Category Archives: Asteroids: Trans-Neptunian Objects

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 Solar System is a mess: Using Big Data to clear it up

Hi there! When you look at our Solar System, you wonder how it came to be that way. I mean, it formed from a nebula, in which grain accreted to create the Sun, the planets,… and all these small bodies. Most of them have disappeared since the origin, they were either ejected, or accreted on a planet, or on the Sun… anyway still many of them remain. You have the Asteroid Main Belt, the Centaurs, the Kuiper Belt, the Oort cloud, the comets… Several studies have tried to determine connections between them, i.e. where does this comet come from? Was it originally a Centaur, a Kuiper Belt Object, something else? And how did it change its orbit? A close approach with a giant planet, maybe?
And to address this question, you simulate the trajectories… which is not straightforward to do. It is pretty classical to simulate a trajectory from given initial conditions, but to answer such a question, you need more.
You need more because you do not know how reliable are your initial conditions. Your comet was there that day… very well. How sure are you of that? You observe a position and a velocity, fine, but you have uncertainties on your measurements, don’t you?
Yes, you have. So, you simulate the trajectories of many comets, which initial conditions are consistent with your observations. That’s better. And you hope that the outcome of the trajectories (trajectories simulated backward, if you want to know the origin) will be pretty much the same, since the initial conditions are very close to each other…
But they are not! This is what we call sensitivity to the initial conditions. This often means chaos, but I do not want to detail this specific notion. But basically, when a comet swings by a giant planet, its trajectory is dramatically deviated. And the deviation is highly sensitive to the location of the comet. So sensitive that at some point, you lose the information given by your initial conditions. C’est la vie.
As a result, there are in the literature many studies presenting their simulations, and which conclusions are sometimes inconsistent with each other.
The study we discuss today, It’s Complicated: A Big Data Approach to Exploring Planetesimal Evolution in the Presence of Jovian Planets, by Kevin R. Grazier, Julie C. Castillo-Rogez, and Jonathan Horner, suggests another approach to clear up this mess. It considers that all of these possible trajectories constitute a reservoir of Big Data. This study has recently been published in The Astronomical Journal.

Architecture of the Solar System

You know the 8 planets of our Solar System, from the closest to the outermost one:

  • Mercury,
  • Venus,
  • Earth,
  • Mars,
  • Jupiter,
  • Saturn,
  • Uranus,
  • Neptune.

And these planets are accompanied by many small bodies, which constitute

  • the Near-Earth Asteroids, which orbit among the 4 terrestrial planets (from Mercury to Mars),
  • the Main Belt Asteroids, which orbit between Mars and Jupiter,
  • the Centaurs, which orbit between Jupiter and Neptune,
  • the Kuiper Belt, which extends between 30 and 50 AU (astronomical units) from the Sun. So, its inner limit is the orbit of Neptune,
  • the scattered disc, which extends to 150 AU from the Sun. These objects are highly inclined. Eris is the largest known of them.
  • the detached objects, like Sedna. This population is very poorly known, and we do not even know if it is truly a population, or just some objects,
  • the hypothetical Oort cloud, which could be as far as one light-year, or 50,000 AU.

Of course, this list is not exhaustive. For instance, I did not mention the comets, which could originate from any of those populations of small objects.

In this study, the authors limit themselves to the orbit of Neptune. They consider 3 populations of objects between the orbits of Jupiter and Saturn, between Saturn and Uranus, and between Uranus and Neptune. And the question is: how do these populations evolve, to the current state? For that, planetary encounters appear to be of crucial importance.

Planetary encounters

Imagine a small body flying by Jupiter. It approaches Jupiter so closely that it enters its sphere of influence, in which the gravity of Jupter dominates the one of the Sun. Virtually, the object orbits Jupiter, but usually this orbit cannot be stable, since the approach is too fast. Locally, its orbit around Jupiter is hyperbolic, and the object does not stay there. Jupiter ejects it, and you do not know where, because the direction of the ejection is highly sensitive to the velocity of the object during its approach. It also depends on the mass of Jupiter, but this mass is very well known. Sometimes, the action of Jupiter is so strong that it fragments the object, as it did for the comet Shoemaker-Levy 9, in July 1994. And you can have this kind of phenomenon for any of the giant planets of the Solar System.

