Ever since the first direct detection of gravitational waves in 2015 by LIGO, binary black holes have become prominent objects of study. The mergers observed so far were in systems of no more than several dozen solar masses in total. These stellar-mass black holes are the remnants of massive stars that died in supernovae. There are many of them in the galaxy, some in binary systems (with stars or other black holes) and some on their own.
LIGO is well-equipped to detect gravitational waves with frequencies on the order of 10 to 1000 Hertz. Sources visible at these frequencies including supernovae, kilonovas, and merging stellar-mass black holes. However, there are gravitational waves at a number of other frequencies, going all the way down to the nanohertz regime, where LIGO can’t see (instead, we have to use pulsar timing arrays). While none of these nanohertz-frequency gravitational waves have been directly detected, the region continues to be probed.
But there’s a slight problem. In order to merge, the black holes must lose a lot of angular momentum. Mechanisms exist for supermassive black hole binaries to lose angular momentum both when they’re far apart (dynamical friction, as well as the scattering of nearby stars) and when they’re close together (gravitational ways). However, at distances of about 1 parsec, there’s no efficient way for the black holes to lose angular momentum, and so it would seem that they should simply stop. This is known as the final parsec problem.
How do supermassive black holes meet?
Most galaxies that host supermassive black holes — and that’s expected to be most massive galaxies — contain only one, usually at their centers. These monsters can have masses of millions to billions of times that of the Sun — which is, surprisingly, negligible compared to the mass of the rest of the galaxy. There are various theories as to how these objects form. Top-down approaches involve the collapse of a massive stellar cluster or cloud of gas in the early universe, or else the violent death of an extremely massive “star” of some sort. Bottom-up approaches involve the coalescence of many smaller black holes early in the galaxy’s lifetime.
Supermassive black hole binaries are harder to form, and are likely the result of galaxy mergers, where two galaxies collide and eventually coalesce into one larger galaxy. If both progenitors contained supermassive black holes, the two will orbit each other and eventually come closer and closer together, remaining in the center of the merger remnant. Once an orbit has been established, the long-term process of merging can begin, barring any future disruptions.
At first, angular momentum loss happens through a process called dynamic friction. The centers of the galaxies have high stellar number densities; as such, the black holes interact with many bodies during and after the early stages of the galaxy merger. They lose energy through each encounter, and thus the orbits shrink. Similar effects involving gas drag also play a role, albeit less important.
Once the black holes get close enough that the mass of stars within their orbits is less than the total mass of the binary, dynamical friction becomes less efficient, and so the second phase of merging begins. During this period, individual stars and stellar systems interact with the black holes at close distances, and are ejected at high speeds. This stage is the problematic one, because it is thought that the black holes will run out of stars to eject, and stall, typically at distances on the order of parsecs. If they could move close enough, they could merge by emitting gravitational waves, but a dearth of stars makes this seemingly improbable.
We have reason to believe that the final parsec problem isn’t much of a problem at all — or at least that there’s a way around it. Our good fortune comes from a quasar three and a half billion light-years away, called PKS 1302–102. Early observations were made in the 1980s and 1990s, as part of large quasar surveys (see, for example, Marziani et al. (1996)). However, data was limited, and there was no evidence that the object was anything special.
The first suggestion that PKS 1302–102 contains a binary black hole came in 2015 (Graham et al. (2015)). A group of astronomers analyzed data from the Catalina Real-time Transient Survey (CRTS), which looks for optical variability in a number of objects — including quasars. Observations had indicated that this quasar was interesting, for several reasons. It’s luminous and relatively close, as quasars go, and has strong radio emission.
The analysis was prompted by prior indications from optical and radio light curves. There was clearly complex structure in the core (it has also been found that the quasar OJ 287, which has a smaller supermassive black hole orbiting its main one, has a light curve with similar features). In fact, the authors found that data taken over two decades showed that there was a periodicity of about 1,884 days, which shouldn’t be expected in a normal quasar.
Three explanations seemed likely. The first was that the quasar’s astrophysical jet could be precessing over time, and coupled with emission from an accretion disk, this precession could lead to variability. However, the periodicity of this type of precession in the case of a single black hole is only likely over much, much longer timescales. The second possibility was that there is a “hot spot” in the accretion disk. However, analysis showed that for this to be true, a lone supermassive black hole would have to be quite massive. The third possibility — which showed some promise in the case of a single supermassive black hole — was that the accretion disk is warped, and this warping disrupts the normal continuum emission on a regular basis.
The first two of these explanations are only likely in the case of a binary system. The third could involve only one supermassive black hole, but a binary system would also be possible. Considering all three, the authors concluded that it is more likely that a binary system resides at the center of PKS 1302 — not a lone black hole. In particular, the maximum expected distance between the two components is expected to be 0.01 parsecs.
Is it a false positive?
Now, the explanation of the variability was challenged by another group (Vaughan et al. (2016)). They noted that quasar emission shows stochastic variability even without a second object disrupting the first. Using statistical analysis, they argued that random variability in the form of “red noise” was much more likely to account for the supposed periodicity. Out of 100,000 simulations, a large fraction fit the data analyzed by Graham et al.
This group held that caution should be used when attempting to identify periodicity in quasar data — and they have a point. PKS 1302–102 was selected from an enormous number of candidates — 250,000. With that number of data points, it is likely that stochastic noise in the quasar’s emission should produce a candidate like PKS 1302–102, thereby producing a false positive.
More data is always a boon when studying an object whose properties have yet to be well-determined, and Vaughan et al. suggested that more data be taken on the quasar. However, they noted that surveys typically don’t have “deep” data on many candidates; they usually have limited data on a large number:
In the short term, however, it is often more practical to ‘go wide’ (light curves from many more targets) than to ‘go deep’ (longer, better quality time series of individual targets), so it is particularly important to calibrate the false positive rate of few-cycle periodicities in irregular and noisy data.
In other words, proper understanding of how many false positives are expected can reduce the likelihood of misidentification.
Regrettably, this amount of uncertainty is essentially the current state of affairs of PKS 1302–102. If more observations are taken — perhaps with a better understanding of the occurence of red noise — then perhaps the binary supermassive black hole hypothesis can be supported or ruled out. Predictions of the frequency of occurrence of these objects could also be compared to the false positive rate. No matter what new data tells us, however, hope remains for solving the final parsec problem.