The Black Holes that Created LIGO’s Gravitational Waves

LIGO merger Bohn
Figure 1. A simulation of the black holes whose mergers LIGO detected. Image due to the Simulating Extreme Spacetimes Collaboration.

A little over a week ago, the LIGO collaboration detected gravitational waves emitted during the in-spiral and merger of two black holes. And the world’s scientists, myself included, collectively went bananas. Last week, I attempted to summarize the event and capture some of the science, and poetry, that has us so excited. In short, gravitational waves provide us a totally new way to look at the universe. LIGO’s one detection has already provided us with a wealth of information about gravity and astrophysics. Today, I summarize some of what we’ve learned.

Black Holes As We Knew Them

In the dark ages before LIGO’s detection, we expected black holes to fall into roughly two categories: supermassive and solar mass. Weighing in at millions or even billions of times the mass of our sun, supermassive black holes are the titans of the universe. Most galaxies, including our own, have a supermassive black hole at their centre. These monsters can drive some of the most energetic events in the universe. For example figure 2 shows the galaxy Centaurus A. The blue stuff you see is radiation being emitted by matter being launched away from the galaxy by its supermassive black hole at a huge fraction of the speed of light.

21901_centaurusABig
Figure 2. The galaxy Centaurus A and the jets from its supermassive black hole. Source.

Solar mass black holes, on the other hand, are tiny in comparison. In the past, we found solar-mass black holes by looking for the light emitted by stuff falling into them. Most of the black holes we found this way were between five times the mass of the sun and ten times. Certainly the biggest we had ever found were about twenty times more massive than the sun. Since we hadn’t found any “solar mass” black holes bigger than that, people questioned whether they even existed. Perhaps there was some mechanism preventing their formation.

Indeed there are good reasons to believe such a mechanism exists. A solar mass black hole is formed by the collapse of a massive star after it runs out of nuclear fuel. And the more massive the black hole, the more massive its progenitor star must have been. So there is a limit to the maximum mass of a solar-mass black hole; it’s based on the mass and make-up of the star from which it formed.

Stellar Winds and Mass

Throughout their lives, stars don’t just emit light. They constantly spit out charged particles like electrons and protons, which then move away from them at high speed. This rapid stream of charged particles is called a stellar wind. Our own star is no exception. Figure 3 shows a comet, Comet Encke, in transit. The comet tail acts as a solar windsock; it is blown away from the sun by all of the charged particles the sun is spitting out.

comet encke billowing in the solar wind
Figure 3. The tail of Comet Encke billowing in the solar wind. Source: ESA/NASA/SOHO

Stellar winds can have a pretty big effect on the final mass of a star. The material in a stellar wind comes from the star itself; it’s literally blowing itself away, losing mass over time. So a star with strong stellar winds will lose a lot of mass by the time it becomes a black hole. Strong solar winds in the progenitor star means low mass black holes.

There’s another factor, too: what the star is made of.

The Life Cycle of Stars

Stars are mostly composed of hydrogen gas. Indeed, young stars exist by harnessing the energy released when hydrogen is converted into helium. As a star ages, it runs out of hydrogen in its core and so converts helium into heavier elements like carbon and oxygen. And when it runs out of helium, it converts those elements into ever-heavier elements, all the way up to iron. But something goes wrong with iron. When a star fuses iron into, say, zirconium, it doesn’t gain energy, it loses it!

So when the star runs out of elements lighter than iron, fusion stops. But without the heat from fusion, the star can no longer resist its own gravity and it undergoes core collapse. The star may explode in a fantastic supernova or it might simply collapse inward. In either case, the end result can be a black hole or a neutron star. The precise mechanisms of core-collapse are not adequately understood; this is one of the things we want to learn via gravitational wave astronomy. A supernova is energetic enough to fuse even heavier elements and eject them into the universe. So over time, as stars form and fuse elements, the amount of heavy elements in the universe increases. This is called stellar nucleosynthesis.

(The story I just described applies only to stars of sufficient mass. Lower-mass stars burn less quickly and can move more of their light elements to their core to burn them. Moreover, they simply cannot produce the pressure required to fuse the heavier elements. So light stars burn for a long time and eventually fade into white dwarves, but they never undergo core collapse.)

Metallicity

As stars go through their life cycles, the number of heavy elements in the universe increases… and so does the number of heavy elements in stars. A star formed in the very early universe will have very few heavy elements. A star formed more recently will have more of them. Scientists quantify this with metallicity, which is defined as the fraction of the star that isn’t either hydrogen or helium. Metallicity is always small, otherwise the star wouldn’t be a star. But as a general rule, stars formed recently have a higher metallicity than stars that formed in the distant past.

Simulations tell us that if the star goes supernova, metallicity has a big effect on the mass of the resulting black hole. The relationship isn’t obvious—it has to do with the chemical and nuclear reactions going on inside the star—but the result is (qualitatively at least) pretty clear. Stars with higher metallicity expel more of their material when they go supernova and thus result in smaller black holes.

LIGO’s Black Holes

The gravitational waves LIGO detected came from the in-spiral and merger of two black holes about 1.3 billion years ago and as many light-years away. By carefully analysing the waveform, the LIGO team determined that each black hole had a mass about thirty times that of the sun. And this is a bit of a surprise. We didn’t know that solar-mass black holes could get that big! But these black holes clearly were that big. So what does this say about the stars from which they formed?