This is how planetary encounters could move, disperse, eject,… entire populations in the Solar System.

The Big Data approach

With so many objects (the authors considered 3 ensembles of 10,000 test particles, the ensembles being the 3 zones between two consecutive giant planets) and so many potential planetary encounters (the trajectories were simulated over 100 Myr), you generate a database of planetary encounters… how to deal with that? This is where the Big Data approach enters the game.

The authors performed it into two stages. The first one consisted to determine close encounter statistics and correlations, for instance with changes of semimajor axis, i.e. how a planetary encounter displaces an object in the Solar System. And the second stage aimed at reconstituting the path of the particles.

And now, the results.

Random walk from one belt to another

It appears that the particles could easily move from one belt to another. Eventually, they can be ejected. As the authors say, the classification of a particle into a population or another is ephemeral. It depends on when you observe it. In other words, a small object you observe in the Solar System could have been formed almost anywhere else. Even in situ. Now let us talk about specific examples.

The origin of Ceres

For instance, Ceres. You know, this is the largest of the Main Belt Asteroids, and the first to have been discovered, in 1801. It has recently been the target of the mission Dawn, which completed in October 2018.

Ceres seen by Dawn. © NASA
Ceres seen by Dawn. © NASA

Ceres is rich in volatiles like ammonia and carbon dioxides, as are other asteroids like Hygeia. Hygeia is itself a large Main Belt Asteroid. Knowing the origin of Ceres could give you the origin of these volatiles… but they could have been partly accreted after the migration… You see, it is difficult to be 100% sure.

Ceres could have formed in situ, i.e. between Mars and Jupiter, but this study shows that it could have originated from much further in the Solar System, and migrated inward.

The origin of trapped satellites

Most of the main satellites of the giant planets are thought to have been formed with the planet, in the protoplanetary nebula.
But in some cases, you have satellites, which orbit far from the parent planet, on an irregular orbit, i.e. a significantly inclined and eccentric one. In such a case, the body has probably not been formed in situ, but has been trapped by the planet. Among them are Saturn’s Phoebe and Neptune’s Triton, which are large satellite. I have discussed the case of Triton here. The trapping of Triton probably ejected mid-sized satellites of Neptune, which are now lost.

Phoebe seen by <i>Cassini</i> in August 2017 © NASA/ESA/JPL/SSI
Phoebe seen by Cassini in August 2017 © NASA/ESA/JPL/SSI
Mosaic of Triton taken by Voyager 2 in 1989. © NASA
Mosaic of Triton taken by Voyager 2 in 1989. © NASA

Phoebe and Triton entered the sphere of influence of their parent planet, but did not leave it. And where did they come from?

It seems probable that Triton was a Trans-Neptunian Object (TNO) before. In that part of the Solar System, the velocities are pretty low, which facilitate the captures. However, several scenarios are possible for Phoebe. The study show that it could have originated from an inner or from an outer orbit, and have jumped to Saturn from close encounters with Jupiter / Uranus / Neptune.

Something frustrating with such a study, which goes back to the origins, is that you lose some information. As a consequence, you can only conclude by “it is possible that”, but you cannot be certain. You have to admit it.

A way to secure some probabilities is to cross the dynamics with the physical properties, i.e. if you see that element on that body, and if that element is thought to have formed there, then you can infer something on the body, and the authors discuss these possibilities as well. But once more, you cannot be 100% sure. How do you know that this element has been formed there? Well, from the dynamics… which is chaotic… And when you see an element at the surface of a planetary body, does it mean that it is rich in it, or just coated by it, which means it could have accreted after the migration?

You see, you cannot be certain…

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.

