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.