Tag Archives: numerical methods

Origin of the ecliptic comets

Hi there! Today we discuss the ecliptic comets. You know the comets, these dirty snowballs which show two tails when they approach the Earth (in fact, they have a tail because they approach the Sun). The study I present today, The contribution of dwarf planets to the origin of low-inclination comets by the replenishment of mean motion resonances in debris disks, by M.A. Muñoz-Gutiérrez, A. Peimbert & B. Pichardo, tells us on the dynamical origin of those of these bodies, which have a low inclination with respect to the orbit of the Earth (the ecliptic). Simulations of their own of the primordial debris disk beyond Neptune show that the presence of dwarf planets, like Eris or Haumea, supplies future ecliptic comets. This study has recently been published in The Astronomical Journal.

The dynamics of comets

As I said, comets are dirty snowballs. They are composed of a nucleus, made of ice and silicates. When the comet approaches the Sun, it becomes hot enough to sublimate the ice. This results in two visible tails: a dusty one, and a tail of ionized particles. Beside this, there is a envelope of hydrogen, and sometimes an antitail, which direction is opposite to the dusty tail.

The comets usually have a highly eccentric orbit. As a consequence, there are huge variations of the distance with the Sun, and this is why their activity is episodic. Their temperature increases with the closeness to the Sun, triggering outgassing.

In fact, a moderately eccentric body may be considered to be a comet, if activity is detected. This is for instance the case of the Centaur Chiron. Chiron was detected as an asteroid, and later, observations permitted to detect a cometary activity, even if it does not approach the Sun that much. But of course, this does not make the kind of beautiful comets that the amateur astronomers love to observe.

Regarding the “classical” comets: they have a high eccentricity. What does raise it? The study addresses this question. But before that, let us talk about the ecliptic comets.

The ecliptic comets

The ecliptic comets are comets with a low inclination with respect to the orbital plane of the Earth. In fact, the detections of comets have shown that they may have any inclination. The ecliptic comets are an interesting case, since they are the likeliest to approach the Earth (don’t worry, I don’t mean collision… just opportunities to observe beautiful tails 😉 ).

These low inclinations could suggest that they do not originate from the Oort cloud, but from a closer belt, i.e. the Kuiper Belt. You know, this belt of small bodies which orbits beyond the orbit of Neptune. The reason is that part of this belt has a low inclination.

It also appears that beyond the orbit of Neptune, you have dwarf planets, i.e. pretty massive objects, which are part of the Trans-Neptunian Objects. The authors emphasize their role in the dynamics of low-inclination comets.

Dwarf planets beyond Neptune

A dwarf planet is a planetary object, which does not orbit another planet (unlike our Moon), and which is large enough, to have a hydrostatic shape, i.e. it is pretty spherical. But, this is not one of the planets of the Solar System… you see it is partly defined by what it is not…

5 Solar System objects are officially classified as dwarf planets. 3 of them are in the Kuiper Belt (Pluto, Haumea and Makemake), while the other two are the Main-Belt asteroid Ceres, and Eris, which is a Trans-Neptunian Object, but belongs to the scattered disc. In other words, it orbits further than the Kuiper Belt. The following table presents some characteristics of the dwarf planets of the Kuiper Belt. I have added 4 bodies, which may one day be classified as dwarf planets. Astronomers have advised the IAU (International Astronomical Union) to do so.

Semi-major axis Eccentricity Inclination Orbital period Diameter
Pluto 39.48 AU 0.249 17.14° 248.09 yr 2,380 km
Haumea 43.13 AU 0.195 28.22° 283.28 yr ≈1,500 km
Makemake 45.79 AU 0.159 28.96° 309.9 yr 1,430 km
Orcus 39.17 AU 0.227 20.57° 245.18 yr 917 km
2002 MS4 41.93 AU 0.141 17.69° 271.53 yr 934 km
Salacia 42.19 AU 0.103 23.94° 274.03 yr 854 km
Quaoar 43.41 AU 0.039 8.00° 285.97 yr 1,110 km

Anyway, the dynamical influence of a planetary object does not depend on whether it is classified or not.

These are objects, which have a significant mass, orbiting in the Kuiper Belt. And they are involved in the study.