Weighing the Kuiper Belt

Hi there! Today, we are back to the Solar System, and more especially the Kuiper Belt. You know, all these small bodies, which orbit beyond Neptune. Instead of speaking of specific cases, like Pluto, Haumea or Sedna, we will see the Kuiper Belt as a whole.
The study I present, Mass of the Kuiper Belt, by E.V. Pitjeva and N.P. Pitjev, constrains its total mass with planetary ephemerides. This study has been recently published in Celestial Mechanics and Dynamical Astronomy.

The Kuiper Belt

I have presented the Kuiper Belt many times. These are objects, orbiting beyond the orbit of Neptune. This zone is named after the Dutch-American astronomer Gerard Kuiper, who hypothesized that it could have been a reservoir of comets, even if he thought that it would be almost clear. At that time, the only known Kepler Belt Object was Pluto. Now, more than 2,000 of them are known, and many more are probably to be discovered.
Most of these objects orbit between 30 and 50 AU (astronomical units) from the Sun.

This study wants to constrain the total mass of the Kuiper Belt, from the motion of the planets. For that, the authors built and used planetary ephemerides.

Planetary ephemerides

Planetary ephemerides give the location of the Solar System objects, especially the planets, at given dates. They have been of strategical importance during centuries for celestial navigation. Now, we still need them, for instance to identify potentially hazardous objects, to guide spacecraft, to detect new objects,…

I can cite 3 institutions, which provide ephemerides:

  • NASA’s JPL,
  • IMCCE, Paris Observatory, France,
  • Institute of Applied Astronomy, Russian Academy of Sciences.

JPL stands for Jet Propulsion Laboratory. It is located near Pasadena, CA, and is associated with the Californian Institute of Technology (CalTech). As part of NASA, it is associated with the American spacecraft.
The IMCCE, for Institute of Celestial Mechanics, is responsible for the French ephemerides. It has been founded in 1795 as the Bureau des Longitudes, in a context of rivalry between France and England. Its goal was then to assist France, to regain control of the seas.
And the Institute of Applied Astronomy, in Russia, is the place where this study has been conducted.

These 3 institutions provide their own ephemerides, i.e. solutions for the orbital motion of the planets, their satellites, the asteroids,… Now, let us see how to include the Kuiper Belt.

The Kuiper Belt as a ring

The orbital motion of planetary bodies come from the numerical integration of the gravitational equations, in which each body is perturbed by all the other ones… this makes many of them. So many that a common computer cannot handle that, when it comes to 2,000 of them. Moreover, there are probably many more Kuiper Belt Objects, which are not discovered yet, but which perturb the motion of the planets…

The authors by-passed this problem in modeling the Kuiper Belt as a ring. Not the whole Kuiper Belt actually. The 31 most massive of these objects are modeled as point masses, ans the remaining ones are embedded into a fictitious rotating ring, which mass perturbs the planets.

If you know the perturbation, you know the mass… Easy, isn’t it? Well, not that easy, actually…

As many data as possible

The authors maintain their ephemerides since many years, and each new version is enriched with new data. The current version, EPM2017, uses about 800,000 positional observations of planets and spacecraft, ranging from 1913 to 2015. Many of the observations of planets are Earth-based astrometric observations, while spacecraft observations include MESSENGER (mission to Mercury), Venus Express (to Venus), Cassini (to Saturn), and the Martian missions Viking-1 & 2, Pathfinder, Mars Global Surveyor, Odyssey, Mars Reconnaissance Orbiter, and Mars Express.

Very small objects like spacecraft are very sensitive to planetary perturbations, this is why their navigation data may be invaluable.

Observed and fitted parameters

Making ephemerides consists in fitting a dynamical model to data, i.e. observed positions. The dynamical model is mainly composed of the gravitational interactions between the planetary bodies, with some relativistic corrections (Einstein-Infeld-Hoffmann equations). These interactions use the masses of the objects as parameters.

When you want to fit the model to the data, you fit the initial conditions, i.e. the location of the objects at the beginning of the simulation, and some of the parameters. Why only some of them? It depends on how well you know them.

