Tag Archives: stability

Asteroids: Trans-Neptunian Objects

Pluto-Charon is dynamically packed

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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.

Outline

The binary Pluto-Charon
Simulations with Orchestra
Probably nothing inside the orbit of Hydra
Could there be something outside?
The study and its authors

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.

Asteroids: Trojans

The fate of Jupiter’s Trojans

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Hi there! Today we discuss about the Trojans of Jupiter. These are bodies which orbit on pretty the same orbit as Jupiter, i.e. at the same distance of the Sun, but 60° before or behind. These asteroids are located at the so-called Lagrange points L4 and L5, where the gravitational actions of the Sun and of Jupiter balance. As a consequence, these locations are pretty stable. I say “pretty” because, on the long term, i.e. millions of years, the bodies eventually leave this place. The study I present today, The dynamical evolution of escaped Jupiter Trojan asteroids, link to other minor body populations, by Romina P. Di Sisto, Ximena S. Ramos and Tabaré Gallardo, addresses the fate of these bodies once they have left the Lagrange points. This study made in Argentina and Uruguay has recently been published in Icarus.

Outline

The Trojan asteroids
These are dark bodies
Asymmetric populations
Numerical simulations
The Greek are more stable than the Trojans
Where are they now?
The study and its authors

The Trojan asteroids

Jupiter orbits the Sun at a distance of 5.2 AU (astronomical units), in 11.86 years. As the largest (and heaviest) planet in the Solar System, it is usually the main perturber. I mean, planetary objects orbit the Sun, they may be disturbed by other objects, and Jupiter is usually the first candidate for that.

As a result, it creates favored zones for the location of small bodies, in the sense that they are pretty stable. The Lagrange points L4 and L5 are among these zones, and they are indeed reservoirs of populations. At this time, the Minor Planet Center lists 7,039 Trojan asteroids, 4,600 of them at the L4 point (leading), and 2,439 at the L5 trailing point. These objects are named after characters of the Trojan War in the Iliad. L4 is populated by the Greeks, and L5 by the Trojans. There are actually two exceptions: (624) Hektor is in the Greek camp, and (617) Patroclus in the Trojan camp.

Location of the Lagrange points.
Location of the Lagrange points.

These are dark bodies

The best way to know the composition of a planetary body is to get there… which is very expensive and inconvenient for a wide survey. Actually a NASA space mission, Lucy, is scheduled to be launched in 2021 and will fly by the Greek asteroids (3548) Eurybates, (15094) Polymele, (11351) Leucus, and (21900) Orus in 2027 and 2028. So, at the leading Lagrange point L4. After that, it will reach the L5 point to explore the binary (617) Patroclus-Menetius in 2033. Very interesting, but not the most efficient strategy to have a global picture of the Trojan asteroids.

Fortunately, we can analyze the light reflected by these bodies. It consists in observing them from the Earth, and decompose the light following its different wavelengths. And it appears that they are pretty dark bodies, probably carbon-rich. Such compositions suggest that they have been formed in the outer Solar System.

Asymmetric populations

We currently know 4,600 Trojan asteroids at the L4 point, and 2,439 of them at the L5 one. This suggests a significant asymmetry between these two reservoirs. We must anyway be careful, since it could be an observational bias: if it is easier to observe something at the L4 point, then you discover more objects.

The current ratio between these two populations is 4,600/2,439 = 1.89, but correction from observational bias suggests a ratio of 1.4. Still an asymmetry.

Numerical simulations with EVORB

The authors investigated the fate of 2,972 of these Trojan asteroids, 1,975 L4 and 997 L5, in simulating their trajectories over 4.5 Gyr. I already told you about numerical integrations. They consist in constructing the trajectory of a planetary body from its initial conditions, i.e. where it is now, and the equations ruling its motion (here, the gravitational action of the surrounding body). The trajectory is then given at different times, which are separated by a time-step. If you want to know the location at a given time which is not one considered by the numerical integration, then you have to interpolate the trajectory, in using the closest times where your numerical scheme has computed it.

When you make such ambitious numerical integrations, you have to be very careful of the accuracy of your numerical scheme. Otherwise, you propagate and accumulate errors, which result in wrong predictions. For that, they used a dedicated integrator, named EVORB (I guess for something like ORBital EVolution), which switches between two schemes whether you have a close encounter or not.