The Solar System originates from a disc

The early Solar System was probably made of a disk of small bodies, which formed after the gravitational collapse of a huge molecular cloud. Then the Sun accreted, planets accreted, which destabilized most of the remaining small bodies. Some of them where just ejected, some bombarded the Sun and the planets, some other accreted…

Here the authors work with the Kuiper Belt as a disc. So, they assume the 8 major planets to be formed. Moreover, they already have dwarf planets in the disc. And the small bodies, which are likely to become comets, are under the gravitational influence of all this population of larger bodies.

For them to become comets, their eccentricities have to be raised. And an efficient mechanism for that is resonant excitation.

Eccentricity excitation by Mean-Motion Resonances (MMR)

A mean-motion resonance (MMR) between two bodies happens when their orbital periods are commensurate. In the present case, the authors considered the 2:3 and 1:2 MMR with Neptune. The 2:3 resonance goes like this: when Neptune makes 3 orbital revolutions around the Sun, the small object makes exactly 2. And when an object makes one revolution while Neptune makes 2, then this object is at the 1:2 MMR. These two resonances are in the Kuiper Belt disc considered by the authors.

Such period ratios imply that the small bodies orbit much further than Neptune. Neptune orbits at 30.1 AU (astronomical units) of the Sun, so the 2:3 MMR is at 39.4 AU (where is Pluto), and the 2:1 MMR is at 47.7 AU.

When a small body is trapped into a MMR with a very massive one, the gravitational perturbation accumulates because of the resonant configuration. And this interaction is the strongest when the two bodies are the closest, i.e. when the small body reaches its perihelion… which periodically meets the perihelion of the massive perturber, since it s resonant. So, the accumulation of the perturbation distorts the orbit, raises its eccentricity… and you have a comet!

But the issue is: in raising the eccentricities, you empty the resonance… So, either you replenish it, or one day you have no comet anymore… Fortunately, the authors found a way to replenish it.

Numerical simulations

The authors ran different intensive numerical simulations of multiple disc particles, which are perturbed by Neptune and dwarf planets. These dwarf planets are randomly located. They challenged different disc masses, the masses of the dwarf planets being proportional to the total mass of the disc.

And now, the results!

Replenishment of the 2:1 Mean-Motion Resonance (MMR)

The authors found nothing interesting for the 3:2 MMR. However, they found that the presence of the dwarf planets replenishes the 2:1 MMR. So here is the process:

  1. When a particle (a km-size body) is trapped into the 2:1 MMR, its eccentricity is raised
  2. It becomes a comet and may be destabilized. It could also become a Jupiter-family comet, i.e. a comet which period is close to the one of Jupiter. This happens after a close encounter with Jupiter.
  3. Other particles arrive in the resonances, and become comets themselves.

One tenth of the ecliptic comets

The authors also estimated the cometary flux, which this process should create. The authors estimate that it can give up to 8 Jupiter-family comets in 10,000 years, while the observations suggest a ten times larger number.
So, this is a mechanism, but probably not the only one.

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.

On the orbital evolution of Saturn’s mid-sized moons

Hi there! On the moons of Saturn today. Of course, you have heard of the Cassini mission, which toured around Saturn during 12 years. Its journey ended one year ago, after the Grand Finale, during which it was destroyed in the atmosphere of Saturn. It provided us during these 12 years a colossal amount of data, which is a chance for science. It is a chance, since it improves our knowledge of the system.

But this also gives birth to new challenges. Indeed, all of these new observations are constraints, with which the models must comply. They must explain why the satellites are where they are, AND why they present the surface features they present, AND why they have their measured gravity field, AND why they have their current shape, AND why the rings are like this, AND why Saturn is like that… You see the challenge. This is why it sparks so many studies.

Today we discuss about Orbital evolution of Saturn’s mid-sized moons and the tidal heating of Enceladus, by Ayano Nakajima, Shigeru Ida, Jun Kimura, and Ramon Brasser. This Japanese team performed numerical simulations to try to understand how the orbits of Enceladus, Tethys and Dione, evolved, with being consistent with their possible heating. The evolution is driven by the dissipation in Saturn, in the satellites, and the pull of the rings. This study has recently been accepted for publication in Icarus.

The mid-sized moons of Saturn

When we speak about the mid-sized satellites of Saturn, usually we mean Mimas, Enceladus, Tethys, Dione, and sometimes Rhea.
The inner moons orbit inner to the orbit of Mimas, and are embedded into the rings. However, Titan, Hyperion, Iapetus and Phoebe are just too far. Besides these, there are small moons which are embedded into the mid-sized system of Saturn.