For instance, in this case, the mass of (1)Ceres is assumed to be accurately known, thanks to the Dawn mission (just finished, by the way). This means that fitting this mass would be counterproductive.

So, the authors have to make critical choices between what they fit and what they don’t, and also how they ponder the observations between each other.

A light Kuiper Belt

From formation models of the Solar System, the initial Kuiper Belt should be as massive as ten times our Earth. However,
fitting the ephemerides gives much smaller numbers. You can find below the outcomes of the previous studies and this last one, by the same team.

Year Kuiper Belt mass (in Earth mass)
2010 0.0258
2013 0.0263
2014 0.0197
2017 0.0228 ± 0.0046
2018 0.0197 ± 0.0035

As you can see

  • the current Kuiper Belt is by far much lighter than the original one. This means that this region of the Solar System has probably been depleted by the gravitational action of the main planets, only few objects remaining,
  • the numbers do not converge very fast, but they converge. In particular, each new measurement is consistent with the previous one, and the uncertainty tends to shrink. Slowly, but it shrinks.

This number of 0.02 Earth mass makes the Kuiper Belt about 2 orders of magnitudes (i.e. between 10 and 1,000) heavier than the Asteroid Main Belt, but some 3 orders of magnitude lighter than the proposed Planet Nine.

The Planet Nine would have a limited influence

You remember the Planet Nine? It is a yet undiscovered body, which is supposed to exist anyway. It should orbit far behind the orbit of Neptune, should be as massive as 10 Earth masses, and would be responsible for the clustering of the pericentres of the Trans-Neptunian Objects (the Kuiper Belt), and for the obliquity of the Sun.

In this study, the authors benefited from the very accurate navigation data of the space mission Cassini, which orbited Saturn until September 2017. And for Cassini, the Kuiper Belt has a much stronger influence than the hypothetical Planet Nine. This makes me think that the author believe that using such ephemerides is not a good strategy for constraining the Planet Nine.

Actually, the planetologists looking for the Planet Nine focus on the individual trajectories of the Kuiper Belt Objects, because these are the most sensitive to it.

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.

Satellites of large TNOs

Hi there! Today, we discuss about the Trans-Neptunian Objects, and more precisely objects orbiting in the Kuiper Belt, i.e. between the orbit of Neptune (~30 astronomical units) and ~50 AU (remember: the Earth orbits at 1 AU, i.e. 150 millions kilometers) for the classical Belt. Scattered objects orbit beyond that limit. During six decades, Pluto was the only known object of them, but the observation surveys with large telescope and adaptive optics has permitted the discovery of more than 100,000 of them! And among them are what we call dwarf planets, i.e. bodies which are large enough to have a pretty spherical shape.
Beside this, many Kuiper Belt objects have a companion, i.e. a satellite. When the satellite is large enough to compete with the primary body, the system is called a binary.
Today, we focus on the satellites of 2 large TNOs, named Eris and Orcus. The study I present, Medium-sized satellites of large Kuiper belt objects, by Michael E. Brown and Bryan J. Butler, tells us that their known satellites are pretty large and dark. This study has recently been published in The Astronomical Journal.

Many TNOs are not alone

Charon, i.e. the companion of Pluto, has been discovered in 1978. At that time, Pluto was the only known Trans-Neptunian Object. Since then, the discoveries of TNOs were often followed by the detection of a companion. There could be more than 20% of binary objects and multiple systems in the low-inclination populations, i.e. the objects which orbital plane is close to the mean one of the classical Kuiper Belt. This fraction seems to be much smaller (maybe 5%) for the inclined objects. But determining a frequency is a tough task, since the detection of such objects challenges the limitations of our observation facilities.

Anyway, there are many binaries among the Kuiper Belt, and this raises the question: how is that possible? How did they form? Does the companion result from an impact? Was it a single object, which have been trapped by the primary one?

Answering these questions requires to consider the properties of the two objects, i.e. their mass ratio, their distance, their composition (do they appear to be similar or not?). And this also raises other questions, related to the stability of these systems (how long can they survive as binaries)?