As I say in previous articles like this one, a close encounter with a planet may dramatically alter the trajectory of a small body. And this is why it should be handled with care. Out of any close encounter, EVORB integrates the trajectory with a second-order leapfrog scheme. This is a symplectic one, i.e. optimized for preserving the whole energy of the system. This is critical in such a case, where no dissipative effect is considered. However, when a planet is encountered, the scheme uses a Bulirsch-Stoer one, which is much more accurate… but slower. Because you also have to combine efficiency with accuracy.

In all of these simulations, the authors considered the gravitational actions of the Sun and the planets from Venus to Neptune. Venus being the body with the smallest orbital period in this system, it rules the integration step. They authors fixed it to 7.3 days, which is 1/30 of the orbital period of Venus.

And these numerical simulations tell you the dynamical fate of these Trojans. Let us see the results!

The Greek are more stable than the Trojans

It appears that, when you are in the Greek camp (L4), you are less likely to escape than if you are in the Trojan one (L5). The rate of escape is 1.1 times greater at L5 than at L4. But, remember the asymmetry in the populations: L4 is much more populated than L5. The rates of escape combined with the overall populations make than there are more escapes from the Greek camp (18 per Myr) than from the Trojan one (14 per Myr).

Where are they now?

What do they become when they escape? They usually (90% of them) go in the outer Solar System, first they become Centaurs (asteroids inner to Neptune), and only fugitives from L4 may become Trans-Neptunian Objects. And then they become a small part of these populations, i.e. you cannot consider the Lagrange points of Jupiter to be reservoirs for the Centaurs and the TNOs. However, there are a little more important among the Jupiter-Family Comets and the Encke-type comets (in the inner Solar System). But once more, they cannot be considered as reservoirs for these populations. They just join them. And as pointed out a recent study, small bodies usually jumped from a dynamical family to another.

The study and its authors

You can find the study here. The authors made it freely available on arXiv, many thanks to them for sharing!

And now, the 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.

Asteroids: Trans-Neptunian Objects

The rings of Haumea

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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.

Outline

The Trans-Neptunian Object (136108)Haumea
Rings beyond Jupiter
Numerical simulations
A gravitational and thermal physical model
A probable excess of small particles
The study and its authors

The Trans-Neptunian Object (136108)Haumea

Discovery

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).

Properties

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.

Zodiacal dust

Dust coorbital to Jupiter

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Hi there! You may have heard of the coorbital satellites of Jupiter, or the Trojans, which share its orbit. Actually they are 60° ahead or behind it, which are equilibrium positions. Today we will see that dust is not that attached to these equilibrium. This is the opportunity to present you a study divided into two papers, Dust arcs in the region of Jupiter’s Trojan asteroids and Comparison of the orbital properties of Jupiter Trojan asteroids and Trojan dust, by Xiaodong Liu and Jürgen Schmidt. These two papers have recently been accepted for publication in Astronomy and Astrophysics.

Outline

The Trojan asteroids
Production of dust
Non-gravitational forces affect the dust
Numerical simulations
Some stay, some don’t…
Lucy is coming
The study and its authors

The Trojan asteroids

Jupiter is the largest of the planets of the Solar System, it orbits the Sun in 11.86 years. On pretty the same orbit, asteroids precede and follow Jupiter, with a longitude difference of 60°. These are stable equilibrium, in which Jupiter and every asteroid are locked in a 1:1 mean-motion resonance. This means that they have the same orbital period. These two points, which are ahead and behind Jupiter on its orbit, are the Lagrange points L4 and L5. Why 4 and 5? Because three other equilibrium exist, of course. These other Lagrange points, i.e. L1, L2, and L3, are aligned with the Sun and Jupiter, and are unstable equilibrium. It is anyway possible to have orbits around them, and this is sometimes used in astrodynamics for positioning artificial satellites of the Earth, but this is beyond the scope of our study.

Location of the Lagrange points.
Location of the Lagrange points.

At present, 7,206 Trojan asteroids are list by the JPL Small Body Database, about two thirds orbiting in the L4 region. Surprisingly, no coorbital asteroid is known for Saturn, a few for Uranus, 18 for Neptune, and 8 for Mars. Some of these bodies are on unstable orbits.

