Monthly Archives: September 2018

Planets

The red spot of Jupiter

Leave a comment

Hi there! Today: the red spot of Jupiter. When you observe Jupiter with a common telescope, you just cannot miss it (if it is on the visible side, of course, since Jupiter rotates in about 9.5 hours). It is a red oval, located in the southern equator of Jupiter, as large as 3 Earth. It is actually an anticyclonic storm, which persists since at least 1830. The different space missions have permitted to observe its evolution and measure the winds composing it. Today I present the result of observations by the spacecraft Juno. The study, The rich dynamics of Jupiter’s Great Red Spot from JunoCam: Juno images, has recently been published in The Astronomical Journal.

Outline

The Red Spot
The spacecraft JUNO
The data: JunoCam images
From raw data to measurements
5 features in the spot
The study and its authors

The Red Spot

This Red Spot has been continuously observed since 1830. To be honest, I don’t know who observed it at that time, but the fact is that it is stable since at least 188 years. Before that, several astronomers, including Giovanni Cassini, claimed to have observed it between 1665 and 1713. It is even depicted by Donato Creti in 1711. But, because of the absence of observations between 1713 and 1830,

  1. we do not know whether it is the same spot or not,
  2. it could have disappeared and reappeared during the 18th century.
Astronomical Observations: Jupiter, by Donato Creti (1711).
Astronomical Observations: Jupiter, by Donato Creti (1711).

And this is possible, since the red spot is currently shrinking. We know it thanks to the different spacecraft having met Jupiter (Pioneer, Voyager, Galileo, Cassini, and now Juno) and the Hubble Space Telescope. It attained its maximal known width by the end of the 19th century, some 25,000 miles (40,000 km), while it is a little more than 10,000 miles (16,000 km) by now. At this rate, it should become a circle by 2040.

Global view of Jupiter, with the Red Spot at 22° South. © Space Telescope Science Institute/NASA
Global view of Jupiter, with the Red Spot at 22° South. © Space Telescope Science Institute/NASA

It rotates counter-clockwise with a period of 6 days, while the atmosphere of Jupiter rotates clockwise. The top of the spot is higher of 8 kilometers than the surrounding clouds, which makes it colder.

The spacecraft JUNO orbits Jupiter since July 2016, and permits a new analysis of the Red Spot.

The spacecraft JUNO

The NASA spacecraft JUNO, for JUpiter Near-polar Orbiter, has been launched to Jupiter from Cape Canaveral in August 2011. It orbits Jupiter since July 2016, on a polar orbit. This means that it flies over the poles of Jupiter. Its orbit is very eccentric, with a period of 53 days.

Contrary to Galileo, it is interested only in the planet itself, not in its satellites. Its payload is composed of 9 instruments, and among its objectives are the map of the magnetic field of Jupiter, the map of its gravitational field, which contains information on the solid core which is beneath the atmosphere, and a better knowledge of the chemical composition of the atmosphere.

Among the nine instruments is the camera JunoCam, which provided the data permitting this study.

The data: JunoCam images

JunoCam has not been conceived as a science, but as an outreach instrument, i.e. designed to give beautiful images. And it does.
But in this case, it appears that its data can be used for science. You can find below some images of the Red Spot by Juno, this video having been made by Gerald Eichstädt, one of the authors of the study. You can find more of them on its Youtube channel.

JunoCam has a field of 58°, and 4 filters:

  • Blue at 480.1 nanometers (nm),
  • Green at 553.5 nm,
  • Red at 698.9 nm. These three filters are in the visible spectrum,
  • while the fourth one is centered in the methane absorption band at 893.3 nm. This last one belongs to the near infrared spectral domain.

The authors used the images taken in visible light, i.e. with the first three filters, during a close fly-by of the Red Spot on 2017 July, 11.

From raw data to measurements

To make good science from raw data, you have to treat them. In particular, the authors needed to

  • consider the exact location and orientation of the spacecraft,
  • correct the images from distortion. For that, they assumed that the camera had Brown-Conrady radial distortion, or decentering distortion, which would be due to physical elements in a lens not being perfectly aligned.

Once they made these corrections, they got 4 images, distributed over 581 seconds. In comparing the location of the cloud features on these four images, they got the wind velocities in the upper level of the spot.

5 features in the spot

And from these velocities, they identified 5 structures, which are listed in the Table below.

Location Size Winds’ velocity
Compact cloud clusters Northern part 500 x 250 km 30-50 m/s
Mesoscale waves Northern boundary 2,000 x 500 km 50 m/s
Internal spiraling vortices South-West 1,000 x 1,000 km 75 m/s
Central nucleus Center 5,200 x 3,150 km 10-20 m/s
Large dark thin filaments Border 2,000-7,000 x 150 km 2-4 m/s

In particular,

  • the compact cloud clusters are composed of between 50 and 60 single wind cells, each with a size between 50 and 70 kilometers. This size suggests ammonia condensation.
  • The mesoscale waves could either be atmospheric gravity waves, i.e. when buoyancy tries to restore equilibrium between two media (see picture below, of atmospheric gravity waves observed on Earth), or shear instability waves, due to high wind.
    • Satellite image of atmospheric gravity waves over the Arabian Sea. Their visibility is due to sunlight, caused by the "impression" of the atmospheric waves on the sea surface. ©Jeff Schmaltz MODIS Rapid Response Team, NASA-GSFC
    Satellite image of atmospheric gravity waves over the Arabian Sea. Their visibility is due to sunlight, caused by the "impression" of the atmospheric waves on the sea surface. ©Jeff Schmaltz MODIS Rapid Response Team, NASA-GSFC
  • The cause of the internal spiraling vortices still needs to be understood.
  • The central nucleus is probably a cyclonic region, with turbulent winds.
  • It is not clear whether the large dark thin filaments are traced by darker aerosols, or represent areas with differetn altitudes and particles densities. They could be Vortex Rossby Waves, which accelerate the tangential winds, and play an important role in hurricanes. You can find more details here.

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: Trans-Neptunian Objects

Satellites of large TNOs

Leave a comment

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

Outline

Many TNOs are not alone
Two large guys: Eris and Orcus
Observations with the Atacama Large Millimeter Array (ALMA)
From the observations to the physical parameters
On the origin of the satellites
The study and its authors

Many TNOs are not alone

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

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

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

Two large guys: Eris and Orcus

Discoveries

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

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

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

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

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

Properties

You can find below some of their properties.

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

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

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

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

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

Observations with the Atacama Large Millimeter Array (ALMA)

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

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

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

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

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

From the observations to the physical parameters

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

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

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

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

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

I see two major elements from these results:

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

This last element suggests that they have a different composition.

On the origin of the satellites: impact of trapping?

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

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

The study and its authors

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

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.

Comets

Origin of the ecliptic comets

Leave a comment

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.

Outline

The dynamics of comets
The ecliptic comets
Dwarf planets beyond Neptune
The Solar System originates from a disk
Eccentricity excitation by Mean-Motion Resonances (MMR)
Numerical simulations
Replenishment of the 2:1 MMR
One tenth of the ecliptic comets
The study and its authors

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.

Satellites of Saturn

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

Leave a comment

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.

Outline

The mid-sized moons of Saturn
Interesting features, hot past
Resonances everywhere
Long-term migration of the satellites
Coping with the observational constraints
4 sets of numerical simulations
Tethys is older than Enceladus
The study and its authors

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.