Two large guys: Eris and Orcus


Eris and Orcus were discovered in 2005 and 2004, respectively, by a team led by Michael Brown, with data from Palomar Observatory.
The discovery of a Solar System object usually happens during a systematic survey of the sky. You take several pictures of a given field of the sky. You first need to reduce them, i.e. you de-noise them to correct for the instrumental and atmospheric problems, then you make an astrometric correction in using the stars which appear on the image, to improve the reliability of the coordinates you use. Once this is done, you see small points on the images. From an image to another, most of the points are fixed. These are the stars. And sometimes, a point is slowly moving. This is a Solar System object. And if this object is not catalogued, it means you have discovered it.

Discovery of Orcus. © NASA
Discovery of Orcus. © NASA

Actually it is a little more complicated than that, you need to re-observe the object to validate the discovery and calculate orbital elements, i.e. determine its orbit. But once an object is observed, it is easier to re-observe it.

And the multiple observations of Eris and Orcus have permitted to infer some of their physical properties, and along with their orbital elements.

Interestingly, there were precoveries of Eris and Orcus. A precovery is an a posteriori identification of an object, after it is known, but on images taken before its discovery. In other words, its presence was on the images, but remained unnoticed. Precovery images have been identified back to September 3, 1954 for Eris, and to November 8, 1951 for Orcus. This means that we have observations over more than 60 years. Of course, these precoveries do not give us any clue on the physics of the object. However, they constrain its motion. If we consider the fact that its period is of the order of a few century, an observation arc of 60 years is highly valuable for determining its orbit.


You can find below some of their properties.

Eris Orcus
Discovery 2005 2004
Semimajor axis 67.781 AU 39.398 AU
Eccentricity 0.44 0.22
Inclination 44° 20.6°
Orbital period 558.04 yr 247.29 yr
Diameter 2326±12 km 910±50 km
Albedo 0.96±0.04 0.23±0.02
Apparent magnitude 18.7 19.1
Satellite Dysnomia Vanth

And it appears that these two objects are indeed very different. Orcus is a plutino, i.e. its orbit is close to the one of Pluto. It is in a 3:2 mean-motion resonance (MMR) with Neptune, i.e. it makes exactly 2 orbital revolutions around the Sun while Neptune makes 3. However, Eris is a scattered object. This means that its orbit does not make it a cold (i.e. unexcited) classical Kuiper Belt object, but it belongs to the objects, which have been somehow dynamically excited. As a consequence, its orbit is significantly inclined with respect to the classical Kuiper Belt, and it orbits far beyond.

Moreover, Eris is just the largest known TNO, even larger than Pluto. When it was discovered, Pluto was still called a planet. Its downgrading to a dwarf planet is the consequence of the discovery of these large TNOs, not only Eris and Orcus, but also Makemake, Haumea, Sedna…

And these two bodies appear to have at least one satellite each! Both were discovered in 2005 by teams led by Michael Brown, during observations of the main Kuiper Belt Objects. The satellite of Eris, Dysnomia, has been discovered thanks to the Keck Observatory, located on the Mauna Kea, Hawaii, while the satellite of Orcus, Vanth, was discovered thanks to the Hubble Space Telescope.

These objects appear so faint that we must use the best facilities to study them.

Observations with the Atacama Large Millimeter Array (ALMA)

The authors used data taken at the Atacama Large Millimeter Array (ALMA). This is an array made with a collection of 12m-antennae, in the Chilean Andes. They benefited from a recent upgrade of the instrument, to obtain spatial resolutions of 10s of milliarcseconds. Observations at this resolution at the frequency of 350 GHz, which is at the boundary between far infrared and sub-millimetric, permits to directly measure the thermal emission of satellites of Kuiper Belt Objects.

You can find in the video below some views of ALMA.

