Category Archives: Satellites of Saturn

Tides in the lakes of Titan

Hi there! The satellite of Saturn Titan has hydrocarbon seas, i.e. lakes made of liquid ethane and methane. When you have a sea, or a lake, you may have tides, and this is what this study is about. I present you A numerical study of tides in Titan’s northern seas, Kraken and Ligeia Maria, by David Vincent, Özgür Karatekin, Jonathan Lambrechts, Ralph D. Lorenz, Véronique Dehant, and Éric Deleersnijder, which has recently been accepted for publication in Icarus.

The lakes of Titan

The presence of hydrocarbons in such a thick atmosphere as the one of Titan has suggested since the spacecraft Voyager 1 than methane and ethane could exist in the liquid state on the surface of Titan. There could even be a cycle of methane, as there is a hydrological cycle on Earth, in which the liquid methane on the surface feeds the clouds of gaseous methane in the atmosphere, and conversely.

The spacecraft Cassini has detected dark smooth features, which revealed to be these hydrocarbon seas. Here is a list of the largest ones:

Location Diameter
Kraken Mare 68.0°N 310.0°W 1,170 km
Ligeia Mare 79.0°N 248.0°W 500 km
Punga Mare 85.1°N 339.7°W 380 km
Jingpo Lacus 73.0°N 336.0°W 240 km
Ontario Lacus 72.0°S 183.0°W 235 km
Mackay Lacus 78.32°N 97.53°W 180 km
Bolsena Lacus 75.75°N 10.28°W 101 km

I present you only the detected lakes with a diameter larger than 100 km, but some have been detected with a diameter as small as 6 km. It appears that these lakes are located at high latitudes, i.e. in the polar regions. Moreover, there is an obvious North-South asymmetry, i.e. there are much more lakes in the Northern hemisphere than in the Southern one. This could be due to the circulation of clouds of Titan: they would form near the equator, from the evaporation of liquid hydrocarbons, and migrate to the poles, where they would precipitate (i.e. rain) into lakes. Let us now focus on the largest two seas, i.e. Kraken and Ligeia Maria.

Kraken and Ligeia Maria

Kraken and Ligeia Maria are two adjacent seas, which are connected by a strait, named Trevize Fretum, which permit liquid exchanges. Kraken is composed of two basins, named Kraken 1 (north) and Kraken 2 (south), which are connected by a strait named Seldon Fretum, which dimensions are similar to the strait of Gibraltar, between Morocco and Spain.

Kraken and Ligeia Maria. © NASA
Kraken and Ligeia Maria. © NASA

Alike the Moon and Sun which raise tides on our seas, Saturn raises tides on the lakes. These tides cannot be measured yet, but they can be simulated, and this is what the authors did. In a previous study, they had simulated the tides on Ontario Lacus.

They honestly admit that the tides on Kraken and Ligeia Maria have already been simulated by other authors. Here, they use a more efficient technique, i.e. which uses less computational resources, and get consistent results.

Numerical modeling with SLIM

Computational fluid dynamics, often referred as CFD, is far from an easy task. The reason is that the dynamics of fluids in ruled by non-linear partial derivative equations like the famous Navier-Stokes, i.e. equations which depend on several variables, like the time, the temperature, the location (i.e. where are you exactly on the lake?), etc. Moreover, they depend on several parameters, some of them being barely constrained. We accurately know the gravitational tidal torque due to Saturn, however we have many uncertainties on the elasticity of the crust of Titan, on the geometry of the coast, on the bathymetry, i.e. the bottom of the seas. So, several sets of parameters have to be considered, for which numerical simulations should be run.

It is classical to use a finite element method for problems of CFD (Computational Fluid Dynamics, remember?). This consists to model the seas not as continuous domains, but as a mesh of finite elements, here triangular, on which the equations are defined.
The structure of the mesh is critical. A first, maybe intuitive, approach would be to consider finite elements of equal size, but it appears that this way of integrating the equations is computationally expensive and could be optimized. Actually, the behavior of the fluid is very sensitive to the location close to the coasts, but much less in the middle of the seas. In other words, the mesh needs to be tighter at the coasts. The authors built an appropriate mesh, which is unstructured and follow the so-called Galerkin method, which adapts the mesh to the equations.