Let us go back to the mid-sized. You can find below some of their characteristics.

Semi-major axis Eccentricity Inclination Orbital period Diameter
Mimas 3.19 R 0.02 1.57° 0.92 d 396 km
Enceladus 4.09 R 0.005 0.02° 1.37 d 504 km
Tethys 5.06 R ≈0 1.12° 1.89 d 1,062 km
Dione 6.48 R 0.002 0.02° 2.74 d 1,123 km
Rhea 9.05 R 0.001 0.35° 4.52 d 1,528 km

The unit “R” in the semimajor axis column is Saturn’s radius, i.e. 58,232 km. You can see that the size of the satellites increases with the distance. This has motivated the elaboration of a scenario of formation of the satellites from the rings, by Sébastien Charnoz et al. In this scenario, the rings would be initially much more massive than they are now, and the satellites would have emerged from them as droplets, removing their mass from the rings. Then they would have migrated outward. In such a scenario, the further satellites would be the older ones, and the massive ones as well. Regarding the mass, this is just true.

Craters, ridges, and internal oceans

This is what Cassini told us:

  • Mimas is known for its large crater Herschel, which diameter (139 km) is almost one-third the diameter of Mimas. It makes it look alike Star Wars’ Death Star. Its widely craterized surface suggests an inactive body. However, measurements of its east-west librations are almost inconsistent with a rigid body. It would contain an internal ocean, but explaining why this ocean is not frozen is a challenge.
  • Mimas seen by Cassini. © NASA / JPL-Caltech / Space Science Institute
    Mimas seen by Cassini. © NASA / JPL-Caltech / Space Science Institute
  • Enceladus may be the most interesting of these bodies, because its surface presents geysers, and tiger stripes, which are tectonic fractures and ridges. This proves Enceladus to be a differentiated and hot, active body. It dissipates energy, and we need to explain why.
  • The tiger stripes at the South Pole of Enceladus. © NASA
    The tiger stripes at the South Pole of Enceladus. © NASA
  • Tethys is quieter. It presents many craters, the largest one being Odysseus. Besides, it has a large valley, Ithaca Chasma. It is up to 100 km wide, 3 to 5 km deep and 2,000 km long. Its presence reveals a hot past.
  • Ithaca Chasma on Tethys © Cassini Imaging Team, SSI, JPL, ESA, NASA
    Ithaca Chasma on Tethys © Cassini Imaging Team, SSI, JPL, ESA, NASA
  • Like Tethys, Dione and Rhea present craters and evidences of past activity.

Interesting features, hot past

Enceladus, Tethys, Dione and Rhea present evidences of activity. Enceladus and Dione have global, internal oceans, while the other two may have one. Mimas presents a very quiet surface, but may have an ocean as well. All this means that these 5 moons are, or have been excited, i.e. shaken, to partly melt, crack the surface, and dissipate energy.

The primordial heat source is the decay of radiogenic elements, but this works only during the early ages of the body. After that, the dissipation is dominated by the tides raised by Saturn. Because of the variations of the distance between Saturn and the satellite, the gravitational torque changes. Its variations generate stress and strain, which are likely to dramatically affect the internal structure of the satellite. Variations of distance are due to orbital eccentricity. As you can see, some of the satellites have a significant one, with the exception of Tethys. And the eccentricity may be excited by mean-motion resonances.

Resonances everywhere

Let us go back to the orbital properties of the satellites. You can see that the orbital period of Tethys is twice the one of Mimas. Same for Enceladus and Dione. This did not happen by chance. These are mean-motion resonances. The 2:1 Enceladus-Dione one excites the eccentricity of Enceladus, and so is responsible for its currently observed activity. However, the Mimas-Tethys resonance, which is a 4:2 one (the reason why it is 4:2 and not 2:1 is pretty technical, see here), excites the inclination of Mimas, and slightly the one of Tethys as well.

As I said, this configuration did not happen by chance. The satellites have migrated since their formation, and once they encountered a resonant configuration, they actually encountered a stable location. And sometimes stable enough to stay there.

Long-term migration of the satellites

Two processes have been identified for being responsible of the long-term migration: the tides and the pull of the rings.

