantly stretching and squeezing like a spring. Our entire universe experiences something of the same, just rather than fluctuations repeating every 24 hours or so, it’s every decade.

Somewhere, far, far away and long, long ago, two supermassive black holes came together, forming a binary system. These black holes have gargantuan masses, at least 100 million times the mass of our sun. They were bound to each other in a seemingly perpetual orbital dance, spending tens of millions of years orbiting each other, creating ripples in the fabric of spacetime that may soon be detectable to us. As the two continue their tango, they lose energy and draw their counterparts in closer and closer. These eonic spirals are dances that we, the authors, spend our brain cycles chasing.

Pulsar pulses are so exact and predictable that they are nature’s original gravitational wave detector.

As we get closer to discovering them, we’re uncovering secrets that could revolutionize the knowledge of the physics governing the most massive black holes known to humanity, the evolution of galaxies, and if the universe on large scales works the way Einstein said it does.

Energy lost by black holes when they merge was first predicted by Einstein in 1916, though he believed that the ripples these black holes make—these gravitational waves—would be too small to ever detect. His theory, general relativity, explains gravity is caused by a massive object curving space and time around it, unified by a new quantity called spacetime. Using the principles dictated by this theory, the concept of gravitational waves was born.

Gravitational waves—ripples in the fabric of spacetime itself—can be created when accelerating masses, such as pairs of black holes, begin to merge. As these gravitational waves plow through the universe, they stretch and squeeze all the fabric of spacetime itself, causing everything to oscillate like a pair of swing dancers as they pass through, onto their next partner.

The prediction of gravitational waves emitted from merging black holes took 100 years to validate. Indeed, it took decades of technological advances to create an instrument sensitive enough to make the first gravitational wave detection, back in 2015. That instrument, called LIGO, can only detect gravitational waves from black holes about 10 times the mass of the sun, called stellar mass black holes. To detect supermassive black holes, we need to build an astronomically larger gravitational wave detector.

Looking back at the slowly orbiting supermassive black holes, gravitational waves are emitted in all directions like an ever-enlarging pirouette. This whirling can be seemingly perpetual: Each orbit lasts years to decades, and the whole merger process can last millions of years, maybe longer. There’s a supermassive black hole at the center of our own Milky Way galaxy, called Sagittarius A*, weighing in at a whopping 4 million solar masses.

Even more interestingly, this isn’t happening with just one supermassive black hole binary. Potentially millions of supermassive black holes are slowly orbiting their partner, with each of their gravitational wave signals stacking up on top of each other to create gravitational noise—or a gravitational wave background. This background has an amplitude which is set by the number of supermassive black hole binaries which create it, their distance from the Earth, and the masses of the black holes themselves. This amplitude also varies as a function of gravitational-wave frequency, from the nanohertz regime to the microhertz regime—millions of times lower frequency than the LIGO detectors can ever measure. But how can we detect such low-frequency gravitational waves? Concretely, a billion solar mass supermassive black hole binary at a frequency of 1 nanohertz takes about 30 years to complete an orbit.

How do these merger signatures manifest in the gravitational wave background? For example, stars and gas are much better at driving black holes to merge when they are widely separated. It’s not until the black holes are very close that gravitational wave emission really takes over. We can predict that the amplitude of the gravitational wave background might be lower than expected at very low frequencies, where the gas and stars are doing most of the work in pushing the black holes together.

Furthermore, these gravitational waves should change the distances between objects by one part in a million billion. To detect such small spacetime perturbations, we turn to the best natural clocks in our galaxy—millisecond pulsars. These pulsars are neutron stars which emit radio waves that can be detected by radio telescopes on Earth each time they spin around. They can also give us insight into this cosmic gravitational interpretative dance. The arrival times of pulsar pulses are so exact and predictable that they can be timed down to hundreds of nanoseconds over a decade—or one part in a million billion—making them nature’s original gravitational wave detector.

Millions of supermassive black holes may be orbiting their partner, creating a gravitational wave background.

