Hi there! Today, we leave the comets for the system of Pluto-Charon. Of course, you know Pluto. Formerly the 9th planet of our Solar System, until 2006, it remains an object of interest. So interesting that it has been visited by the spacecraft New Horizons in July 2015. You know, the same spacecraft which gave us these amazing images of Ultima Thule (also known as 2014 MU₆₉).
Anyway, we are not done with Pluto. It has a large satellite, Charon, which makes Pluto-Charon a binary object, i.e. Pluto and Charon orbit about a common barycenter, which is significantly outside of Pluto. And around this binary, you have (at least) 4 small satellites, which are Styx, Nix, Kerberos and Hydra. I say at least, because the authors of the study I present today address the following question: could there be more? I mean, if you add a satellite somewhere, will it survive? If no, then you can say that the system is dynamically packed. This the opportunity for me to present A Pluto-Charon sonata: The dynamical architecture of the circumbinary satellite system, by Scott J. Kenyon and Benjamin C. Bromley. This study has recently been published in The Astronomical Journal.

The binary Pluto-Charon

I guess you have already heard of the discovery of Pluto by Clyde Tombaugh in 1933 (see here). It appeared that Pluto had been observed at least 16 times before, the first of these precoveries dating back to 1909.
The launch of the spacecraft New Horizons in 2006 motivated the observations of the binary Pluto-Charon by the most efficient observing facilities, in particular the Hubble Space Telescope. This telescope permitted the discoveries of 4 moons of the binary: Nix and Hydra in 2005, Kerberos in 2011, and Styx in 2012. You can find some of their properties below.

	Discovery	Diameter	Semimajor axis	Orbital period	Spin period
Pluto	1933	2376.6 km	39.48 AU	248 years	6.39 days
Charon	1978	1212 km	19591 km	6.39 days	6.39 days
Styx	2012	16x9x8 km	42656 km	20.16 days	3.24 days
Nix	2005	53x41x36 km	48694 km	24.85 days	1.83 d
Kerberos	2011	19x10x9 km	57783 km	32.17 days	5.31 days
Hydra	2005	65x45x25 km	64738 km	38.20 days	10.3 hours

As you can see, the binary Pluto-Charon is doubly synchronous, i.e. Pluto and Charon have the same spin (rotation) period, and Charon has that same orbital period around Pluto. It would be accurate to say that Pluto and Charon have both this orbital period around their common barycenter. It can be shown that this state corresponds to a dynamical equilibrium, which itself results from the dissipation of rotational and orbital energy by the tidal interaction between Pluto and Charon.

However, the four other moons are much smaller, and much further from Charon. They spin much faster than they orbit, which means that the tides were not efficient enough to despin them until synchronization. Hydra spins in hours, while the others ones, which are closer to the binary, spin in days. So, they may have despun a little after all, but not enough.

No additional moon has been discovered since, even by New Horizons. The authors wonder whether that would be possible or not. For that, they ran intensive numerical simulations.

Simulations with Orchestra

They disposed of the numerical code Orchestra, which they developed themselves. This code is composed of several modules, permitting

• N-body simulations,
• to simulating planetary formation, especially the growth of the accreting bodies.

For this specific study, the authors considered only the N-body simulations. For that, they added massless particles in the binary, i.e. these particles were perturbed by the gravitational action of Pluto, Charon, and their four small moons. The simulations were ran over several hundreds of Myr.

I would like the reader to be aware that the stability, i.e. survival, of such particles is not trivial at all. You can imagine that if you come too close to a satellite, then you might be ejected. But this is not the only possible cause for ejection.

In such a system, you have many mean motion resonances. Imagine, for instance, that you are a massless particle (happy to be massless, aren’t you? trust me, it is not that fun), and that you orbit around Pluto-Charon exactly twice faster than Hydra (this is just an example). Every two orbits, your closest distance with Hydra will be at the same place. This will result in cumulative effects of Hydra on you, and since you are massless, you are very sensitive to these effects (which are actually a gravitational perturbation). And the outcome is: you might be ejected. Let us see now the results of the simulations.

Probably nothing inside the orbit of Hydra

Yes, because of these resonances, most of the massless particles orbiting inner to Hydra are unstable. In fact, some of them may survive, but in specific locations: either inner to the orbit of Styx, which is the innermost of the small moons, or outside the orbit of Hydra, i.e. outside of the known boundaries of the binary. In-between, you may have some particles, which would be coorbital to the small moons. This phenomenon of 1:1 mean-motion resonances appears in several locations of the Solar System. For instance, Jupiter has its Trojan asteroids, with which it shares its orbit. This also happens among the satellites of Saturn. Why not around Pluto-Charon? Well, you have to see them to be convinced they exist. These simulations just give you a theoretical possibility, i.e. this is not impossible.
Anyway, the preferred locations for yet-undiscovered moons is outside the orbit of Hydra. The challenge would be to discover such objects. Inside, the system appears to be dynamically packed.

Could there be something outside?

The authors present a discussion on the future possibility to detect them. First, they mention the stellar occultations.
Imagine the system of Pluto-Charon gets aligned between a terrestrial observer and a distant star. Then you can hope that, if there is something which is still unknown in that system, then it may occultate the light of the star, at least to some terrestrial observers. Of course, this may vary on from where on Earth you observe. For such a discovery to happen, you must be very lucky. But remember that the rings of Chariklo and Haumea were discovered that way.

Another hope for discovery is in the future instruments. The authors mention the JWST (Jawes Webb Space Telescope), which should be launched in March 2021. A kind of upgrade to HST (Hubble), its primary having a diameter of 6.5 meters, instead of 2.4 for Hubble. Moreover, it will be more efficient in the infrared, but unable to observe in the ultraviolet.

The study and its authors

• You can find the study here. The authors made it also freely available on arXiv, and some animations here. Many thanks to them for sharing!
• The website of Scott J. Kenyon,
• and the one of Benjamin C. Bromley.

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.