There are 40 quintillion black holes in the observable Universe. More or less.

How many black holes are there?

I don't mean near the Sun, or even in the galaxy. I mean, how many black holes are there in the entire observable Universe?

Turns out about 40 billion billion of them.

For those who like numbers, that's 40,000,000,000,000,000,000. In exponential notation that's 4 x10¹⁹.

In English, that's holy crap that's a lotta black holes.

When I first read about this I had to think about it for a sec, but honestly that sounds about right. And it's not made up. It's calculated: That's what a team of scientists came up with when they crunched the numbers (link to paper). That wasn't really their end goal, though. What they really wanted is the black hole mass function across cosmic time.

So, yeah, let's back up a bit.

Artwork based on a real Hubble observation of NGC 6397 showing black holes swarming in its core. Credit: ESA/Hubble, N. Bartmann

If you look at our Milky Way galaxy right now and counted the stars in it, you'd find something like 200 billion, give or take. But they're not all the same: Some are like the Sun, with a few more massive, and very few that are really massive — say, 100 times the mass of the Sun — and a whole lot of dinky ones like red dwarfs with half the Sun's mass or less. In broad terms, 80% of all stars are less massive than the Sun, 10% around the same, and 10% higher.

That's what we call a stellar mass function: how many stars are in a bin of a given mass. But it's actually more complicated than this. Stars change. They're born, they die. High-mass stars don't live long, while lower mass ones live for trillions of years. So that mass function changes over time. There's an initial mass function, which is, say, how many stars of what mass are born out of a single giant cloud of gas and dust at the same time. Then that changes over time as stars change.

You can do this with black holes, too. It's a little different, for two main reasons: One is that black holes take time to form, after massive stars explode and their cores collapse to form black holes. The other is that once you make a black hole, it's yours to keep. They don't go away. In fact, they can actually gain mass as they feed on stuff, and sometimes two black holes can merge. That messes things up because now you have one black hole of higher mass, which removes two lower mass ones from their bin in your function.

So yeah, this is a bit tricky. But it's also important to know, since black holes can profoundly affect a galaxy they're in. Knowing how many there are, their masses, and how that changes over time can really help astronomers understand how galaxies work.

Artwork depicting two black holes orbiting each other. Credit: LIGO/Caltech/MIT/Sonoma State (Aurore Simonnet)

That's why a group of astronomers tackled this problem. Their goal was to figure out the spread of masses of black holes, how many are in a given mass bin — like, say, 3-5 times the Sun's mass, 5–10, and so on, up to supermassive black holes that can have billions of solar masses to them — and moreover how that changes over time. Hence that line above about the black hole mass function across cosmic time.

The details are… complex, but what they did is used a well-known suite of software to calculate how stars are born — the stellar mass function — and couple it with software that looks at data for galaxies and how they change over time. For example, stars are born from gas clouds, but there is only so much gas in a galaxy. Back in the day, a few billion years ago, most galaxies were cranking out stars faster than they are now. And that rate depends on lots of other things, like what kind of galaxy it is, how many massive stars are in it, and much more.

And it gets worse. Some stars make black holes when they explode, but some are in binary systems, orbiting another star. Sometimes they can feed mass to the other star, and then it explodes and makes a second black hole. Sometimes these binary black holes merge, sometimes they don't. Like I said, it's complex.

Cranking all this through their code, the end result is table with a lot of numbers: How many black holes of a given mass there are at different points in the history of the Universe. Wow.

The very first image of the "shadow" of a supermassive black hole. This shows the region around a black hole with a mass 6.5 billion times that of the Sun, located 55 million light years away from Earth in the core of the galaxy M87. Credit: NSF

They do get some interesting numbers. For example, in the nearby Universe, they see the number of black holes in a given bin is pretty flat from 5–50 times the mass of the Sun; for any given mass in that range you'll see roughly the same number of black holes. But very far away from us, where we see the Universe being younger^*, black holes tend to have a higher value, more like 30–50, with fewer low-mass ones. In the early Universe there were fewer heavy elements — these are made in massive stars which explode and scatter them, and early there hadn't enough time for this to happen much. Stars with fewer heavy elements can be more massive, so the black holes they make are bigger, too.

Looking at binaries, they found that rate at which binary black holes spiral together and merge matches the numbers seen by the LIGO/Virgo observatories, which detect gravitational waves from these events. That's reassuring, since it means their code is at least in the ballpark of reality.

And, once they have the number of black holes per mass over time, they can then add them all up. When they do that, they get that number up top: 40 billion billion of them.

Sounds like a lot, doesn't it? But it's actually less than 1% of the total mass of normal matter in the Universe! And normal matter is only about 15% of the total mass of matter, because dark matter heavily outnumbers it.

So yeah, that's a lot of black holes, but there's a lot more stuff out there in total. And funny — that number is not in their paper, but it is in the press release. The total number over all time isn't nearly as scientifically interesting as the mass function is, but it's certainly interesting in a whoa that's so cool kind of way.

I'm OK with that. Black holes are critically important to how galaxies form and evolve, how stars are born and how they die, and much more. But honestly? They really are cool, too.

^*Light travels very fast, but not infinitely fast. So when we look at a galaxy 7 billion years away we're seeing it as it was 7 billion years ago. It's actually more subtle and complicated than that, but this gives you the idea. Basically farther away = seeing it younger.