Black Hole Sun

This week, my son Zack has been shadowing me at work. This is an official internship that all 9th graders in France do. He talked to some other researchers in my department (the Laboratoire d’Astrophysique de Bordeaux) and visited the labs where they build cool stuff (like electronics for radiotelescopes and pieces used in space missions).

I also wanted to give him his own project. After talking about it together, he decided to do some N-body simulations of planets around a black hole. Along the lines of some crazy things I’ve talked about on the blog, but never actually simulated directly. And, he volunteered to make a blog post out of it.

Enter Zack…..

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Imagine this:
You wake up, yawn like they do in the movies, then are on your way. On your drive to work you have to make sure, as you do everyday, to shield your eyes from the Suns. Sun-4 is looking mighty bright today. As you follow the curve of the highway leading you left, you see E-27 looking better than ever. And man, that supermassive black hole still looks as awesome as always.

You finally get to your workplace and remember why you chose to work here. The room is perfectly shaded from the Suns and has an exquisite view of E-29. “Man, this planet is so much better than E-73”, you say, sighing happily.

After an hour or so of ‘working’ (you spent most of this time playing games on your computer), your boss calls you into his office, which is much less shaded from the Suns than yours. You stare out the large glass window that acts as a wall for this building while slowly making your way to the Boss Room™. You notice that Sun-4 is now to the right of the now-blazing Sun-6. Well, when you have 10 Suns, you can’t get attached to any of them for too long but hey, Sun-4 will be back soon. You wonder if your family back on E-68 are able to see it yet, it was always their favorite Sun. You never understood why, though. They all look exactly the same. You always did think they were weird.

Before you end up lost in your thoughts, you hear a sound you’re very, very used to: your boss yelling. “I told you to be in there a minute ago, you idiot! It’s a 24.1 second walk! Stop your dilly-dallying, dammit!” Well, E-28 can’t be better than E-73 in every way, can it? You finally walk the last few steps to the Boss Room™, praying he won’t say what you think he might.

“Sonny boy,” He says, looking angry, yet also disappointed, “you ain’t been here long and yet management already wants you transferred to our best location. Lucky man. You’re goin’ to E-1.” You stare at him in disbelief, waiting for a “Get pranked, buddy boy”, but none ever comes. You’ll have to take the train to get that far, won’t you?

A few months later, you’re finally getting used to the plethora of snooty rich people on your new planet but, hey, what else would you expect from the original Earth, E-1 of 100 that humans have built? And you’ve heard of plans to start development on a couple hundred more. Scientists have predicted that there would be upwards of 1000 sharing the same path around the Supa Troopa (that’s what you call the supermassive black hole in the center of your solar system) within the next 30 orbits. Sounds exciting! Let’s hope they don’t accidentally blow everyone up. That would kinda suck, not gonna lie.

Okay, so that story was cool and all, but is any of it actually physically possible?

Well, the short answer is yes. The long answer is yeeeeeeeeeeessssssssssssssss. But how is it possible to fit 100 earths on the same orbit? Or 10 suns?

The answer is: Hill Radius.

There’s a bunch of math involved, but basically, the more massive the object in the center of the solar system (or, as I like to call it, a black holar system), the more tightly packed planets can be. If you do the math, in theory you should be able to fit 5235 earths on 1 orbit! Or 75 suns (see more in the black hole ultimate solar system)! Holy cow! That’s, how should I put this, quite a lot. But does that actually work in practice? Well, I’m glad you asked, dear reader. The answer is abso-freakin-lutely.

In this here simulation, you can see the conditions that I stated in the story: 100 earth-mass planets and 10 suns orbiting around a million solar mass black hole. The sizes are not to scale, but the orbits are. The distance from the Sun to the black hole is 1 au (au=distance from the earth to the sun in our solar system). This simulation was originally done with 1000 earth mass planets but you couldn’t visually tell them apart (it would still have been stable) , so I had to only do 100. As you can see, this black holar system is stable. It would still be stable if it had 75 suns and 5235 earths!

I also had to do a bit more math to know the distance the earths would have to be from the suns for them to be able to have liquid water and thus sustain life. The math isn’t too complicated, but if you’re too lazy to do it yourself (like me), the earth in this simulation is 3.17 au away from the black hole.

You might be wondering why this little animation only runs for half a day instead of a year like some other blog posts here. The reason for that is: because of the extreme mass of the black hole, the suns’ orbit takes about 0.4 earth days, and the planets’ orbit takes only about 2 days. Having this simulation go for a year would have taken a lot of time to simulate and a hell of a lot of time to watch.