Understanding the formation of these bodies is challenging, in particular explaining why Saturn has no coorbital asteroid. However, once an asteroid orbits at such a place, its motion is pretty well understood. But what about dust? This is what the authors investigated.

Production of dust

When a planetary body is hit, it produces ejecta, which size and dynamics depend on the impact, the target, and the impactor. The Solar System is the place for an intense micrometeorite bombardment, from which our atmosphere protects us. Anyway, all of the planetary bodies are impacted by micrometeorites, and the resulting ejecta are micrometeorites themselves. Their typical sizes are between 2 and 50 micrometers, this is why we can call them dust. More specifically, it is zodiacal dust, and we can sometimes see it from the Earth, as it reflects light. We call this light zodiacal light, and it can be confused with light pollution.

It is difficult to estimate the production of dust. The intensity of the micrometeorite bombardment can be estimated by spacecraft. For instance, the spacecraft Cassini around Saturn had on-board the instrument CDA, for Cosmic Dust Analyzer. This instrument not only measured the intensity of this bombardment around Saturn, but also the chemical composition of the micrometeorites.

Imagine you have the intensity of the bombardment (and we don’t have it in the L4 and L5 zones of Jupiter). This does not mean that you have the quantity of ejecta. This depends on a yield parameter, which has been studied in labs, and remains barely constrained. It should depend on the properties of the material and the impact velocity.

The small size of these particles make them sensitive to forces, which do not significantly affect the planetary bodies.

Non-gravitational forces affect the dust

Classical planetary bodies are affected (almost) only by gravitation. Their motion is due to the gravitational action of the Sun, this is why they orbit around it. On top of that, they are perturbed by the planets of the Solar System. The stability of the Lagrange points results of a balance between the gravitational actions of the Sun and of Jupiter.

This is not enough for dusty particles. They are also affected by

  • the Solar radiation pressure,
  • the Poynting-Robertson drag,
  • the Solar wind drag,
  • the magnetic Lorentz force.

The Solar radiation pressure is an exchange of momentum between our particle and the electromagnetic field of the Sun. It depends on the surface over mass ratio of the particle. The Poynting-Robertson drag is a loss of angular momentum due to the tangential radiation pressure. The Solar wind is a stream of charged particles released from the Sun’s corona, and the Lorentz force is the response to the interplanetary magnetic field.

You can see that some of these effects result in a loss of angular momentum, which means that the orbit of the particle would tend to spiral. Tend to does not mean that it will, maybe the gravitational action of Jupiter, in particular at the coorbital resonance, would compensate this effect… You need to simulate the motion of the particles to know the answer.

Numerical simulations

And this is what the authors did. They launched bunches of numerical simulations of dusty particles, initially located in the L4 region. They simulated the motion of 1,000 particles, which sizes ranged from 0.5 to 32 μm, over more than 15 kyr. And at the end of the simulations, they represented the statistics of the resulting orbital elements.

Some stay, some don’t…

This way, the authors have showed that, for each size of particles, the resulting distribution is bimodal. In other words: the initial cloud has a maximum of members close to the exact semimajor axis of Jupiter. And at the end of the simulation, the distribution has two peaks: one centered on the semimajor axis of Jupiter, and another one slightly smaller, which is a consequence of the non-gravitational forces. This shift depends on the size of the particles. As a consequence, you see this bimodal distribution for every cloud of particles of the same size, but it is visually replaced by a flat if you consider the final distribution of the whole cloud. Just because the location of the second peak depends on the size of the particles.

Moreover, dusty particles have a pericenter which is slightly closer to the one of Jupiter than the asteroids, this effect being once more sensitive to the size of the particles. However, the inclinations are barely affected by the size of the particles.

In addition to those particles, which remain in the coorbital resonance, some escape. Some eventually fall on Jupiter, some are trapped in higher-order resonances, and some even become coorbital to Saturn!

As a conclusion we could say that the cloud of Trojan asteroids is different from the cloud of Trojan dust.

