Now that we can detect gravitational waves, a new generation of stargazers is turning its attention to the Universe and using observatories that can be disrupted by a passing rabbit. Gravitational-wave detectors are going to give us an entirely new view of our place in the cosmos.

As with all new techniques, we are still in the age of crude and not-very-sensitive. That means we can only search for the biggest and baddest of events: black-hole mergers. So far, LIGO has detected three and a half mergers—the third merger is right on the edge of the detection limit, so it is provisional. But those black holes have been larger than expected, which raises an intriguing question: is that their first merger, or have they grown through previous mergers?

Now (arXiv version) scientists have determined how to figure out if black holes are first-time cannibals or recidivist cannibals.

Stars going to the dark side

A black hole is one of the possible end points for stars. A star has a huge mass of material, all of which is pressing inward. The high temperature and pressure from all that mass pressing inward ignites fusion. One of the products of fusion is energy, which provides enough outward force to balance the inward collapse of the star. But, cosmologically speaking, this is a moment of peace before all hell breaks loose. Hydrogen burns to form helium, which burns to form lithium and beryllium, and onwards until the heart of the star is made of iron. At that point, fusion stops. Gravity, having taken its union-enforced, four-billion-year break, goes back to work, and all of that matter collapses inward.

Now, if the mass is small, then the collapse ends in a whimper, and the star glows like a dying coal as it turns into a celestial paper weight. These are white dwarfs. At larger masses, the star explodes spectacularly in a last extravagant display of power. Emerging from the explosion is one of the two densest objects known to the Universe: a neutron star or, if the original star is heavy enough, a black hole.

But the conversion of matter into very strange states doesn't end there. All of these objects are drifting through space, and they are very (ahem) attractive. Get them close enough, and neutron stars and black holes consume each other (and possibly other nearby objects, like white dwarfs). This could allow neutron stars to gain enough mass to graduate to black-hole-dom or allow black holes to grow to larger masses. So, when we observe two black holes merging, can we tell if this was the first merger, or are we looking at voracious black holes?

A story of distributions

The way to figure this out is to look at mass distributions. Every black hole has a minimum mass below which they can't form. And, while stars go up to a tremendous 200 times our Sun's mass or more, not all of that ends up trapped in a black hole. So the researchers stuck to an initial generation of black holes with up to 50 solar masses. From there, these black holes encounter each other, giving rise to more and more massive black holes. The mass ratio of black holes involved in further mergers then changes depending on how many black holes each has previously consumed.

(The authors also consider the spin of the black holes, but we don't have very good resolution on our measurements of that yet.)

To get an idea of what this might mean in terms of observations, the team examined how the mass distribution changed after several mergers. In the first generation, black holes are freshly created from dying stars. Pairs of these merge to create second-generation black holes. After that are two possibilities: a second-generation and a first-generation black hole merge, or two second-generation black holes merge.

But everything that follows comes down to the properties of the first generation of black holes. Now, since we don't have an enormous catalog of black holes from which to grab data, the researchers chose a range of mass and spin distributions. Using these distributions, researchers randomly merged black holes and calculated the resulting mass, spin, and merger-mass ratios. This provides a distribution of second-generation black holes. So now we have two groups of black holes, each with a different range of masses and spins.

Random mergers between these two populations (between two second-generation black holes, or between a first- and second-generation black hole) provide two more populations, each with different mass distributions.

Given all of this, the researchers can also calculate about how far in the past these mergers occurred. Essentially, mergers between second-generation black holes have to occur after their progenitors merge. That means—and I find this utterly mind-bending—the second-generation mergers that we observe now are more likely to occur closer to us than first-generation mergers.

Waiting for observations

OK, to summarize: we start with an expected mass and spin distribution. We have three expected distributions of the ratios between masses during a merger, and we have spin distributions. And, just to make it a little easier, all of these distributions should be present at different (but overlapping) times in the past. The question is, will observing this be possible?

The answer is, quite likely, yes. According to the researchers, after about 20 black-hole mergers, we should be able to distinguish between two first-generation black holes and mergers between two second-generation black holes. To separate out mergers between first- and second-generation mergers will take about 100 observations.

And this is at current design sensitivity. Assuming that the planned upgrades to LIGO and Virgo go well, then the sensitivity goes up and the job becomes a lot easier. In addition, the upgraded hardware will be more sensitive to black-hole mergers that occurred in the more distant past, allowing scientists to sample a much broader range of the distribution.

What, you ask, might we gain from this? Well, it provides a window into the dynamics of galaxies and the black holes contained within them. Depending on how galaxies are put together, we should observe different rates of mergers and different population distributions for different generations. These observations will test astrophysical models in a way that has not been possible before.

Physical Review D, DOI: 10.1103/PhysRevD.95.124046 (About DOIs).