The authors then integrated the equations with their homemade SLIM software, for Second-generation Louvain-la-Neuve Ice-ocean Model. The city of Louvain-la-Neuve hosts the French speaking Belgian University Université Catholique de Louvain, where most of this study has been conducted. The model SLIM has been originally built for hydrology, to model the behavior of fluids on Earth, and its simulations have been successfully confronted to terrain measurements. It thus makes sense to use it for modeling the behavior of liquid hydrocarbons on Titan.

In this study, the authors used the 2-dimensional shallow water equations, which are depth-integrated. In other words, they directly simulated the surface rather than the whole volume of the seas, which of course requires much less computation time.
Let us now see their results.

Low diurnal tides

The authors simulated the tides over 150 Titan days. A Titan day is 15.95 days long, which is the orbital period of Titan around Saturn. During this period, the distance Titan-Saturn varies between 1,186,680 and 1,257,060 km because the orbit of Titan is eccentric, and so does the intensity of the tidal torque. This intensity also varies because of the obliquity of Titan, i.e. the tilt of its rotation axis, which is 0.3°. Because of these two quantities, we have a period of variation of 15.95 days, and its harmonics, i.e. half the period, a third of the period, etc.

It appeared from the simulations that the 15.95-d response is by far the dominant one, except at some specific locations where the tides cancel out (amphidromic points). The highest tides are 0.29 m and 0.14 m in Kraken and Ligeia, respectively.

Higher responses could have been expected in case of resonances between eigenmodes of the fluids, i.e. natural frequencies of oscillations, and the excitation frequencies due to the gravitational action of Saturn. It actually appeared that the eigenmodes, which have been computed by SLIM, have much shorter periods than the Titan day, which prevents any significant resonance. The author did not consider the whole motion of Titan around Saturn, in particular the neglected planetary perturbations, which would have induced additional exciting modes. Anyway, the corresponding periods would have been much longer than the Titan day, and would not have excited any resonance. They would just have given the annual variations of tides, with a period of 29.4 years, which is the orbital period of Saturn around the Sun.

Fluid exchanges between the lakes

SLIM permits to trace fluid particles, which reveals the fluid exchanges between the basins. Because of their narrow geometry, the straits are places where the currents are the strongest, i.e. 0.3 m/s in Seldon Fretum.
The volumetric exchanges are 3 times stronger between Kraken 1 and Kraken 2 than between Kraken and Ligeia. These exchanges behave as an oscillator, i.e. they are periodic with respect to the Titan day. As a consequence, there is a strong correlation between the volume of Kraken 1, and the one of Kraken 2. Anyway, these exchanges are weak with respect to the volume of the basins.

The attenuation is critical

The authors studied the influence of the response with respect to different parameters: the bathymetry of the seas (i.e., the geometry of the bottom), the influence of bottom friction, the depth of Trevize Fretum, and the attenuation factor γ2, which represents the viscoelastic response of the surface of Titan to the tidal excitation. It appears that γ2 plays a key role. Actually, the maximum tidal range is an increasing function of the attenuation, and in Seldon and Trevize Fretum, the maximum velocities behave as a square root of γ2. It thus affects the fluid exchanges. Moreover, these exchanges are also affected by the depth of Trevize Fretum, which is barely constrained.

Another mission to Titan is needed to better constrain these parameters!

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 and Facebook. And let me wish you a healthy and happy year 2018.

Water-ice boundary on Titan

Hi there! Titan may be the most famous satellite in the Solar System, I realize that I never devoted a post to it. It is high time to make it so. I present you Does Titan’s long-wavelength topography contain information about subsurface ocean dynamics? by Jakub Kvorka, Ondřej Čadek, Gabriel Tobie & Gaël Choblet, which has recently been accepted for publication in Icarus. This paper tries to understand the mechanisms responsible for the location of the boundary between the icy crust and the subsurface ocean. This affects the thickness of the crust, which itself affects the topography of Titan.

