# What is the upper bound of number of stable interacting stars in a star system?

I remember very well reading in an article that it's impossible to have a stable star system of 4 or more stars. The article justified its claim discussing about the complexity such systems would have in terms of mass, velocity and distance to be stable. Further more I think there was a constriction related to our 3-dimensional universe, unless I confuse it with an other article about why solar systems cannot form in 4 dimensions... I don't remember though where I read the article.

And since then I thought there couldn't be star system with more than 3 stars and that belief was enforced with the movie Contact when Jody Foster traveled through space and encountered a quadruple star system. What an opportunity for a movie to claim the existence of something so exotic, right?

Recently there's been a fuss about the TIC 168789840 six-tuple system. So either I'm very behind in astronomy news or I confuse the terms Star System and Solar System in the article I read...

Here an article about the aforementioned system.

There is no true upper bound. You could argue that a galaxy is a vast multiple star system, with hundreds of billions of stars. Natural galaxies are not perfectly stable (random encounters eject stars over very long timescales), but one can construct stable systems by taking pairs of similar-mass binaries and placing them into a remote circular orbit around each other. This can then be repeated indefinitely, with $$2^n$$ stars forming a vast system.

In practice such neat systems are unlikely to form naturally (4 levels seem to be the max observed and often involves very unequal masses) and very wide systems will encounter other stars often enough to be destabilized. Eccentricities tend to have a triangular $$f(e)=2e$$ isothermal distribution, making things less stable. See (Duchêne & Kraus 2013) for more statistics.

(As an aside, Jaron Lanier and Piet Hut have suggested constructing such vast hierarchical systems as a clear indicator that there is intelligent life present.)

• "4 levels seem to be the max" Cool, is there a citable example of this? – uhoh Jan 25 at 15:10
• constructing vast hierarchical systems of stars to communicate messages doesn't seem very intelligent.... I mean if you could form such systems then you might as well travel to the recipient and hand the message yourself ... And of-course the constellation should face the recipient otherwise the topology would make no sense ... – Demis Jan 25 at 15:26
• Then the article I read did not talk about the number of stars in a star system but a number of stars in a solar system witch makes sense. You can't have a big number of stars and expect a planet to be trapped in such a way to orbit all of them. – Demis Jan 25 at 15:27
• @uhof - Added some references. – Anders Sandberg Jan 25 at 15:58
• @Demis Not a direct communication system, just evidence that they exist. A bit like marking territory. "We are here, and we can move stars. Tread carefully." – notovny Jan 25 at 16:23

Either three, or unbounded, depending on your definition.

A three-star system would be one of the stable solutions to the n-body problem: a large star dominating the system, a smaller star orbiting it, and a very small star (eg. a red dwarf) in the smaller star's L4 or L5 point.

In the unbounded case, you have two stars orbiting a common center of mass (a stable two-body system). You then set two such pairs orbiting each other; if they are sufficiently far apart, each pair acts gravitationally as if it were a single body. You can keep stacking pairs of pairs, and pairs of pairs of pairs, and so on, until you run out of room in the Universe for them.

• There are analytic solutions to the 4-body problem too: nature.com/articles/nature17896 – Anders Sandberg Jan 26 at 11:12
• @AndersSandberg, they're not stable, though: perturb something in the L4 point, and it wobbles around a bit, staying in the same general area. Perturb one of the analytic four-body solutions, and the whole system falls apart. – Mark Jan 26 at 21:24
• @Mark my answer suggests that, except in an otherwise empty universe, there is an upper limit to the diameter of a stable star system, and thus to the number of stars that could be in stable orbits in that system. – M. A. Golding Jan 26 at 21:41

The most stars in a known system are seven, and eight seems like the theoretical maximum. But it is possible that in extreme situations stable systems with more than seven stars might be theoretically possible.

Long Asnwer:

Part One of Four: Stable Star Systems are Hierarchical.

In stable star systems the orbits of individual stars and pairs of stars are arranged in a hierarchical order.

The two stars in a pair will orbit each other more closely than any other pairs or single stars will. A planet or star or pair of stars will have to orbit a pair of stars at a distance of at least a few times their separation in order to have a stable orbit. That is the reason for the hierarchical orbit types discussed in the article.

Part two: The Ultimate solar System and its limits.

There is a blob by astronomer Sean Raymond called PlanetPlanet, with a section called The Ultimate Solar System, where Raymond designs plausible imaginary solar systems, the goal to be a system with the maximum possible, though statistically very rare and improbable, number of habitable planets.

https://planetplanet.net/the-ultimate-solar-system/[2]

So Raymond tries putting the greatest possible number of planetaryorbits inside the circumstellar habitable zone of a single star. He tries trojan systems, with two or three planets sharing an orbit. He tries putting giant planets in the circumstellar habitable zone of a star, with several giant moons large enough to be habitable orbiting each giant planet.

Then he tries assembling more and more stars into the system, each with as many habitable planets as possible.

In "part 6: A system with many stars" he designs his masterpice, a system with 16 stars arranged in a hierarchy of 8 binary stars arranged in 4 quatenary stars arranged in 2 octenary stars, and a total of 384 to 576 habitable worlds.

And in the next post, "The biggest tragedy in the history of the universe" he describes how such a solar system would be torn about and most of the once habitable worlds collide with other planets, fall into a star, or be ejected into the cold of interstellar space.

The two 8 star systems making oup the 16 star system would have to be spaced so far apart that galacic tital forces, and the gravity of passing star systems, would turn their once almost circular orbits more and more elliptical. This effect would trickle down to the four star systems and the pairs of stars, and eventually the oribits of all the planets would be disrupted.

Here is a link to an article on the subject:

https://www.sciencedaily.com/releases/2013/01/130106145751.htm[3]

So if that is correct, a system with a four level hierarchy and with at most eight stars would seem to be the limit.

And as a matter of fact, the two known systems with the most stars are believed to be septenary systems with seven stars, Nu scorpii and aR Cassiopeiae.

https://en.wikipedia.org/wiki/Nu_Scorpii[4]

https://en.wikipedia.org/wiki/AR_Cassiopeiae[5]

Part Three: Possible eExceptions.

I suggest that if a star system was alone in the universe, or at least floating in intergalactic space hundreds or thousands of light years or parsecs from the nearest other star, a system with many more than eight stars should be dynamically stable.

And Raymond spaced the stars in each basic binary pair of his ultimate solar system far enough apart that each star could have planets in its habitable zone. But if the stars in each pair were spaced a fraction that far, too close to have planets orbiting each star, then the two sets of eight stars could also orbit each other much closer, perhaps close enough to avoid disruption.

So if it is not required that the pairs of stars are spaced far enough apart to have plantary systems, the whole 16 star system might be tight enough to avoid disruption and have stable orbits. Of course such a vast solar system without any planets would seem like a waste to science fiction fans, but it might be physically possible.

Part Four: Rings of Stars.

However, there is one way way it is theoretically physically possible for a star system to have more than seven stars in stable orbits.

"The Ultimate Engineered Solar System"

https://planetplanet.net/2017/05/03/the-ultimate-engineered-solar-system/[6]

features a star with a ring of planets sharing the same orbit. Actually several rings of planets in the stars habitable zone. Raymond says that between 7 and 42 astronomical objects can share a stable orbit if they have equal mass and are equally spaced along the orbit. An arrangement which would probably have to be created by a super advanced civiization instead of happening naturally.

His source is this paper: