Space News Deep Dive: HD 110067 and Orbital Resonance

Specifically, David wanted to know more about the concept of orbital resonance, which is of major importance in this system. It’s a great question and an intriguing topic and I get to talk about fun gravity stuff, so let’s meet this crazy new exoplanet system and talk a bit about resonance in the universe.

HD 110067

This new exoplanet system orbits the star HD 110067, a star almost the size of the Sun about a hundred light years away in the direction of the constellation Coma Berenices. The system has at least six planets in it, and has proven itself remarkable in several different ways.

First of all, this is the brightest star we’ve seen with more than four planets (so far). Generally the systems we find with larger numbers of planets are around smaller, dimmer red dwarfs. Our planet-finding techniques just make it easier that way—planets have a more noticeable effect on smaller stars than on bigger ones. But HD 110067 isn’t a red dwarf. It may not be quite up to the Sun, but it’s close.

So already this exoplanet system is worthy of attention. But wait, there’s more! All six planets orbiting this star are sub-Neptunes (also occasionally called mini Neptunes, which has more personality), between Earth and Neptune in size. Planets of this size seem to be very common in the Milky Way, but it’s something we can’t study up close because, for some reason, we don’t have one in our solar system. Having six a hundred light years away puts them cosmically in our backyard, meaning we may be able to learn a lot about this sort of planet that so many stars other than our Sun seem to have.

But wait, there’s more! I haven’t gotten to the resonance part yet! All six of the planets in this system are in resonance with each other! Isn’t that cool?? What’s that, you don’t know what that means? You mean planetary orbital resonance isn’t something you think about on a regular basis?

What is Resonance?

The Merriam-Webster Dictionary actually notes seven different definitions for “resonance”, the last of which is: “a synchronous gravitational relationship of two celestial bodies (such as moons) that orbit a third (such as a planet) which can be expressed as a simple ratio of their orbital periods.” Which is clear as mud, so let’s break it down.

To start with, orbital period refers to the amount of time it takes something to complete one orbit. Earth’s orbital period around the Sun, for instance, is 365.25 days. So resonance deals with the time it takes two objects to orbit a third. This can be moons orbiting a planet, like Merriam-Webster says, but in the case of HD 110067 it’s planets orbiting a star.

Resonance occurs when the two amounts of time it takes these objects to complete orbits around that third thing are multiples of each other. For instance, let’s say you have two moons, let’s call them Avocado and Bacon, orbiting planet Croissant (what? I’m making up these celestial bodies so I get to make up the names) with Avocado closer in so it takes less time to orbit Croissant than Bacon does.

Let’s say in the time it takes Avocado to complete one orbit Bacon completes exactly half its orbit. Or, to put it another way, for every orbit Bacon completes, Avocado completes exactly two orbits. When this happens, we say Avocado and Bacon are in a 2:1 resonance. If Avocado completed three orbits for every one of Bacon’s, we’d say they were in a 3:1 resonance. If Avocado completed five orbits for every three of Bacon’s, we’d say they were in a 5:3 resonance.

As long as there is a ratio of orbit numbers that can be expressed as whole numbers, Avocado and Bacon will be considered in resonance with each other. That said, the lower the numbers the more powerful an effect Avocado and Bacon can have on each other. If they were in, say, a 73:69 resonance (numbers I stole from Naiad and Thalassa, a pair of Neptunian moons with that resonance ratio), that wouldn’t have much effect on them. Because resonance can have a powerful effect. More on that later.

Why is Resonance?

Okay, so that’s what resonance is, but where does it come from? Gravity of course. When in doubt, just guess gravity and you have at least a decent chance of being right, at least if you’re talking about space. And that’s also where the powerful effects can come in (I’ll get to it, I swear).

Given some time and an undisturbed system, the mutual gravity of two objects orbiting a third will generally pull them into a resonance. It’s like a path of least resistance that physics likes to slide into. This, of course, begs the question of why everything isn’t in a close resonance relationship. Why isn’t Earth in a close resonance with Mars? Why isn’t Jupiter in resonance with Saturn?

Actually, they almost are. A Martian year is almost two Earth years. Jupiter is so close to a 5:2 resonance with Saturn I’m sure it can almost taste it, or would if it had taste buds. Neptune is in a 2:3 resonance with Pluto.

But remember what I said before: given some time and an undisturbed system. We think a lot of solar systems may start out with planets in resonance the way they are in HD 110067, but they don’t stay that way. Resonances between planets can be easy to disrupt. They can be thrown off by the gravity of passing stars (young solar systems often form in star clusters), by the gravity of other planets in the system (young planets like to migrate), or by things like huge impacts (young solar systems are often like shooting galleries). Once upon a time we think Jupiter was in resonance with Saturn. It’s just not anymore.

Where is Resonance?

We may not have planetary orbital resonance in our solar system, but we do see resonance. I’ve already pointed out the Neptune/Pluto relationship (no, Pluto is not a planet, it’s been nearly 18 years and it’s time to move on). But there’s a reason the Merriam-Webster definition calls out moons. We see a lot of resonance patterns amongst outer solar system moons.

The most famous example is between Jupiter’s moons Io, Europa, and Ganymede. For every four Io orbits, Europa orbits twice and Ganymede once. The trio is in a 4:2:1 resonance. And it is this resonance that makes Io and Europa two of the most unique worlds in the solar system.

Here’s where that powerful effect comes in: objects in resonance with each other can have a greater gravitational effect on each other’s orbits than they otherwise would. For instance, Io’s orbit isn’t circular. It should be. It should have settled into a more or less circular orbit over the last 4.5 billion years due to Jupiter’s gravity, but it hasn’t. And it hasn’t because of the extra effect of the gravity from Ganymede and Europa due to their resonance with Io.

So what? Well, this means Io is closer to Jupiter at some times than others. Not by much, but enough that the difference in gravitational pull from Jupiter at varying points in Io’s orbit causes Io to stretch and flex. It’s basically experiencing tides, but in rock rather than water. This heats up its insides and turns Io into the most volcanically active world in our solar system.

A similar effect heats up the inside of Europa, only in this case it doesn’t cause volcanoes. It just keeps Europa’s subsurface layers warm enough to maintain its massive global liquid water ocean. This ocean is one of the most likely places in the solar system for us to find life, and resonance makes it possible.

Back to HD 110067

The resonances in HD 110067 are, to be succinct, delightful. The six planets, planets b, c, d, e, f, and g (see? Weren’t “Avocado” and “Bacon” better?), form a resonance chain with each other. Planet b is in a 3:2 with c, which is in a 3:2 with d, which is in a 3:2 with e, which is a 4:3 with f, which is in a 4:3 with g. All that also adds up to put Planet b in a 6:1 resonance with g.

This isn’t the first time we’ve found an exoplanet resonance chain, but we’ve never seen such a long one! And they’re rare. Many systems start out this way but only about 1% are estimated to remain so. And HD 110067 isn’t a baby system—it’s at least a billion years old. Somehow this solar system, with so many planets, has maintained a pristine state from its earliest days.

And it’s so close (well, again, cosmically speaking)! It’s a perfect target for something like the James Webb Space Telescope to be able to study these worlds in the kind of detail that might prove impossible if they were farther away. And again, as a reminder, we don’t have worlds of this size in our solar system. This is an amazing opportunity! We are definitely going to be hearing more about this one.

And, quite aside from the magnificent haul of science already obtained and coming our way about this system, there is something exceptionally lovely about the movements of its planets. It’s the beauty of pure mathematical harmony playing out in the gravitational dance of entire worlds. Orbital resonance is the closest thing you can actually get to the music of the heavens.

1. An artistic illustration of the exoplanet system HD 110067 and the patterns caused by the orbital resonances of its planets. Credit: ESA
2. The star HD 110067 is in the little-known constellation Coma Berenices, which is near Ursa Major in the northern sky. Image created by the author using Stellarium.
3. A diagram showing how far each planet in the system HD 110067 travels in the time it takes the second planet, planet c, to complete one orbit. Credit: Hugh Osborn (University of Bern)
4. A volcano erupting on Jupiter’s moon Io. Credit: NASA
5. A diagram showing the orbital resonance ratios of the HD 110067 system. Credit: ESA