Titan

The existence of Titan is known since 1655 thanks to the Dutch astronomer Christiaan Huygens. It was the only known satellite of Saturn until the discovery of Iapetus in 1671. It is the second largest natural satellite of the Solar System (mean radius: 2,575 km), and it orbits Saturn in almost 16 days, on a 3% eccentric and almost equatorial orbit (actually, a small tilt is due to the gravitational influence of the Sun).

It has interesting physical characteristics:

  • A thick atmosphere (pressure at the surface: 1.5 bar) mainly composed of nitrogen, with clouds of methane and ethane.
  • A complex surface. We can find hydrocarbon seas, i.e. lakes of methane and ethane (Kraken Mare, Ontario Lacus…), we also have a mountain chain, which features have been named after Tolkien’s Lords of the Rings (Gandalf Colles, Erebor Mons,…). There are some impact craters as well, but not that many, which suggests a geologically young surface. There is probably cryovolcanism on Titan, i.e. eruptions of volatile elements. The surface and the atmosphere interact, i.e. there are exchange between the liquid methane and ethane of the lakes and the gaseous ones present in the atmosphere, and the atmosphere is responsible for erosion of the surface, for winds which are likely to create dunes, and for heat exchanges.
  • A global subsurface ocean, lying under the icy crust.
Map of Titan.
Map of Titan.

The quest for the internal ocean

An internal, water ocean is considered to be of high interest for habitability, i.e. we cannot exclude the presence of bacteriological life in such an environment. This makes Titan one of the priority targets for future investigations.

The presence of the ocean was hinted long ago, from the consideration that, at some depth, the water ice covering the surface would be in such conditions of temperature and pressure that it should not be solid anymore, but liquid. The detection of this ocean has been hoped from the Cassini-Huygens mission, and this was a success. More precisely:

  • The rotation of the surface of Titan is synchronous, i.e. Titan shows on average the same face to Saturn, like our Moon, but with a significant obliquity (0.3°), which could reveal the presence of a global ocean which would decouple the rotation of the crust from the one of the core.
  • A Schumann resonance, i.e. an electromagnetic signal, has been detected by the lander Huygens in the atmosphere of Titan, during its fall. This could be due to an excitation of a magnetic field by a global conductive layer, i.e. a global subsurface ocean.
  • The gravitational Love number k2, which gives the amplitude of the response of the gravity field of Titan to the variations of the gravitational attraction of Saturn, is too large to be explained by a fully solid Titan.

All of these clues have convinced almost all of the scientific community that Titan has a global subsurface ocean. Determining its depth, thickness, composition,… is another story. In the study I present you today, the authors tried to elucidate the connection between its depth and the surface topography.

Modeling the ice-water boundary

The authors tried to determine the depth of the melting point of the water ice with respect to the latitude and longitude. This phase boundary is the thickness of the icy crust. For that, they wrote down the equations governing the viscoelastic deformation of the crust, its thermal evolution, and the motion of the boundary.

The viscoelastic deformation, i.e. deformation with dissipation, is due to the varying tidal action of Saturn, and the response depends on the properties of the material, i.e. rigidity, viscosity… The law ruling the behavior of the ice is here the Andrade law… basically it is a Maxwell rheology at low frequencies, i.e. elastic behavior for very slow deformations, viscoelastic behavior when the deformations gets faster… and for very fast excitation frequencies (tidal frequencies), the Maxwell model, which is based on one parameter (the Maxwell time, which gives an idea of the period of excitation at the transition between elastic and viscoelastic behavior), underestimates the dissipation. This is where the more complex Andrade model is useful. The excitation frequencies are taken in the variations of the distance Titan-Saturn, which are ruled by the gravitational perturbations of the Sun, of the rings, of the other satellites…

These deformations and excitations are responsible for variations of the temperature, which are also ruled by physical properties of the material (density, thermal conductivity), and which will determine whether the water should be solid or liquid. As a consequence, they will induce a motion of the phase change boundary.