The authors disposed of 4 ALMA observations of the pair Orcus-Vanth, taken in October and November 2016, and 3 observations of Eris-Dysnomia, made in November and December 2015. The four observations of Orcus-Vanth gave an obvious resolution of the two bodies, while it is not that clear for Eris-Dysnomia. A combination of the 3 observations into a single image has anyway allowed a detection with a very good confidence, and using an a priori knowledge of the location of Dysnomia, due to previous studies.

The authors also supplemented their Orcus-Vanth dataset with unresolved data (i.e. on which you cannot separate the two objects) due to the infrared Spitzer Space Telescope and the Herschel Space Observatory.

Once they have these data, they should invert them to extract physical parameters. And this is not easy.

From the observations to the physical parameters

The difficulty comes from the accuracy of the observations. Remember that each of them is indeed a challenge.

If all of the observations had a perfect accuracy, you would just need a few images to get the position of the velocity of a planetary body, and then its orbital elements… But, if you try to do that on two different datasets related to the same object, you would get different numbers! And the reason is in the accuracy of the observations. Just an example: in using an orbital solution for Vanth resulting from a previous study, the authors got a difference of 11° in the longitude, i.e. Vanth is 11° in advance on its orbit on these observations, with respect to the predictions, which are derived from previous observations. This should give you an idea of the difficulty of the task.

And the authors should find a best fit between the models and the observations. They model Eris, Dysnomia, Orcus and Vanth as spherical bodies, which have an orbital motion and a thermal emission. These things depend on parameters, and you should find the numbers for these parameters, which give the best match between observations and models.

For that, they used the Markov Chain Monte Carlo scheme. This consists in testing a collection of parameters, which are distributed following a probability law. You can find below some of the results.

Dysnomia Vanth
Diameter 700±115 km 475±75 km
Albedo 0.04±0.02 0.08 ±0.02
Orbital period 15.79 days 9.54 days

I see two major elements from these results:

  1. The satellites are pretty large,
  2. they are much darker than their parent body (Eris for Dysnomia, Orcus for Vanth).

This last element suggests that they have a different composition.

On the origin of the satellites: impact of trapping?

An elegant scenario for the creation of a double system is an impact on the proto-primary body. This impact would have excavated a significant mass, which would have then formed the secondary. This is the most popular explanation for the formation of the Moon, and this seems to work for Pluto-Charon.

But the difference in albedo between the primary and the secondary, for these two pairs, could rule out this scenario, just because the surfaces seem to be too different. This could also mean that the secondary is essentially made of material, which initially belonged to the impactor. But this enforces another scenario as well, which is the trapping of the secondary by the binary. Originally there would have been two independent bodies, which would have met, and got gravitationally bound. Why not? That would be consistent with a difference in the composition.

The study and its authors

  • You can find the study here. The authors made it freely available on arXiv, thanks to them for sharing!
  • The homepage of Michael E. Brown. He discovered several Trans-Neptunian Objects, including Eris and Orcus, and is strongly involved in the quest for the Planet Nine. You cann see his blog here.
  • and the one of Bryan J. Butler.

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The rings of Haumea

Hi there! I guess you have heard, last year, of the discovery of rings around the Trans-Neptunian Object Haumea. If not, don’t worry, I speak about it. Rings around planets are known since the discovery of Saturn (in fact a little later, since we needed to understand that these were rings), and now we know that there are rings around the 4 giant planets, and some small objects, which orbit beyond Saturn.

Once such a ring is discovered, we should wonder about its origin, its lifetime, its properties… This is the opportunity for me to present a Hungarian study, Dynamics of Haumea’s dust ring, by T. Kovács and Zs. Regály. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

The Trans-Neptunian Object (136108)Haumea


The discovery of (136108) Haumea was announced in July 2005 by a Spanish team, led by José Luis Ortiz, observing from Sierra Nevada Observatory (Spain). This discovery was made after analysis of observations taken in March 2003. As a consequence, this new object received the provisional name 2003 EL61.