The tides are the result of the interaction with Saturn, the satellites being finite-size bodies. As a consequence of their size, the different parts of the satellite undergo a different torque from Saturn, and this generates stress and strain, i.e. dissipation of energy. But the satellite exerts a torque on Saturn as well. The consequence is a competition between the two processes, resulting in a variation of the orbital energy of the satellite. If the satellite gains energy, then it moves outward. However, if it dissipates energy, it moves inward. The tides also tend to circularize the orbits, i.e. damp the eccentricities.

Beside this, the rings exert a pull on the satellites. The main effect is on Mimas, because of its distance to the rings, its limited size, and the fact that it has a resonance with the rings. It has a 2:1 mean-motion resonance with the inner edge of the well-known Cassini Division, i.e. a 4,500-km wide depletion of material in the rings. At the inner edge of the Division, which is actually the outer edge of the B ring, you have an accumulation of material. This accumulation tends to push Mimas outward.

Coping with the observational constraints

The spacecraft Cassini gave us numbers. In particular

  • We have an estimation of the tidal response of Saturn,
  • we know the masses of the rings and of the satellites,
  • we can estimate the current dissipation, in particular for Enceladus,
  • we know the main geological features, in particular the impacts and the ridges, to estimate the energies which has created them.

If you want to explain something, you should better try to not violate any of these observations. A very tough task.

4 sets of numerical simulations

To elaborate an acceptable scenario for the orbital evolution of the mid-sized system, the authors ran 4 sets of intensive numerical simulations:

  1. SET 1a: Enceladus older than Tethys. This is suggested by the backward extrapolation of the orbits of Enceladus and Tethys, without mutual interaction, but migrating because of a highly dissipative Saturn… which can be allowed by the data. The consequence of such a scenario is that Tethys is originally closer to Saturn than Enceladus, and must cross its orbit to be further.
  2. SET 1b: Enceladus and Tethys starting with the same semimajor axis. Actually an end-member of the previous case.
  3. SET 2a: Tethys is older than Enceladus, and the rings affect only the semimajor axes.
  4. SET 2b: Almost the same as SET 2a, with the exception that the rings also affect the eccentricities of the satellites.

And now, the results.

Tethys is older than Enceladus

The hypothesis that Enceladus is older than Tethys should probably be discarded. Indeed, the simulations end up in collisions between the two bodies, which is inconsistent with the fact that we can actually see them.

So, this means that Tethys is older than Enceladus. However, the simulations of the sets 2a/b are not entirely satisfying, since the satellites end up in resonances, in which they are not now, which constitutes a violation of the observational data. This is particularly true if you include Dione in the simulations.

These resonances should have been encountered before the current ones. In other words, either the satellites were not trapped, but the simulations show they were, or they escaped these resonances after trapping. Some studies suggest that a catastrophic event could do that. A catastrophic event is an impact, and the surfaces of these bodies show that they underwent intense bombardments. Why not?

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 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

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.

An Artificial Intelligence identifies the Lunar craters

Hi there! Today we discuss about an algorithm. I guess you have already heard of Artificial Intelligence, and especially of some futuristic anticipations in which the world would be governed by robots… Fortunately, we are very far from that.

An Artificial Intelligence (AI), Google DeepMind’s AlphaGo, beat the Go professional player Lee Sedol in March 2016. Another AI, IBM’s DeepBlue, beat the then chess world champion Garry Kasparov in May 1997. These realizations of specific tasks belong to Narrow AI, while General AI would be Star Trek’s Data, i.e. a man-made system able to interact with its environments, and react better than a human would do.

Brent Spiner performing Data in Star Trek. © CBS Television Distribution
Brent Spiner performing Data in Star Trek. © CBS Television Distribution

In the context of planetary sciences, AI has recently permitted the discovery of exoplanets, from data analysis. The study I present today, Lunar crater identification via Deep Learning, by Ari Silburt et al., is another example of the way Artificial Intelligence may assist science. In this paper, the author challenge the computer to identify craters from images of the Moon and of Mercury, and the results appear to be very promising. This study has recently been accepted for publication in Icarus.

Craters in the Solar System

Let us forget AI for a short while. This is a blog of planetary sciences, remember? AI is a tool, not a goal. This study challenges a tool, which goal will be to identify craters. Hence, the goal is the craters.

