Let’s do a thought experiment.
You belong to a super-advanced civilization. You are an engineer with the technology to build planets and place them in any orbit you choose. You create remarkable orbital structures. Let’s call you Slartibartfast.
The problem at hand: your home star is evolving fast. Your species needs to flee to another system.
Your challenge: to build a time capsule to commemorate that this star once hosted your species.
The time capsule must serve as a beacon. Any other civilization that detects it should immediately suspect that it is of artificial origin. In other words, it should look non-natural. Perhaps most importantly, it needs to survive for countless billions of years.
On the main sequence stars fuse hydrogen into helium in their cores. They brighten slowly on the main sequence, but the real action comes when they run out of fuel (no more hydrogen in their cores).
For a star like the Sun, it takes about 10 billion years for this to happen. Fusion of hydrogen continues in a shell, and this puffs the star up into a red giant. Red giants are cooler than Sun-like stars (hence their redness) but are very bright because they are ginormous. Betelgeuse, Orion’s bright right shoulder, is a good example.
A red giant Sun is 100-200 times larger than the Sun today, about as big in size as Earth’s orbit. It will only remain a red giant for a few hundred million years (during which Saturn’s moon Titan will be in the habitable zone). The Sun’s evolution (at least the interesting part) will finish with a series of explosions and the removal of its outer layers to create a planetary nebula (no relation to planets, just a badly-chosen name).
The core of the red giant Sun is left behind after the outer layers of gas are blown away. This is a white dwarf: a very dense object that is only about the size of Earth but almost the mass of the Sun. White dwarfs just passively cool off for eons.
Here we will stick with Sun-like stars, but it’s worth noting that other stars evolve slightly differently than the Sun. More massive stars evolve faster and more explosively whereas low-mass stars burn through their hydrogen fuel so slowly that they last hundreds of billions to trillions of years on the main sequence.
What happens to planetary systems as their stars evolve?
The case of the Solar System has been studied pretty carefully. When the Sun becomes a red giant, Venus and Mercury will be swallowed whole, and Mars and the giant planets will be pushed outward. Earth is on the cusp; it is uncertain whether it will be swallowed or pushed away.
Many white dwarfs show signs of “pollution” in the form of contamination of their surfaces by rocky or icy material. This may be evidence that leftover asteroids and comets are raining down on these white dwarfs, driven by the shifting orbits of as-yet-undetected planets. In the same way, the white dwarf Sun may be polluted by asteroids and comets 7-8 billion years in the future.
A Jupiter-like planet was recently discovered on a relatively wide orbit around a white dwarf. It is probably the surviving remnant of a planetary system that underwent this same kind of evolution as its star became a red giant and then a white dwarf.
Back to our cosmic time capsule challenge.
I can help construct a time capsule planetary system. On this blog I’ve shown how to build some pretty wild systems and used orbital dynamics to figure out which ones can remain stable. Some of these systems are stable for billions of years but so elaborate that they are unlikely to be formed by nature (like the Ultimate Engineered Solar System).
But which systems would survive as the Sun evolves? I need help to figure that out.
Enter Dimitri Veras, astrophysicist extraordinaire. He is the world leader in understanding how planets’ orbits change as stars evolve off the main sequence. Dimitri and I have known each other for more than 15 years and have worked together on a bunch of projects over the years (including figuring out some interesting things about free-floating planets and ‘Oumuamua).
Dimitri even has a code to simulate the evolution of any planetary system I give him as the Sun becomes a red giant and then a white dwarf. He has used it extensively in his research and was willing to run some simulations for this blog post.
We decided to test three types of planetary systems:
- Rings of planets. These come in two flavors. Lagrange-style rings have planets that are equally spaced by 60 degrees such that neighboring planets are in their mutual Lagrange L4/L5 points. In what I’m calling “ring-style” systems a given number of planets is evenly spaced along the same orbit, as in the ultimate Engineered Solar System.
- Cohorts of planets. These are arcs of planets that all share the same orbit. The planets can again be spaced either in a Lagrange-style (which limits the number of possible planets) or in a ring-style.
- A prime number resonant chain. This system has planets on concentric orbits in which the orbital periods of neighboring planets form a mathematically-distinct pattern. If the innermost planet’s orbital period (aka year) is 1 unit, then moving outward the neighboring planets’ orbital periods are prime numbers: 2 units, then 3, 5, 7, and 11.
In Dimitri’s simulations we couldn’t go quite as bonkers as I might have liked because we were limited to a relatively modest number of planets so that the simulations didn’t take forever to run. But we still tested some pretty crazy systems, including up to 36 Earths in a single ring, and cohorts with up to 10 planets.
The prime number resonant chain is an interesting beast.
David Kipping (the brains behind the amazing Cool Worlds YouTube channel) explained to me the idea that the mathematical pattern built into this system would serve as a beacon for intelligent species. The system itself was constructed by Matt Clement (of Early Instability model fame). Matt used simulations to gently migrate the planets into the resonant chain, and ended up varying the planets’ masses to maintain the system’s integrity. The inner four planets are each 20 Earth masses and the outer two are 2 Earth masses.
Armed with this pile of potential “time capsule” systems, Dimitri and I tested the stability of planetary systems over an 8 billion year time span. The central star is a star just like the Sun. The starting point of Dimitri’s simulations is just at the end of the Sun’s main sequence lifetime.
Dimitri’s code tracks the orbits of each of the planets as the star evolves through several stages. The star first puffs up into a red giant for a billion years or so. It loses some mass and jumps on the asymptotic giant branch phase, then loses another big chunk of its mass (as a planetary nebula), leaving behind a white dwarf. After that, nothing happens for a long long time.