(Well, to be more accurate, we didn’t know that TWO solar mass black holes could get that big and then merge. The merger of two black holes, each fifteen times the mass of the sun would produce a black hole that’s thirty times the mass of the sun. But it seems incredibly unlikely that such a black hole would end up in orbit around another black hole that formed in the same way.)

The stars that collapsed into LIGO’s black holes must have been very large. This means that they cannot have had a very strong stellar wind, because if they did, they wouldn’t have been massive enough by the time they went supernova. Similarly, they must have had very low metallicity—if the metallicity was too high, the supernova would have ejected too much material and the remnant black hole wouldn’t be large enough. And this means that the stars that became LIGO’s black holes might have been some of the first stars ever formed in the universe.

These facts are summarized in figure 4.ย The red and blue horizontal bars are LIGO’s black holes. The left panel shows black hole mass as a function of metallicity for both strong and weak solar winds. The bottom-left corner is high-metallicity with low mass and the top-right corner is low-metallicity and high mass. If the solar wind is too high, the black hole will never be sufficiently massive, no matter the metallicity. The right panel shows the mass of the black hole as a function of the mass of the original star for a few different metallicities. This tells us that if the metallicity is too high, the supernova will jettison too much mass and a sufficiently heavy black hole will never form.

mass of ligos black holes
Figure 4. A summary of the effects of metallicity and stellar winds on the mass of a black hole remnant. LIGO’s black holes are the blue and red horizontal bars. The left pane shows that LIGO’s black holes must have had weak stellar winds. The right pane shows that LIGO’s black holes must have had low metallicity. Source: LIGO Scientific Collaboration but data and plots originally generated by Spera et al.

Forming the Binary

When LIGO’s black holes merged, they were orbiting each other. There are two ways this probably happened. Either they began their lives together as a binary star system (most stars form this way) or they began their lives separately but eventually found each other. In the latter case the stars probably would have formed in a dense cluster of stars, gone supernova, then “sunk” into the centre of the cluster and joined together. It’s not possible to figure out from which of these situations LIGO’s black holes emerged.

We’ll Learn More Soon

LIGO has only claimed one detection. And yet even this one measurement has provided us with a wealth of information about astrophysics and (as I’ll discuss in a later post) general relativity. From this one detection, we’ve been able to tenuously extrapolate a lot about the stars that formed the black holes LIGO heard. But with more detections we’ll know more. We’ll learn, for example, whether these very massive black holes are the exception or the norm. And we’ll learn more about their distribution in the sky. Through gravitational wave astronomy, LIGO has opened a whole new lens through which we can view the universe. And that effort is already bearing fruit.

Related Reading

If you enjoyed this post, you may like reading my other posts on LIGO and black holes.

  • In this post, I attempt to capture the science—and poetry—of LIGO’s gravitational waves.
  • In this post, I describe how the merger of a neutron star and a black hole can produce a gamma ray burst.
  • In this post, I discuss Carlo Rovelli’s speculative proposals that black holes can explode.
  • In this post, I describe why black holes glow.

Technical Resources

  • This is the LIGO detction paper.
  • This is LIGO’s paper on how they figured out the masses of the black holes.
  • This is LIGO’s paper on the astrophysics of the black holes they measured.
  • This is one of the many papers that calculated black hole remnant mass as a function of metallicity.
  • This is NASA’s press release for Comet Encke.

11 thoughts on “The Black Holes that Created LIGO’s Gravitational Waves

    1. Well that’s worrying—I recently changed the font with the intent of making it EASIER to read. I’ll experiment. Maybe I need a serif font.

      Thanks for letting me know.

  1. Jonah, you have a little doodad in your sidebar that sez “follow me on Twitter” but it doesn’t do anything. Are you there?

    I pretty much Tweet all your posts, anyway, but if you have a profile, I’ll link it.

    1. Yes I am on Twitter! My handle is @thephysicsmill ๐Ÿ™‚ The little doodad on the right should be above a panel containing my recent tweets. Is that missing for you? If so, perhaps I should add another link lower down.

  2. I’m afraid I am a heretic when it comes to conventional wisdom concerning black holes.
    E.g., There are stellar black holes such as you describe, plus a category of nuclear and other black holes that originated from the segmentation of an early universe energy/mass filament, which I call Omega Bodies. These went on to found illuminated galaxies and an unknown number remained as dark galaxies. Omega bodies were of all weight sizes, some in the billions of solar masses.
    It’s interesting that when an Omega body, after conversion to a galactic nuclear black hole, constructs a ‘family’ of progeny galaxies that conform to one of four possible configurations. k

  3. > So there is a limit to the maximum mass of a solar-mass black hole; itโ€™s based on the mass and make-up of the >star from which it formed.

    The most massive star currently known is probably R136a in the LMC Tarantula nebula at 300 solar masses(Ms). If we assume that’s about the most massive stars get, the black hole that will produce has an absolute mass maximum of 300 which could only occur if R136a doesn’t lose any mass from now and when it dies (false) and if it doesn’t lose any mass when it collapses (large iron core stars can completely collapse into the black hole in models and there are low luminosity SN where a lot of mass falls back onto the black hole and is absorbed). If it wind loss was about 10 Ms since formation and will lose 10 more as a guess, when it dies I would still be much more massive than the biggest stellar black holes known. Even if half that mass is ejected the R136a black hole is still ~150 Ms.

    1. As a back-of the-envelope estimate, that seems eminently reasonable.

      So then the question is: does that match our observations… testing these estimates is reason (of many) that this first GW measurement is so interesting. ๐Ÿ™‚

What do you think?