Craters are ubiquitous in the Solar System, since it is intensively bombarded. This is especially true for the inner Solar System, since the impactors, i.e. small rocky bodies, are gravitationally attracted by the Sun. And while passing by, they may hit us, or the Moon, Mercury, Mars,… And we are lucky, since the current bombardment is much less intense than it was in the youth of the Solar System. Anyway, we have been intensively bombarded, we still are, but our atmosphere protects us in destroying the impactors, which reach the terrestrial surface as meteorites. A huge impactor is thought to be responsible for the extinctions of the dinosaurs, and may be one day… no, better not to think about it.

There are not so many craters at the surface of the Earth, partly because our atmosphere has eroded them, and partly because the geophysical activity relaxed them. But what about atmosphereless bodies like our Moon? Craters are everywhere!

And craters are the clock of the surface. If you see only craters, it means that the surface has not changed since the impact. The surface did not heat, did not melt, there was no geophysical activity creating failures, ridges,… For instance, in the satellites of Jupiter, you see almost no craters on Io and Europa, since there are active bodies. You see some on Ganymede, which is less active, and much more on Callisto, which is quieter.

The surfaces of the Galilean satellites of Jupiter Europa (left), Ganymede (middle), and Callisto (right), seen by Galileo. © NASA
The surfaces of the Galilean satellites of Jupiter Europa (left), Ganymede (middle), and Callisto (right), seen by Galileo. © NASA

This is why it is worthwhile to catalogue the craters of a given planetary body. But since it is a difficult and exhausting task, it is probably a good idea to tell a computer how to do it. This is where AI and Deep Learning come into play.

Artificial Intelligence, Machine Learning, and Deep Learning

As I told you, we are here interested in narrow AI: we want a computer to perform a specific task, and only that task, better than a human would do. And we want the computer to learn how to do it: this is Machine Learning. We give images of craters, tell the computer that they are craters, and we hope it to identify craters on images, which have not been studied yet, i.e. new data. Very well.

A common algorithm for that is Deep Learning. I do not want to go into specifics, but this uses several layers of neurons. Here, neurons should be understood as computing nodes performing a specific sub-tasks, and interacting with each others. The analogy with the human brain is obvious. In this specific case, the authors used convolutional neural networks, in which neurons layers are structured to perform a discrete convolution (a mathematical operation) between their inputs and a filter, which is represented by weights. These weights permit to ponder the relative roles of the different inputs of the system, i.e. which input is more relevant than another one…

The inputs are the planetary data.

Use of Digital Elevation Models of the Moon

Fortunately, we dispose of numerous topographic data of the Moon, which make it the ideal target for elaborating such an algorithm.

The authors used digital elevation maps (DEM) of the Moon, resulting from 2 different missions:

  1. the Lunar Reconnaissance Orbiter (LRO). This is an American mission, which orbits the Moon since 2009. It has made a 3-D map of the Moon’s surface at 100-meter resolution and 98.2% coverage, thanks to the Lunar Orbiter Laser Altimeter (LOLA), and the Lunar Reconnaissance Orbiter Camera (LROC).
  2. The Japanese mission SELENE (Selenological and Engineering Explorer), which is also known as Kaguya. It was composed of 3 spacecraft, i.e. a main orbiter and two satellites. It operated during 20 months, between September 2007 and June 2009. It was then intentionally crashed near the crater Gill.

The authors used such data to train the system, i.e. to make itself an expert in crater identification.

Algorithm of crater identification

Historically, the first identifications of craters were made by visually examining the images. Of course, this is an exhaustive task, and the human being has failures. Moreover, if a small crater looks like a circle, larger ones, i.e. with a diameter larger than 20 km, may have a central peak, may contain other craters, and/or may be altered by the topography (mountains…).

The consequence is that beside the time spent to perform this task, you would have false detections (you think this is a crater, but it is not), and miss some craters, especially the smallest ones. If someone else does the same task, from the same data, (s)he would get a significantly different list. Comparing these lists would be a way to estimate the identification errors.

So, you can see that the use of the numerical tool is inescapable. But how would you do that? Some algorithms identify the circles on the images thanks to a Hough transform (I do not want to go into specifics, but this is a mathematical transformation of your images which tells you “there is a circle there!”), some identify the edges of the craters, some do both… And Deep Learning is learning by itself how to identify craters.

This consists essentially of 3 steps:

  1. training,
  2. validation,
  3. tests.