But meanwhile, this object was observed since several months by the American team of Michael Brown, from Cerro Tololo Inter-American Observatory, in Chile, who also observed Eris. This led to a controversy. Eventually, the Minor Planet Center, which depends on the International Astronomical Union, credited Ortiz’s team for the discovery of the object, since they were the first to announce it. However its final name, Haumea, has been proposed by the American team, while usually the final name is chosen by the discoverer. Haumea is the goddess of fertility and childbirth in Hawaiian mythology. The Spanish team wished to name it Ataecina, after a popular goddess worshipped by the ancient inhabitants of the Iberian Peninsula.

Reanalysis of past observations revealed the presence of Haumea on photographic plates taken in 1955 at Palomar Observatory (we call that a precovery).


You can find below some numbers regarding Haumea.

Semi-major axis 43.218 AU
Eccentricity 0.191
Inclination 28.19°
Orbital period 284.12 yr
Spin period 3.92 h
Dimensions 2,322 × 1,704 × 1,138 km
Apparent magnitude 17.3

As a massive Trans-Neptunian Object, i.e. massive enough to have a pretty spherical shape, it is classified as an ice dwarf, or plutoid. This shape is pretty regular, but not that spherical actually. As you can see from its 3 diameters (here I give the most recent numbers), this is a triaxial object, with a pretty elongated shape… and this will be important for the study.

It orbits in the 7:12 mean-motion resonance with Neptune, i.e. it performs exactly 7 revolutions around the Sun while Neptune makes 12. This is a 5th order resonance, i.e. a pretty weak one, but which anyway permits some stability of the objects, which are trapped inside. This is why we can find some!

We can also see that it has a rapid rotation (less then 4 hours!). Moreover, it is pretty bright, with a geometrical albedo close to 0.8. This probably reveals water ice at its surface.

And Haumea has two satellites, and even rings!

Two satellites, and rings

Haumea has two known satellites, Namaka and Hi’iaka, named after two daughters of the goddess Haumea. They were discovered by the team of Michael Brown in 2005, simultaneously with its observations of Haumea, i.e. before the announcement of its discovery. You can find below some of their characteristics.

Namaka Hi’iaka
Semi-major axis 25657 km 49880 km
Eccentricity 0.25 0.05
Orbital period 18.28 d 49.46 d
Mean diameter 170 km 310 km
Keck image of Haumea and its moons. Hi'iaka is above Haumea (center), and Namaka is directly below. © Californian Institute of Technology
Keck image of Haumea and its moons. Hi’iaka is above Haumea (center), and Namaka is directly below. © Californian Institute of Technology

Usually such systems are expected to present spin-orbit resonances, e.g. like our Moon which rotates synchronously with the Earth. Another example is Pluto-Charon, which is doubly synchronous: Pluto and Charon have the same spin (rotational) period, which is also the orbital period of Charon around Pluto. Here, we see nothing alike. The rotational period of Haumea is 4 hours, while its satellites orbit much slower. We do not dispose of enough data to determine their rotation periods, maybe they are synchronous, i.e. with spin periods of 18.28 and 49.46 days, respectively… maybe they are not.

This synchronous state is reached after tidal dissipation slowed the rotation enough. Future measurements of the rotation of the two satellites could tell us something on the age of this ternary system.

And last year, an international team led by José Luis Ortiz (the same one) announced the discovery of a ring around Haumea.

Rings beyond Jupiter

In the Solar System, rings are known from the orbit of Jupiter, and beyond:

  • Jupiter has a system of faint rings,
  • should I introduce the rings of Saturn?
  • Uranus has faint rings, which were discovered in 1977,
  • the rings of Neptune were discovered in 1984, before being imaged by Voyager 2 in 1989. Interestingly, one of these rings, the Adams ring, contains arcs, i.e. zones in which the ring is denser. These arcs seem to be very stable, and this stability is not fully understood by now.
Arcs in the Adams ring (left to right: Fraternité, Égalité, Liberté), plus the Le Verrier ring on the inside. © NASA
Arcs in the Adams ring (left to right: Fraternité, Égalité, Liberté), plus the Le Verrier ring on the inside. © NASA

Surprisingly, we know since 2014 that small bodies beyond the orbit of Jupiter may have rings:

  • An international team detected rings around the Centaur Chariklo in 2014 (remember: a Centaur is a body, which orbits between the orbits of Jupiter and Neptune),
  • another team (with some overlaps with the previous one), discovered rings around Haumea in 2017,
  • observations in 2015 are consistent with ring material around the Centaur Chiron, but the results are not that conclusive.