All this results from numerical simulations. It would be interesting to compare with observations…

Lucy is coming

But there are no observations of dust at the Lagrange points… yet. NASA will launch the spacecraft Lucy in October 2021, which will explore Trojan asteroids at the L4 and L5 points. It will also help us to constrain the micrometeorite bombardment in these regions.

The study and its authors

You can find below the two studies:

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.

Asteroids: Centaurs, Asteroids: Trans-Neptunian Objects

Origin and fate of a binary TNO

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Hi there! I have already told you about these Trans-Neptunian Objects, which orbit beyond the orbit of Neptune. It appears that some of them, i.e. 81 as far as we know, are binaries. As far as we know actually means that there are probably many more. These are in fact systems of 2 objects, which orbit together.

The study I present you today, The journey of Typhon-Echidna as a binary system through the planetary region, by Rosana Araujo, Mattia Galiazzo, Othon Winter and Rafael Sfair, simulates the past and future orbital motion of such a system, to investigate its origin and its fate. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

Outline

Binary objects
The TNO-Centaurs region
(42355) Typhon-Echidna
It should originate from the TNO-Centaurs region
It should be destroyed before 200 Myr
Will it remain a binary?
The study and its authors

Binary objects

Imagine two bodies, which are so close to each other that they interact gravitationally. You can say, OK, this is the case for the Sun and the planets, for the Earth and the Moon, for Jupiter and its satellites… Very well, but in all of those cases, one body, which we will name the primary, is much heavier than the other ones. This results as small bodies orbiting around the primary. But what happens when the mass ratio between these two bodies is rather close to unity, i.e. when two bodies of similar mass interact? Well, in that case, what we call the barycenter of the system, or the gravity center, is not close to the center of the primary, it is in fact somewhere between the two bodies. And the two bodies orbit around it. We call such a system a binary.

Binary systems may exist at every size. I am not aware of known binary giant planets, and certainly not in the Solar System, but we have binary asteroids, binary stars… and theory even predicts the existence of binary black holes! We will here restrict to binary asteroids (in the present case, binary minor planets may be more appropriate… please forgive me that).

So, you have these two similar bodies, of roughly the same size, which orbit together… their system orbiting around the Sun. A well-known example is the binary Pluto-Charon, which itself has small satellites. Currently some approximately 300 binary asteroids are known, 81 of them in the Trans-Neptunian region. The other ones are in the Main Belt and among the Near-Earth Asteroids. This last population could be the most populated by binaries, not only thanks to an observational bias (they are the easiest ones to observe, aren’t they?), but also because the YORP effect favors the fission of these Near-Earth Asteroids.

Anyway, the binary system we are interested in is located in what the authors call the TNO-Centaurs region.

The TNOs-Centaurs region

The name of that region of the Solar System may seem odd, it is due to a lack of consistency in the literature. Basically, the Trans-Neptunian region is the one beyond the orbit of Neptune. However, the Centaurs are the asteroids orbiting between the orbits of Jupiter and Neptune. This would be very clear if the orbit of Neptune was a legal border… but it is not. What happens when the asteroid orbits on average beyond Neptune, but is sometimes inside? You have it: some call these bodies TNO-Centaurs. Actually they are determined following two conditions:

  1. The semimajor axis must be larger than the one of Neptune, i.e. 30.110387 astronomical units (AU),
  2. and the distance between the Sun and the perihelion should be below that number, the perihelion being the point of the orbit, which is the closest to the Sun.

The distance between the Sun and the asteroid varies when the orbit is not circular, i.e. has a non-null eccentricity, making it elliptic.

When I speak of the orbit of an asteroid, that should be understood as the orbit of the barycenter, for a binary. And the authors recall us that there are two known binary systems in this TNOs-Centaurs region: (42355) Typhon-Echidna, and (65489) Ceto-Phorcys. Today we are interested by (42355) Typhon-Echidna.

(42355) Typhon-Echidna

(42355) Typhon has been discovered in February 2002 by the NEAT program (Near-Earth Asteroid Tracking). This was a survey operating between 1995 and 2007 at Palomar Observatory in California. It was jointly run by the NASA and the Jet Propulsion Laboratory. You can find below some orbital and characteristics of the binary around the Sun, from the JPL Small-Body Database Browser:

Typhon-Echidna
Semimajor axis 38.19 AU
Eccentricity 0.54
Perihelion 17.57 AU
Inclination 2.43°
Orbital period 236.04 yr

As you can see, the orbit is very eccentric, which explains why the binary is considered to be in this gray zone at the border between the Centaurs and the TNOs.

