Black holes can get really, REALLY big

May 29, 2023   Issue #570

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My book

This is about Under Alien Skies, isn’t it? Yes. Yes it is.

I was interviewed by Britt Duffy Atkins for Celestial Citizen, a podcast (and newsletter!) about making space exploration more diverse and building a supportive community. It’s pretty cool. We talked about my book among many other things.

You can listen to the interview on her podcast. I had a lot of fun!

Astro Tidbit

A brief synopsis of some interesting astronomy/science news

I recently wrote about what might be a truly a gigantic black hole discovered in a distant galaxy. If the measurements are correct, it’s over 30 billion times the Sun’s mass.

That’s a lot. But in that article I ask a question that’s actually pretty interesting: How big can a black hole get?

By that I really meant mass, how much stuff is in the black hole. The Sun is a decent astrophysical unit for this — it has a mass of 2 x 10^30 kilograms, or 2 octillion tons (333,000 times the mass of the Earth, if that helps). We call this a solar mass, and use it all the time. For example, a massive star might have ten times the Sun’s mass: 10 solar masses. The Milky Way has a total mass of about 700 billion solar masses (though note that doesn’t equal the number of stars; first of all this number includes dark matter, but also red dwarfs with a fraction of the Sun’s mass are the most common, which throws off that number).

We do the same for black holes. The theoretically lowest-mass stellar black hole (one that formed via death of a massive star) should have roughly 3 times the Sun’s mass. The Milky Way’s central supermassive black hole, Sgr A*, is a bit over 4 million solar masses.

Here’s a fun thing, though. If you add mass to a star it tends to get bigger in size. That’s familiar; if you add mass to something it usually does get bigger. If you have a lump of clay and add another same-sized lump of clay to it it’ll be twice as big, right?

Well, no. It’ll have twice the volume. The volume of a sphere is =

so, inverting that, the radius only increases by the cube root of the volume! To get a sphere twice as wide you need 8 times as much volume. I know, confusing, but hey, that’s reality.

Anyway, black holes don’t work like that. Weirdly, their effective diameters increase linearly with mass. So, double the mass and you get an event horizon (the Point Of No Return™) twice as wide. That’s just the way the equations of General Relativity work out when you solve them; it helps to remember that black holes are weird and don’t behave the way a normal matter does.

If you do the math, you find that if you shrank the Sun enough to become a black hole, it would have an event horizon 6 km across. That means a one solar mass black hole would be 6 km across*.

Now wait a sec. If the mass of a black hole is measure in solar masses, and the diameter of the event horizon of a black hole increases as the mass increases in a linear (that is, simple multiplicative) fashion, then a 3 solar-mass black hole will have a diameter of 3 times that of the black hole Sun, or 18 km.

Oh wow. Suddenly this gets easy to figure out how big a black hole is. Take its mass in solar masses and multiply it by 6, and that’s the answer in kilometers.

So the black hole I wrote about in that earlier article is roughly 30 billion x 6 = 180 billion km across. That’s huge. Neptune’s orbit is 9 billion km across, so that black hole could easily swallow the entire planetary part of the solar system whole. Yikes. Good thing it’s 2 billion light-years away.

OK, so where am I going with this? Well, NASA recently put out a short video showing how big some known black holes are, using this same math. For some reason they decided to use the black hole’s shadow as the diameter, which is roughly 2.5 times the event horizon diameter, but that’s fine. Whatevs**.

The video starts with the Sun, and pulls out to show bigger parts of the solar system, with the black holes shown to scale. The black hole in the galaxy J1601+3113 — the first one shown in the video — has roughly 100,000 solar masses, so its shadow diameter is 100,000 x 3 x 2.5 = 750,000 km. That’s about half the size of the Sun, and you can see that’s about how big it looks compared to the Sun in the video.

Good? Good. Now, watch:

Yegads, TON 618’s black hole is a beast. It has a mass measured at 66 billion solar masses, so its shadow is 66 billion x 3 x 2.5 = 500 billion km across. That’s big enough to reach to the Oort Cloud, the population of rocky, icy bodies way out past Neptune. Immense.

I’ll note that the masses of these black holes are estimates, measured using various methods. They could be off by a factor of 2 here or there, maybe more, but the overall idea shown is still about the same.

And back to the original question at the beginning of all this: How big can a black hole get? I talk about that briefly in the linked article at the top, but it depends on how fast a black hole can eat and grow, and how much time it has had to do so. The age of the Universe — call it 14 billion years, give or take — is the upper limit for how long the black hole’s had. If it eats too fast the material falling in gets really hot, starts blowing out a very strong wind of particles, and blows all the rest of the matter outside it away, cutting off the food supply. So it can only eat so fast to prevent that, which is called the Eddington Limit.

TON 618 has about as big a black hole as we think they can be. It’s possible to get one bigger — say, by eating other black holes — but I doubt they can be too much bigger.

I’m OK with that. A black hole as big as our entire solar system including the Oort Cloud is plenty big enough for me!

* Technically, astronomers prefer to use the radius because it makes the math easier, but I’m using diameter here for reasons that become obvious later in the article.

 ** In a nutshell — like any of this can be explained briefly — the gravity of a black hole is so strong photons of light can actually orbit around it. The distance from the black hole where this can happen is what defines the black hole shadow; inside it photons can still orbit but their orbits shrink until they fall into the event horizon proper and are gone forever. Outside that distance light can reasonably escape. This distance is more technically called the photon sphere, but shadow is more poetic, and does describe what we see.

Et alia

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