A planet’s orbit expands as its host star loses mass. The planet has been tethered in place by the star’s gravitational force, and when that force gets weaker (because there is less mass), the planet drifts farther away. Very distant objects can be lost from their systems entirely.
For our case, the size of the orbit of each planet roughly doubles as the Sun transitions to a white dwarf. Lots of systems can be destabilized during this orbital expansion (Dimitri has written scientific papers on exactly this topic).
Let’s get to the outcomes of the simulations.
This plot shows the evolution of a cohort of 5 Earths that spanned an arc of 80 degrees, starting 3 astronomical units from its Sun (remember, an astronomical unit is just the Earth-Sun distance). You can see how the planets’ orbits expand in two different phases, to almost twice their starting size. But you can’t tell the different planets’ orbits apart because all five planets continue to share the same orbit and so the line shows all five planets on top of each other.
This is the only example I’ll show from the cohorts and rings, because all of the stable cases look the same! (Because all the planets share the same orbit and so their orbital distances plot on top of one another).
Next up: the 6-planet prime number resonant chain.
This case is more visually appealing because you can see how each planet’s orbit expands as the star loses mass. Yet the planets nicely maintain their prime number resonant configuration and remain nice and stable for the full 8 billion years.
When one of these systems goes unstable it’s not much different than when a system goes unstable around a non-evolving star. The planets’ orbits cross, leading to either a collision between planets (the most common outcome for low-mass planets like Earths or Neptunes), or to scattering and ejection (the likely outcome for Saturns and Jupiters, which can then destroy any nearby rocky planets).
Let’s go through the outcomes of the simulations Dimitri ran.
All of the ring systems with Earth-mass planets were stable. This included Lagrange-style rings (with 6 planets 60 degrees apart) at orbital distances of 2 and 10 astronomical units, and ring-style systems with 9, 12, 24 and 36 planets. In contrast, none of the rings that we tested with Neptunes or Saturns remained stable.
The cohort systems were a mixed bag. Lagrange-style cohorts were remarkably stable. Three Neptunes or Saturns separated by 60 degrees were stable at 5, 10 and 20 astronomical units. Ring-style cohorts of Earths were only stable with a relatively small number of planets that were widely spaced. Cohorts with 4 or 5 planets spanning 80-90 degrees were stable (at 3, 5 and 10 astronomical units), but those with 7 or 10 Earths were always unstable (this is actually quite close to the stability limits on cohorts I calculated in this post).
Finally, as we saw, the prime number resonant chain was stable and maintained its resonant structure. It’s worth noting that not all resonant chain systems remain stable as their stars evolve. Dimitri recently simulated the future of the HR8799 system that contains 4 mega-Jupiters in a 1:2:4:8 resonant chain and found that it will not survive.
There are lots of choices for systems that Slartibartfast can build. Let’s put together a few time capsule systems.
We could easily just grab the systems we simulated and declare them time capsules. But I want to make things more exciting. I’ll add a twist in the form of moons.
As long as the planets stay far enough apart, the orbits of moons should remain stable. And we know the planets are staying far enough apart because otherwise the planetary systems would not survive. One big moon should easily remain stable around each Earth-mass planet and a few (maybe up to five) around each giant planet. The amount of real estate for moons is determined by the size of the planets’ Hill radii, which grow larger as the planets are pushed farther from the star and the star loses mass.
Below are three Time Capsule systems. Time Capsule system 1 contains three Saturn-mass planets in a Lagrange-style arc, each hosting a system of five large moons. Time Capsule system 2 is a ring of Earth-mass planets, each with its own large moon. We could have fit three times as many planets on a single orbit, but that is both harder to visualize and a little less stable since the planets are closer together. Time Capsule system 3 is the prime number resonant chain with four moons included around each of the four inner Neptune-mass planets, and one large moon around each of the outer two rocky planets (of 2 Earth masses each).
[Of course, we could go nuts and create a special type of orbital structure among the moon systems. Co-orbital systems would not remain stable in the face of tides, but prime number resonant chains should.]
Seen from a large distance, would each of these systems properly serve as a beacon indicating an artificial origin?
I think the answer is clearly yes. I don’t think nature can make these systems, even though their orbits would be stable for billions of years if they could form. Prime number resonant chains are the least unlikely of these systems to form naturally, but I expect them to be exceedingly rare.
For my day job I study how planets form, and have created tens of thousands of artificial planetary systems in different types of computer simulations. The number of 3-Saturn Lagrange-style arc systems I have seen is zero. Likewise, I have never seen a ring of planets. Resonant chains are actually a very common outcome of planet formation (due to the migration phase), but it’s really unusual for planets to end up in resonances like 11:7 and 7:5 — much more common are simpler ones like 3:2 and 2:1. I have never seen a resonant chain of prime numbers form in a simulation.
So if an advanced civilization detected any of these Time Capsule systems, they should immediately suspect that it was created intentionally by a super-advanced species (as long as their civilization includes some planet formation modelers like me!).
And astronomers are searching for these types of systems as we speak! One example is the TROY project (to search for Trojan planets).
Finally, I can’t help wondering what an advanced civilization would leave behind in their time capsule systems for visitors to find in the distant future. Their most cherished works of art? Databases of all their knowledge (but in what format)? Maybe… books of astronomy poems (wink, wink)?
Additional Resources
- Websites of Dimitri Veras, Matt Clement, and David Kipping (see also his Cool Worlds YouTube channel)
- Wikipedia article on stellar evolution
- Reading Earth’s destiny in the “blood spatter” around other stars (article for Nautilus)
- The Ultimate Engineered Solar System (blog post)
- Cohorts of co-orbital planets (blog post)
- Slartibartfast from The Hitchhiker’s Guide to the Galaxy by Douglas Adams.
- My astronomy poems
PLANETPLANET 
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