The algorithm detects crater rims from their pixel intensities, then fits a circle on them, and give as outputs the coordinates of the center and the mean radius of the crater. The authors then compared the results with existing catalogues.

The relevant parameters

The detection of the craters uses parameters, for instance the threshold for the detection of variation of pixel intensities. And the efficiency of the algorithm is measured with

  1. the true positives Tp (the algorithm tells you there is a crater, and you know there is actually one),
  2. the false positives Fp (the algorithm tells you there is a crater, but there is none),
  3. the false negatives Fn (the algorithm tells you nothing, while you know there is a crater),

and these quantities are recombined as

  • the precision P = Tp/(Tp+Fp) (if the algorithm tells you there are 100 craters, how many are actually present?),
  • the recall R = Tp/(Tp+Fn) (over 100 craters, how many are detected by the algorithm?)
  • F1 = 2PR/(P+R), which permits to use a single-parameter metric.
  • The goal is of course to maximize F1.

    Beside this, the authors also compared the coordinates and radii of the detected craters with the ones present in the catalogues, i.e. which had been previously determined by other methods. And all of this works pretty well!

    Success for the Moon

    The algorithm detected 92% of the known craters. Moreover, it also announced to the authors the detection of 361 new craters, and showed to be particularly efficient for craters with a diameter smaller than 5 km. Not only these small craters are a challenge for the human eye, but their regular shape makes the automatic detection more reliable. So, you here have an example of a task, for which the computer could be more efficient than the human. Among these 361 new craters, the authors estimate 11% of them to be false positives (Fp). This last number has some uncertainty, since the validation of a crater is made by a human eye, and the outcome depends on the brain, i.e. the human, behind the eye.

    This is very promising but would that work on another body? It seems so…

    Successful transfer-learning to Mercury

    Finally, the authors asked the computer to identify craters on the surface of Mercury. Remember that the computer was trained with Lunar data. This is called a domain shift, and this is a challenge, since the surface of Mercury has not exactly the same properties of the Lunar one. The bombardment activity was different, Mercury was possibly partly resurfaced, the material itself is different…

    The Moon is on the left, and Mercury on the right.
    The Moon is on the left, and Mercury on the right.

    But the results are pretty good, i.e. many craters are actually detected.

    The algorithm needs some refinements. For instance, it may be lured by circular depressions, which are not true craters (false positives). But the results are very encouraging, in particular for identifying craters on bodies, for which no catalogue exists at this date. The last space missions have given Digital Elevation Models for Venus, Mars, Vesta, and Ceres, and this algorithm may prove very useful to identify their craters.

    Deep Learning is the future!

    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.

Forming Mars

Hi there! Of course, you know the planet Mars. You can here from it these days, since it is exceptionally close to our Earth. Don’t worry, this is a natural, geometrical phenomenon.

Anyway, it is a good time to observe it. But I will not speak of observing it, today. We will discuss its formation instead, because the issue of the formation of Mars remains a challenge. This is the opportunity to present The curious case of Mars’ formation, by James Man Yin Woo, Ramon Brasser, Soko Matsumura, Stephen J. Mojzsis, and Shigeru Ida. Astronomy and Astrophysics will publish it pretty soon.

Mars is too small

The following table gives you comparative characteristics of Venus, the Earth, and Mars.

Venus Earth Mars
Semimajor axis 0.723 AU 1.000 AU 1.524 AU
Eccentricity 0.007 0.017 0.093
Inclination 3.39° 1.85°
Orbital period 224.7 d 365.25 d 686.96 d
Spin period -243.02 d 23.93 h 24.62 h
Mean diameter 12,104 km 12,742 km 6,779 km

The last line reveals a problem: Venus and the Earth are about the same size, while Mars is much smaller! But this is not the only problem: the compositions of the Earth and Mars are VERY different.

It is pretty easy to know the composition of the Earth: you just analyze samples. And for Mars? Just the same!

Interestingly, there are Martian meteorites on Earth. These are ejecta from impacts, which were ejected from Mars, and then traveled in the Solar System, until reaching our Earth.

