PLANETPLANET

Let’s keep building the ultimate Solar System. In Part 1 we chose our star.  In Part 2 we chose our planets. In Part 3 we chose our planets’ orbit.  In Part 4 we learned two ninja moves about orbits.  In Part 5 we put the pieces together.

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In this post we will take the Ultimate Solar System to the next level.  The key ingredient that we will add is multiplicity. There will be many stars in this system, not just one or two.

A quick recap.  In part 5 we came up with two different ways of packing planets into our star’s habitable zone, where our worlds could host life.  Ultimate Solar System 1 only included Earth-like (rocky) planets (in a funky orbital configuration).  In Ultimate Solar System 2, half of the Earth-like worlds were not planets but moons of giant planets.

I couldn’t choose between these two ultimate Solar Systems so I chose them both.  I put them in a binary star system:

Looking back, I don’t think the Ultimate Solar System was ambitious enough.  Sure, we crammed 60 possibly life-bearing planets into one system.  But we can do better!

In this post I will focus on one aspect of the system we can build on: increasing the number of stars in the system. I was inspired by a recent post in which I generated a system in which a planet had five Suns in the sky (it was a 3-part series: see here, here and here).  What we are going to do is to build a system containing many stars, each of which has its own habitable zone packed full of planets. This gets us into murky philosophical waters because how broadly should we define a “planetary system”?  We are going to skip that discussion, jump in and build a new Multiple-Star Ultimate Solar System (if you have an opinion about this, feel free to leave a comment).

Here we go.

A lot of stars have companion stars.  A binary system is simply two stars that orbit each other. Our original Ultimate Solar System formed a binary system with the two stars separated by about 100 Astronomical Units.  There are lots of known triple, quadruple, quintuple, and even sextuple star systems.  For example, this is what the Castor 6-star system looks like:

Star systems follow a standard blueprint that keeps their orbits stable.  They are organized in a hierarchical setup.  What that means is that each set of orbits is on a different size scale.  The sizes of stars’ orbits do not go 1-2-3, they go 1-10-100. Any one star is only really close to one other star.  After that, other stars are much farther away.

Here is a cartoon of a hierarchical 8-star system:

This system is hierarchical because each close pair of stars (stars a and b, b and c, etc) is much closer to each other than any other stars (or pairs of stars).  The separation between stars a and b is much smaller than the separation between stars a+b and c+d, which is much smaller than the separation between stars a+b+c+d and e+f+g+h.  Let’s say that the separation between the closest binaries is 0.1 Astronomical Units, the separation between each pair of close binaries is 1 Astronomical Unit, and the separation between clumps of 4 stars is 10 Astronomical Units.

A hierarchical setup can double the number of stars for every additional level of hierarchy. For example, let’s start from the 8-star system in the image above. We can take two 8-star systems and put them in orbit around each other. We need to ensure that the new orbit is very wide, about ten times larger than next level down. In our setup, the two 8-star systems would need to be about 100 Astronomical Units apart for the whole system to be stable.

Let’s keep going.  We can indeed take two 16-star hierarchical systems and place them in orbit around each other.  Now the size of the largest orbit is 1000 Astronomical Units, and there are 32 stars in the system.

How far can we go with this?  How big of a hierarchical star system can we reasonably build?  (Is it really turtles all the way down?)  If a system becomes too big then it feels gravitational kicks from the Galaxy itself, from other stars and giant gas clouds. These extra kicks start changing the stars’ orbits when the stars are about 1000 Astronomical Units apart.  Orbits larger than about 100,000 Astronomical Units are really at the borderline, and can be broken at almost any time.

Now let’s introduce planets into hierarchical star systems.  For now we won’t worry about planets themselves but rather just the stars’ habitable zones.

In contrast with our previous thinking (from part 1 of this series), now the type of star really does matter.  Smaller, lower-mass stars are fainter so their habitable zones are more compact than the habitable zones of larger, more massive stars.  In our quest to increase the number of stars in a given system, it makes sense to choose low-mass stars, sometimes called red dwarfs.

In the hierarchical star systems above, the closest binary stars were 0.1 Astronomical Units apart.  Let’s switch out the two stars in those close binaries for one stars and its habitable zone.  For this to fit, we need stars whose habitable zones are about 0.1 Astronomical Units away.  That is 10 times closer than the Sun’s habitable zone, which means that the stars we want are 100 times fainter than the Sun. We want M dwarfs. (The kind that are a little cooler than Kepler-186). M dwarfs are much more common in the Galaxy than Sun-like stars, so it makes some sense to use them to build a star system.

After the switch, here is what the 8-star hierarchical system looks like:

Instead of two stars orbiting each other, the closest binary stars are now M dwarfs orbited by habitable zones.  These habitable zones are stable and can each host planets. We will come back to that.

The next step is simply to add another level of hierarchy.  Let’s put two systems — each with 4 stars with stable habitable zones — in orbit around each other:

Now we’re up to 8 stars, each with a stable habitable zone that can host planets.  Let’s go ahead and add one more layer, and double the number of stars one last time. Here is what we get :

We have reached the limit.  We cannot add another layer of hierarchy without treading into dangerous waters, with Galactic gravitational perturbations playing the role of the crocodile.

We have the infrastructure for our multiple-star ultimate Solar System. It contains 16 M dwarf stars. Each star’s habitable zone is well-separated from any other stars and is dynamically stable. Even with so many stars in the system, the light from the other stars does not have an appreciable effect on the habitable zone, since the closest star is 10 times farther away and 100 times fainter.

Let’s fill these habitable zones with planets! We know (from part 3 and part 4 of this series) how to pack as many planets as possible into the habitable zone while keeping their orbits stable.  As we saw in part 5, we can fit about thirty life-bearing worlds into the habitable zone (24 in Ultimate Solar System 1 and 36 in Ultimate Solar System 2).

It is tempting simply to choose 16 copies of Ultimate Solar System 2.  This would give 576 habitable worlds in the system, versus only 384 if we chose 16 copies of Ultimate Solar System 1.  However, M dwarf stars don’t have as many gas giant planets as Sun-like stars.  So Ultimate Solar System 1 is a more reasonable choice than Ultimate Solar System 2 for most of the stars in this system. And as long as there are a few Ultimate Solar System 2’s, the number of planets is still higher than 400. Not too shabby.

Here is what our 16-star Ultimate Solar System looks like:

We did it! This is a big step up from the original Ultimate Solar System, from 60 habitable worlds to 400 or more! Some might say that it’s even “Ultimater”!

SUMMARY: We built a giant (1000 Astronomical Unit-wide) hierarchical system with 16 stars and stable habitable zones.  By packing planets into those habitable zones we  created a system containing more than 400 (and up to 576) potentially habitable worlds. Boom!

Imagine the stories to be told in a system like this.  Astronomical battles pitting one world against another. Rivalries between planets orbiting different stars. Alliances among creatures on moons, Trojan planets, or binary planets. Hostile Takeovers of planets and moons. Imagine a lovable band of swarthy vagabonds exploring different parts of the system, chasing adventure while fleeing their pasts (I’m thinking of Firefly; I love that show).  How long would it take for the inhabitants of one planet to discover the planets orbiting other stars?  What would the sky look like on these worlds?

Speaking of storytelling, I have a confession.  This post is really just a setup for a story that I will tell in the next post.  Something not-so-cheery is brewing in the 16-star Ultimate Solar System…  Read on to learn what happens when a good planetary system goes bad.