Discovery of Typhon in Feb. 2002, then known as 2002 CR<sub>46</sub>. © NEAT
Discovery of Typhon in Feb. 2002, then known as 2002 CR<sub>46</sub>. © NEAT

And you can find below the orbital characteristics of the orbit of Echidna, which was discovered in 2006:

Semimajor axis 1580 ± 20 km
Eccentricity 0.507 ± 0.009
Inclination 42° ± 2°
Orbital period 18.982 ± 0.001 d

These data have been taken from Johnston’s Archive. Once more, you can see a very eccentric orbit. Such high eccentricities do not look good for the future stability of the object… and this will be confirmed by this study.

In addition to these data, let me add that the diameters of these two bodies are 162 ± 7 and 89 ±6 km, respectively, Typhon being the largest one. Moreover, water ice has been detected on Typhon, which means that it could present some cometary activity if it gets closer to the Sun.

The remarkable orbit of the binary, which is almost unique since only two binaries are known in the TNOs-Centaurs region, supplemented by the fact it is a binary, motivated the authors to specifically study its long-term orbital migration in the Solar System. In other words, its journey from its past to its death.

It should originate from the TNOs-Centaurs region

For investigating this, the authors started from the known initial conditions of the binary, seen as a point mass. In other words, they considered only one object in each simulation, with initial orbital elements very close to the current ones. They ran in fact 100 backward numerical simulations, differing by the initial conditions, provided they were consistent with our knowledge of them. They had to be in the confidence interval.

In all of these trajectories, the gravitational influence of the planets from Venus to Neptune, and of Pluto, was included. They ran these 100 backward simulations over 100 Myr, in using an adaptive time-step algorithm from the integrator Mercury. I do not want to go too deep in the specific, but keep in mind that this algorithm is symplectic, which implies that it should remain accurate for long-term integrations. An important point is the adaptive time-step: when you run numerical integrations, you express the positions and velocities at given dates. The separation between these dates, i.e. the time-step, depends on the variability of the force you apply. The specificity of the dynamics of such eccentric bodies is that they are very sensitive to close encounters with planets, especially (but not only) the giant ones. In that case, you need a pretty short time-step, but only when you are close to the planet. When you are far, it is more advisable to use a larger time-step. Not only to go faster, but also to prevent the accumulation of round-off errors.

It results from these backward simulations that most of the clones of Typhon are still in the TNOs-Centaurs regions 100 Myr ago.

But the authors also investigated the fate of Typhon!

It should be destroyed before 200 Myr

For that, they used the same algorithm to run 500 forward trajectories. And this is where things may become dramatic: Typhon should not survive. In none of them. The best survivor is destroyed after 163 Myr, which is pretty short with respect to the age of the Solar System… but actually very optimistic.

Only 20% of the clones survive after 20 Myr, and the authors estimate the median survival time to be 5.2 Myr. Typhon is doomed! And the reason for that is the close encounters with the planets. The most efficient killer is unsurprisingly Jupiter, because of its large mass.

Interestingly, 42 of these clones entered the inner Solar System. This is why we cannot exclude a future cometary activity of Typhon: in getting closer to the Sun, it will warm, and the water ice may sublimate.

All of these simulations have considered the binary to be a point-mass. Investigating whether it will remain a binary requires other, dedicated simulations.

Will it remain a binary?

The relevant time-step for a binary is much shorter than for a point mass, just because the orbital period of Typhon around the Sun is 236 years, while the one of Echidna around Typhon is only 19 days! This also implies that a full trajectory, over 200 Myr, will require so many iterations that it should suffer from numerical approximations. The authors by-passed this problem in restricting to the close encounters with planets. When they detected a close encounter in an orbital simulation of Typhon, they ran 12,960 simulations of the orbit of Echidna over one year. Once more, these simulations differ by the initial conditions, here the initial orbital elements of Echidna around Typhon.

The authors concluded that it is highly probable that the binary survived close encounters with planets, as a binary. In other words, if Typhon survives, then Echidna should survive.

The study and its authors

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