As the gravitational waves travel through our galaxy, stretching and squashing the fabric of spacetime, the pulsar pulses arrive a little bit early and a little bit late since the pulsars get a little bit closer, and then farther away. Since we know exactly when the pulsar pulses should arrive, changes to this can signal the presence of gravitational waves. This collection of pulsars and radio telescopes used to time the pulsars is called a pulsar timing array (PTA), and it effectively turns the entire galaxy into a gravitational wave detector.

It’s been astounding to learn that the universe can gift us ultra-precise data from millisecond pulsars. This is especially mind-blowing, given how hard it was to build the ground-based gravitational wave detectors like LIGO. The level of sensitivity required to detect fluctuations with LIGO took over 40 years to achieve and billions of dollars; meanwhile ultra-stable millisecond pulsars—discovered in 1982—are naturally occurring gravitational-wave detectors. Sapiens, sometimes, have nothing on nature.

Of course, life doesn’t stop for anyone, not even a neutron star. There are still internal processes in the pulsar that could potentially contribute to the changes in the period. How does one account for this signal?

By cross-correlating the pulsar arrival times, we can search for a common signal in all the pulsars and beat down any intrinsic pulsar noise. The more pulsars we add to our array, the better our signal gets. After carrying this cross-correlation in the pulsar arrival times, two signals should survive since they are common to all the pulsars: the amplitude of the gravitational-wave background and the distinctive Hellings and Downs curve.

A fundamental paper written in 1983 by R.W. Hellings and G.S. Downs introduced the idea that cross-correlated pulsar pairs will respond distinctively to the presence of a gravitational wave background. When we have a large number of pulsars, as we do in the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the point-by-point correlation function appears to form a curve. This is called the Hellings and Downs curve. It shows how the amplitude of the gravitational wave background is modified as a function of the angle separating each pulsar pair. This distinctive shape can’t be created by any other natural process and is largely considered to be the smoking gun for the presence of a gravitational wave background in a pulsar timing array.

NATURAL CURVE: The distinctive shape shown in the Heiling and Downs chart (above) can’t be created by any other natural process. It’s considered to be the smoking gun for the presence of a gravitational wave background. Credit: Chiara Mingarelli.

By finding both the presence of the Hellings and Downs curve in our cross-correlated pulsar data, together with a common amplitude signal of the gravitational wave background, we can bring our millions of dancing supermassive black hole pairs to the fore.

As pulsar timing arrays become more and more sensitive, they will be able to measure how the amplitude of the gravitational wave background evolves as a function of frequency, which can give us clues as to what is creating the gravitational wave background. While it is widely held that supermassive black holes should generate this low-frequency background, other sources of low-frequency gravitational waves include primordial gravitational waves from inflation, the quantum fluctuations from a fraction of a second after the Big Bang, and exotic networks of cosmic strings, the theoretical, super dense filaments of matter-energy, which can be the size of the entire universe.

Probing this background will give us deeper insights into open problems in astrophysics. The secrets that are hidden within pulsar timing array data may lead to answering critical questions for astronomers. We will be able to say, for example, what will happen to our supermassive black hole, Sagittarius A*, when our galaxy collides with neighboring Andromeda.

We will also be able to say general relativity has, or has not, passed another test when huge gravitational forces are in play. Indeed, some theories predict that gravity, in very strong gravitational regimes—such as in supermassive black hole mergers—behaves differently than what Einstein suggested. According to general relativity, a supermassive black hole binary’s orbit should shrink in a specific way while emitting gravitational waves. Deviations from this could indicate new physics beyond general relativity. Gravitational waves, like light, are also polarized. General relativity predicts two polarizations (called plus and cross), but others could also exist, again pointing to either extensions of general relativity or entirely new physics.

Hopefully, within our lifetime, astronomers will gain insights into these and more open questions, all due to a whole lot of shimmies taking place throughout the universe.

Melize Ferrus has been doing research on smaller black hole mergers with the Flatiron Institute’s Center for Computational Astrophysics.

Chiara Mingarelli is an assistant professor of physics at Yale University and has been thinking about supermassive black hole mergers for over a decade.

Lead illustration by Olena Shmahalo for NANOGrav