In fact, over the tens of thousands of meteorites which have been found on Earth, a little more than one hundred were significantly different than the other ones, i.e. younger formation ages, a different oxygen isotopic composition, the presence of aqueous weathering products… Most of these meteorites were known as SNC, after the three groups they were classified into:

  • S for Shergottites, after the Shergotty meteorite (India, 1865),
  • N for Nakhlites, after the Nakhla meteorite (Egypt, 1911),
  • C for Chassignites, after the Chassigny meteorite (France, 1815).

Such a significant number of similar meteorites, which are that different from the other ones, suggests they come from a large body. Mars is an obvious candidate, which has been confirmed after the discovery that trapped gases in these meteorites are very similar to the ones, which are present in the atmosphere of Mars.

The Martian meteorite NWA (Northwest Africa) 2046, found in September 2003 in Algeria. This is a Shergottite. © Michael Farmer and Jim Strope.
The Martian meteorite NWA (Northwest Africa) 2046, found in September 2003 in Algeria. This is a Shergottite. © Michael Farmer and Jim Strope.

After that, the numerous space missions improved our knowledge of the Martian composition. And it finally appeared that both planets are essentially made of chondritic material. The Earth should accrete about 70% of enstatite chondrite (and same for the Moon), while Mars only about 50%. Chondrites are non-metallic meteorites, the enstatite chondrites being rich in the mineral enstatite (MgSiO3). These numbers are derived from the documented isotopic compositions of the Earth and Mars, i.e. the ratio of the different chemical elements. An isotope is a variant of a particular chemical element, which differs in neutron number.

If you want to convincingly simulate the formation of Mars, the product of your simulations should be similar to Mars in mass AND in composition. And this is very challenging. Let us see why, but first of all let us recall how to form planets from a disk.

Forming planets from a disk

At its early stage, a planetary system is composed of a proto-star, and a pretty flat disk, made of gas and dust. Then the dust accretes into clumps, which then collides to form planetary embryos, i.e. proto-planets. These embryos continue to grow with collisions, until forming the current planets. Meanwhile, the gas has dissipated.

Anyway, interactions between the protoplanets and between them and the gas can lead to planetary migration. This means that we cannot be sure whether the planets we know formed close to their current location. This makes room for several scenarios.

Two models of planetary formation

The obvious starting point is to assume that the planets formed close to their current locations. This so-called Classical model works pretty well for Venus, the Earth, Jupiter, Saturn… but not for Mars. The resulting Mars is too massive.

An idea for by-passing this problem is to start with a depletion of material at the location of Mars. This is equivalent to an excess inside the terrestrial orbit. In such a configuration, less material is available to the proto-Mars, which eventually has a mass, which is close to the present one.

You can get this excess of material inside the terrestrial orbit if you buy the Grand Tack scenario: when Jupiter formed, it created a gap in the inner disk, and the mutual interaction resulted in an inward migration of Jupiter, until reaching the present orbit of Mars. In moving inward (Type II migration), Jupiter pushed the material inward. Then, a 3:2 mean-motion resonance with Saturn occurred, which created another gap, and made Jupiter move outward, until its present location.

This way, you can form a planetary object, which is similar to Mars in mass and location.

But what about its composition?

The composition challenge

This is still a challenge. The composition of a planetary object is strongly affected by the one of the disk, where the object formed… which may not be its present location.

The authors added a free parameter to the model: the break location, which would split the protoplanetary disk into an inner and an outer region. The inner region would be rich in enstatite chondrites, while the outer one would be rich in ordinary chondrites.

A break location at 1.3 AU gives the best fit for the difference of composition between Mars and the Earth, for both formation scenarios (Classical and Grand Tack).

So, the Grand Tack with a break location at 1.3 AU could be the right scenario. But another possibility exists: the Classical scenario says that if Mars formed where it is, then it should be heavier. But what if Mars formed actually further from the Sun, and then migrated inward? Then, it would not need any depletion of material to have the right mass. And the break barrier should have been further than 1.3 AU. But you have to explain why it migrated inward.

Anticipating the composition

One of the good things with scenarios of formation is that thr gives more details on the outcomes, than actually observed. For instance, this study predicts the isotopic composition of 17O, 50Ti, 54Cr, 142Nd, 64Ni and 92Mo, in the Martian mantle. Further data, collected by space missions, will give additional constraints on these parameters, and test the validity of the present study. 8 missions are currently operational in orbit or on Mars, and InSight is en-route, after having been launched in May 2018. It should land on Mars on November 26, and will study its interior with a seismometer, and a heat transfer probe.

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.