These last discoveries were made thanks to stellar occultations: the object should occult a star, then several teams observe it from several locations. While the planetary object is too faint to be observed from Earth with classical telescopes, the stars can be observed. If at some point no light from the star is being recorded while the sky is clear, this means that it is occulted. And the spatial and temporal distributions of the recorded occultations give clues on the shape of the body, and even on the rings when present.

Why rings around dwarf planets?

Rings around giant planets orbit inside the Roche limit. Below this limit, a planetary object cannot accrete, because the intense gravitational field of the giant planet nearby would induce too much tidal stress, and prevent the accretion. But how can we understand rings around dwarf planets? Chiron presents some cometary activity, so the rings, if they exist, could be constituted of this ejected material. But understanding the behavior of dust around such a small object is challenging (partly because it is a new challenge).

In 2015, the American planetologist Matthew Hedman noticed that dense planetary rings had been only found between 8 and 20 AU, and proposed that the temperature of water ice in that area, which is close to 70 K (-203°C, -333°F), made it very weak and likely to produce rings. In other words, rings would be favored by the properties of the material. I find this explanation particularly interesting, since no ring system has been discovered in the Asteroid Main Belt. That paper was published before the discovery of rings around Haumea, which is far below the limit of 20 UA. I wonder how the Haumea case would affect these theoretical results.

In the specific case of Haumea, the ring has a width of 70 kilometers and a radius of about 2,287 kilometers, which makes it close to the 3:1 ground-track resonance, i.e. the particles constituting the ring make one revolution around Haumea, while Haumea makes 3 rotations.

Numerical simulations

Let us now focus of our study. The authors aimed at understanding the dynamics and stability of the discovered rings around Haumea. For that, they took different particles, initially on circular orbits around Haumea, at different distances, and propagated their motions.
Propagating their motions consists in using a numerical integrator, which simulates the motion in the future. There are powerful numerical tools which perform this task reliably and efficiently. These tools are classified following their algorithm and order. The order is the magnitude of the approximation, which is made at each timestep. A high order means a highly accurate simulation. Here, the authors used a fourth order Runge-Kutta scheme. It is not uncommon to see higher-order tools (orders between 8 and 15) in such studies. The motions are propagated over 1 to 1,000 years.

A gravitational and thermal physical model

The authors assumed the particles to be affected by

  • the gravitational field of Haumea, including its triaxiality. This is particularly critical to consider the ground-track resonances, while the actually observed ring is close to the 3:1 resonance,
  • the gravitational perturbation by the two small moons, Namaka and Hi’iaka,
  • the Solar radiation pressure.

This last force is not a gravitational, but a thermal one. It is due to an exchange of angular momentum between the particle, and the electromagnetic field, which is due to the Solar radiation. For a given particle size, the Solar radiation pressure has pretty the same magnitude for all of the particles, while the gravitational field of Haumea decreases with the distance. As a consequence, the furthest particles are the most sensitive to the radiation pressure. Moreover, this influence is inversely proportional to the grain size, i.e. small particles are more affected than the large ones.

And now, the results!

A probable excess of small particles

The numerical simulations show that the smaller the grains size, the narrower the final ring structure. The reason is that smaller particles will be ejected by the radiation pressure, unless they are close enough to Haumea, where its gravity field dominates.

And this is where you should compare the simulations with the observations. The observations tell you that the ring system of Haumea is narrow, this would be consistent with an excess of particles with grain size of approximately 1 μm.

So, such a study may constrain the composition of the rings, and may help us to understand its origin. Another explanation could be that there was originally no particle that far, but in that case you should explain why. Let us say that we have an argument for a ring essentially made of small particles.

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.