The detection of a black hole merger through gravitational waves signaled the opening up of new ground in astronomy. Until that moment, astronomers had only one way to observe the Universe: via the electromagnetic spectrum. It is hoped that gravitational waves will let us see further back in time and deeper into general relativity than ever before.
The first generation of gravitational wave detectors, which are able to detect spatial movement on the order of 10-21m, are the finest and most sensitive listening devices ever made. And now they are listening for black hole mergers.
Unfortunately, in practice, the current generation of gravitational wave detectors is a bit like your granddad. No, they are not deaf, but you still need to shout to get their attention. Or, to put it more directly, only the most energetic and closest events are going to get the attention of advanced LIGO and advanced VIRGO. As a result, researchers are asking themselves if clever signal processing can be used to extract more information from the instruments that are coming online now.
The basic idea is this: we can’t see into a black hole, so how can we figure out if our theories are correct? Astrophysicists are hoping that they can glean insight by watching black holes collide. Essentially, we want to use a black hole to measure a black hole. Now, of course, black holes themselves are famous for not emitting much in the way of light (although the environment nearby does). So, instead of looking for them, we listen for the gravitational waves they emit as they collide.
Even though we can detect a merger quite clearly, the details of individual mergers—the things that make each event distinctive—are hidden in the background detector noise. In other words, all black hole mergers will look the same. The only variations are due to the mass of the black holes that are merging.
Under these circumstances, researchers have two options at their disposal: kvetch while waiting for better detectors or use a clever way to combine the signals from different mergers.
I don’t know anyone with the fortitude to complain for 20 years, and that includes astrophysicists. So, researchers have been investigating how to combine the signals from different black hole mergers to overcome the noise from their instruments and reveal hidden details that are common to all black hole mergers.
The basic idea is relatively simple. As the two black holes begin their death spiral, they emit gravitational waves that start with a very low amplitude and frequency. The amplitude and frequency increase rapidly as the black holes approach each other. Then, at the point of merger, the signal sharply decays away. The gravitational waves emitted just after the merger come from the event horizon of the black hole ringing like a bell.
A ringing bell has a main tone, and lots of overtones as well. So, too, should a black hole merger, but the overtones are much weaker than the main tone and much harder to detect. Unfortunately, you can’t just blindly combine the signals either, because the ringing has both a phase and an amplitude. That means that, if you combine the signals with the phases of the overtones wrong, then the amplitudes will sum to zero. In other words, in trying to increase your signal, you’ve destroyed it.
It seems an intractable problem: to combine the signals, you need to know the phase of each tone. But, to obtain the phase, you have to measure it, which can’t be done because the detector isn’t sensitive enough. And, if the detector were sensitive enough, you wouldn’t need to combine the signals.
On the other hand, we do have a theory of gravity and the gravitational waves we measured during the inspiral to predict the phase and frequency of the main tone and the overtones. Is the prediction accurate enough to allow us to add separate events together nicely?
To answer that question, researchers modeled the signals from black hole mergers and added the instrumentation noise expected from advanced LIGO. They then used this signal to estimate the phase and frequency of the main tone and the first overtone from each merger. This information was used to scale the frequencies of the tones so that they matched, no matter the mass of the black holes, and to use the phase information to add the signals together correctly.
Now, the critical point: does it work? The answer seems to be yes. From their artificial data set, the researchers estimated that advanced LIGO has about a 28-percent chance of detecting the first overtone of the ring down from a black hole merger in one year of observational data. But, by adding mergers together, that chance increases to about 97 percent.
These absolute percentages should be taken with a grain of salt, though, since they make assumptions about how many black hole mergers will be observed per year. Even if the rate of observed mergers is much lower, though, it is pretty clear that it should eventually be possible to add the signals and extract overtones.
Normally, I would think this approach is quite dubious because it uses the theory that it is testing to extract the signal from the noise, the kind of circular reasoning that makes me nervous. However, black holes are an exception. It is thought that all the physics of a black hole are determined by just three properties: the mass, the electric charge, and how fast it is spinning. It should certainly be possible to determine if this idea is incorrect from the overtone modes.
Those three properties underpin a lot of our ideas about black holes, so it would be nice to test our understanding at some level. And, this is only the beginning. Over the next century, the frequency range over which our gravitational wave sensors operate will get wider and wider. Like the beginning of a show, when the lights come up and slowly reveal the stage, I’m anticipating some wonderful and surprising things to be revealed by gravitational wave observatories.
Physical Review Letters, 2017, DOI: 10.1103/PhysRevLett.118.161101