This paper was part of a fun, quick project where we had an idea about how to figure out whether there are any supermassive black hole binaries nearby (where by "nearby," I mean within 300 million light years) and we did it using a pretty funky method: we used pulses of light. You don't normally think of light when you think of black holes (hence why they're called black holes) but we were able to place limits on binaries using an indirect method using some pretty strange objects called pulsars. I actually think this is such a clever idea (it was thought of a few decades ago and damn those guys were smart) so bear with me a moment and I'll explain.
Pulsars are really cool: they're highly magnetized neutron stars which emit bright beams of light as they rotate. The ones that are most useful for my purposes are millisecond pulsars, which spin ~1000 times per second... Just contemplate that for a moment, a star that is several times more massive than the sun, that is roughly the size of Manhattan (yeah, neutron stars are extremely dense), that is rotating with a frequency that is roughly the same as an opera singer's high C. So these objects are weird and extreme, which makes them excellent places for seeking out exotic physics. They also have a really large angular momentum, which they get by gravitationally cannibalizing gas from companion stars. All this angular momentum makes their rotation very stable, which means the pulses arrive with a very precise cadence. In other words, pulsars are like atomic clocks in outer space. And as Einstein taught us, gravity stretches space and time, making these outer space clocks excellent probes of relativity. In particular, there are several collaborations monitoring dozens of millisecond pulsars in an effort to detect gravitational waves (ripples in space and time itself!) passing by, which would cause the pulses to arrive too early or too late. Pretty neat, eh?
Based on how often they observe the pulsars and for how long they observe them, these collaborations are sensitive to a wide range of gravitational wave frequencies, which happens to be centered roughly at a frequency of ~10 nHz (which is about 1 inverse year, 100 billion times slower than the rotation of the pulsar itself.) This is where things get really cool: the strongest expected source of gravitational waves with this frequency is supermassive black hole binaries. Just to reiterate how truly bizarre this is, we are using something bright and incredibly fast to detect something fundamentally dark and slow. Anyway, supermassive black hole binaries (which are between 10,000 and 10 billion times more massive than our sun) are expected to form pretty often in a cosmological sense. Binaries should form when galaxies merge (which happens "often" when you have 13 billion years' worth of time and the entire universe to consider), since galaxies in general each contain one supermassive black hole. The two supermassive black holes initially pass by each other as the galaxies merge but they slowly get closer and closer by ejecting stars and gas (via, for example, gravitational slingshot). What happens next to the binary isn't known with confidence (this is where theory and observation will have to duke it out over the next few years), but at some point the black holes end up so close to each other that their orbit starts to decay via the emission of gravitational waves. Yes, that's right, gravitational waves are literally taking energy away from the black holes so they can't keep going fast enough to maintain their orbit. These are the gravitational waves that we could see using our nifty cosmic clocks, aka pulsars. We expect to see a whole mess of these binaries emitting gravitational waves, and the gravitational waves will likely be so abundant that the whole sky will be full of a relatively uniform gravitational wave background. In addition to the background, there might be a few nearby black hole binaries emitting gravitational waves strong enough to overpower the background. These are the binaries that we were interested in for the purposes of this project. By the way, no one has ever detected gravitational waves or supermassive black hole binaries, they're both totally theoretical at this point (although we have mountains of reasons to believe they're both there.) So this is some pretty cutting edge stuff going on!
We also made some pretty sweet maps of our prospective black hole binaries relative to the pulsars (darker purple circles mean more massive black hole systems, which means potentially stronger gravitational waves.) It turns out that if you have a pulsar whose position on the sky is close to the source of gravitational waves, then the pulsar is more sensitive to those gravitational waves. So you should be excited about dark purple circles near lots of stars. We actually didn't take this angular variability into account because we didn't have the full data and analysis pipelines at the ready. However, we anticipate that applying our simple analysis to the pulsar timing data in a more rigorous way will likely make our statements even sharper and more rigorous. So it may be the case that supermassive black hole binaries get either discovered or ruled out, both of which will be very exciting and will lead to a flurry of scientific activity. So stay tuned!
Some of the binaries were so constrained that they had to have a mass ratio of less than around 1:50. In other words, one black hole would have to be 50x more massive than the other one. Intuitively, you can imagine that having one big black hole sitting there while one puny little black hole orbits it isn't going to emit as strong of gravitational waves. If you had two similarly sized black holes vigorously orbiting each other, that would create much more of a ripple effect in the surrounding spacetime. Also, for technical reasons, having binaries with very uneven masses causes the orbits to be rather eccentric which suppresses the pulsar timing signal. So basically what we've shown is that even if the constrained black hole systems did have a binary, there's no way that the binary will emit gravitational waves that we'll be able to detect. So basically, our constraints are so tight that we've ruled out the detectability of supermassive black hole binaries in a handful of galaxies.
With Chung-Pei Ma
We took existing upper bounds on the gravitational waves from the pulsar timing folks, which have gotten pretty stringent in recent years. We combined this with additional information, namely where the most massive galaxies are and the total measured mass of their supermassive black hole systems. Since the mass of the galaxy and mass of the black hole system are tightly correlated, we were also able to include black hole systems that haven't been directly measured, since we can infer their mass just by knowing the mass of their host galaxy (which tends to be way easier to measure). We included galaxies from the ongoing MASSIVE survey, which consists of the most nearby and most massive galaxies. Massiveness and closeness are two of the main criteria for the emission of a detectable gravitational wave by a black hole binary, so the MASSIVE survey is a great place to look for possible sources of gravitational waves. By knowing all of this information, we were able to place limits on the mass ratio between the two black holes assuming that the black hole system is actually a binary. And we found that even with our rough exploratory analysis, we could already constrain around a dozen supermassive black hole binaries!