Pluto-Charon is dynamically packed

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.

Hydra as seen from NASA’s New Horizons spacecraft. © NASA/JHUAPL/SwRI
Hydra as seen from NASA’s New Horizons spacecraft. © NASA/JHUAPL/SwRI

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

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.

The rotation of 67P/Churyumov-Gerasimenko

Hi there! Today, we go back to the famous comet 67P / Churyumov-Gerasimenko. As you may know, this comet was the target of the European space mission Rosetta. In particular, it was the first comet to be landed by a spacecraft, in November 2014. Rosetta gave us invaluable information on 67P, which could be extrapolated to many comets, with caution of course. Today we discuss Comet 67P/Churyumov-Gerasimenko rotation changes derived from sublimation induced torques, by T. Kramer, M. Läuter, S. Hviid, L. Jorda, H.U. Keller and E. Kührt.
It addresses the following issue: when you try to assess the forces affecting the orbit and the rotation of the comet, you have troubles. Among these forces are the gravitational perturbations of the Sun and the planets, which are very well known, but also torques and forces due to non-gravitational effects. When the comet approaches the Sun, its ice sublimates, and the resulting outgassing deviates the comet and affects its rotation. This last effect is only poorly constrained, and this is why in situ observations, as made by Rosetta, are essential to understand them. This study has recently been accepted for publication in Astronomy and Astrophysics.

The discovery of 67P / Churyumov-Gerasimenko

This comet has been discovered by chance in September 1969 at Alma Ata Observatory, now in Kazakhstan, then in USSR. Svetlana Ivanova Gerasimenko took images of a field containing the comet 32P/Comas Solá, and Klim Ivanovich Churyumov detected there a new object close to the edge of an image. This object appeared on several images, which permitted to characterize its motion. That object was itself a comet, a periodic one (“P”), and more precisely the 67th to be discovered. So was it named 67P / Churyumov-Gerasimenko. You can find below some of its characteristics.

Discovery 1969
Semimajor axis 3.463 AU
Perihelion 1.243 AU
Aphelion 5.68 AU
Eccentricity 0.64
Inclination 7.04°
Orbital period 6.44 yr
Spin period 12 h 24 min
Diameter 4 km
Density 0.53 g/cm3

As you can see, its orbit is pretty elongated, and has a period of almost 6.5 years. This means that every 6.5 years, 67P/Churyumov-Gerasimenko approaches the Sun, at its perihelion, and at that time gets heated. This results in the sublimation of some of its material, which deviates it and alters its spin. The last passage at the perihelion occurred in August 2015, while the next one will be in November 2021. Rosetta orbited the comet from 2014 to 2016, which encompassed the perihelion passage, allowing to observe and measure the peak and evolution of its cometary activity.

A rugged terrain

We will see later that modeling the rotation of a planetary object requires to know its shape. Fortunately for us, we know this shape very accurately, thanks to Rosetta. Unfortunately for the authors, 67P/Churyumov-Gerasimenko is far from a ball.

This is actually a bilobal object, i.e. roughly like a bone, of some 4 km in its larger dimension. Moreover, its terrain is very rugged. Rosetta actually observed, over only two years, alterations in the terrain, e.g. a landslide associated with an outburst. This makes the behavior of the comet all the more difficult to constrain… For instance, if you want to consider an outburst, from which region will it emerge?

Rugged terrain on 67P © ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA
Rugged terrain on 67P © ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA

The data brought by Rosetta

We know the shape and rotation state of 67P/Churyumov-Gerasimenko thanks to Rosetta/OSIRIS images. OSIRIS, for Optical, Spectroscopic, and Infrared Remote Imaging System, is an imager composed of 2 cameras, a WAC and a NAC (Wide-Angle and Narrow-Angle Camera, respectively). From images brought by OSIRIS, it was possible to build a set of approximately 25,000 control points. Multiple observations of these control points, at different dates, permitted to understand that

  • the comet spun around a single axis, which orientation has been determined,
  • its rotation period was 12 hours and something (on purpose, I do not detail this something here),
  • the rotation state varies with time. Rosetta observed a reorientation of the spin axis of 0.5°, and a shortening of the rotation period by 21 minutes (this is why I did not detail the something).

Moreover, these data permitted to elaborate a shape model of the comet, made of 3,996 triangular surface elements. From this shape model, you can determine what is called the tensor of inertia of the comet, i.e. its mass distribution, in assuming its composition to be homogeneous (you always have to make hypotheses).

Now, let us see how the rotation is affected.

The torques affecting the comet

In the study, the comet is assumed to be rigid, i.e. its shape is constant. You have no elasticity, this is probably a good approximation over such a limited time span. The equations of the rigid rotation tell you that the angular momentum of the comet (the angular momentum is the tensor of inertia, which is multiplied by the rotation) is affected by two kinds of torques:

  • the gravitational torque of the surrounding bodies, which is almost entirely due to the mass of the Sun,
  • non-gravitational torques, due to ice sublimation and heating by the Sun.

You put all this into an equation, you solve it numerically, and you can predict it, and understand the rotation measurements… Easy, isn’t it? Well, not that easy, since you have only few constraints on the ice sublimation.

Modeling its rotation

BUT you have measurements of the rotation. So, what you can do is fit the parameters you don’t know, to the observed rotation. And more particularly to the changes in the rotational state.

More precisely, the authors modeled the torque due to the sublimation of water ice with a Fourier representation, i.e. as a sum of periodic quantities. These contributions are assumed to have a period, which is due to the rotation of the comet, and they are treated separately. The authors managed to match the Fourier amplitudes with the observed torque. And now let us go to the conclusions.

What it tells us on the activity

Fitting the Fourier coefficients to the observed rotation finally tell us that:

  • you can constrain the active fraction of the surface, with respect to the different areas (the authors considered 38 different zones on the surface),
  • the sublimation increases much faster than linearly with respect to insolation. In other words, when you are twice closer to the Sun, the quantity of sublimated water ice is much more than twice than before. This was already known from other studies, but the study of the rotation confirms this fact. You should see it as a validation of the method.

So, this paper shows that we can definitely make a link between water production and the changes in rotation rate. Outgassing also produces CO2, but this is not considered, since this production is more uniform than the one of water, and so should not affect the reorientation of the spin axis.

The study and its authors

  • You can find the study here. The complete reference is Kramer T., Läuter M., Hviid S., Jorda L., Keller H.U. & Kührt E., 2019, Comet 67P/Churyumov-Gerasimenko rotation changes derived from sublimation-induced torques, Astronomy and Astrophysics, in press. The authors made it also freely available on arXiv, many thanks to them for sharing! And now, let us see the authors:
  • the website of Tobias Kramer, first author of the study,
  • the webpage of Matthias Läuter,
  • the IAU page of Laurent Jorda,
  • the one of Horst Uwe Keller,
  • and the ResearchGate profile of Ekkehard Kührt.

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.