Resolution by spectral decomposition

The equations ruling the variables of the problem are complex, in particular because they are coupled. Moreover, we should not forget that the density, thickness, temperature, resulting heat flows… not only depend on time, but also on where you are on the surface of Titan, i.e. the latitude and the longitude. To consider the couplings between the different surface elements, the authors did not use a finite-element modeling, but a spectral method instead.

The idea is to consider that the deformation of the crust is the sum of periodic deformations, with respect to the longitude and latitude. The basic shape is a sphere (order 0). If you want to be a little more accurate, you say that Titan is triaxial (order 2). And if you want to be more accurate, you introduce higher orders, which would induce bulges at non equatorial latitudes, north-south asymmetries for odd orders, etc. It is classical to decompose the tidal potential under a spectral form, and the authors succeeded to solve the equations of the problem in writing down the variables as sums of spherical harmonics.

The role of the grain size

And the main result is that the grain size of the ice plays a major role. In particular, the comparison between the resulting topography and the one measured by the Cassini mission up to the 3rd order shows that we need grains larger than 10 mm to be consistent with the observations. The authors reached an equilibrium in at the most 10 Myr, i.e. the crust is shaped in a few million years. They also addressed the influence of other parameters, like the rigidity of the ice, but with much less significant outcomes. Basically, the location of the melting / crystallization boundary is ruled by the grain size.

In the future

Every new study is another step forward. Others will follow. At least two directions can be expected.

Refinements of the theory

The authors honestly admit that the presence of other compounds in the ocean, like ammonia, is not considered here. Adding such compounds could affect the behavior of the ocean and the phase boundary. This would require at least one additional parameter, i.e. the fraction of ammonia. But the methodology presented here would still be valid, and additional studies would be incremental improvements of this one.
A possible implication of these results is the ocean dynamics, which is pretty difficult to model.

More data?

Another step forward could come from new data. Recently the mission proposal Dragonfly has been selected as a finalist by the NASA’s New Frontiers program. It would be a rotorcraft lander on Titan. Being selected as a finalist is a financial encouragement to refine and mature the concept within the year 2018, before final decision in July 2019 (see video below).

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 and Facebook.

The mountainous equator of Iapetus

Hi there! You may have heard of Iapetus, a large satellite of Saturn which orbits very far. Today I will tell you about its equatorial ridge. This is the opportunity for me to present you Testing models for the formation of the equatorial ridge on Iapetus via crater counting, by Amanda L. Damptz, Andrew J. Dombard & Michelle R. Kirchoff, which has recently been accepted for publication in Icarus.

The satellite Iapetus

The satellite of Saturn Iapetus was discovered by Giovanni Domenico Cassini in October 1671. It orbited then on the western side of Saturn. During many years, i.e. until 1705, he was unable to observe it on the eastern side, since it was two magnitudes fainter. This has two implications:

  1. Iapetus has a two-tone coloration, i.e. a dark and a bright hemisphere,
  2. its rotation is synchronous. Like our Moon, it is locked in the synchronous 1:1 spin-orbit resonance, constantly showing the same face to Saturn.

Beside this, Iapetus is a large body (diameter: 1,470 km), which orbits at 3.5 millions km from Saturn (for comparison, Titan orbits almost thrice closer), with an orbital eccentricity of 0.028, very close to the one of Titan. It has an unexpectedly high orbital inclination, i.e. 15.47° with the equator of Saturn, and 8.13° with the Laplace Plane. We should imagine the proto-Saturn nebula, from which Iapetus has probably been formed. It was pretty much like a disc, but distorted by the Sun if you were far enough from Saturn, which is the case for Iapetus. What I mean is that the gravitational action of the Sun tends to shift the equilibrium orbital plane from the equatorial one, this is why we need to distinguish it, and we call it the Laplace Plane. In that case, the orbital inclination of Iapetus with respect to the Laplace Plane should be very small, but it is not. This probably contains an information on the history of Iapetus, but we do not know which one yet.

Let me go back to the rotation. Iapetus is so far from Saturn that it needs almost 80 days to complete one revolution, and 80 days for a rotation, since it is synchronous. This is the largest known spin period for a natural satellite in the Solar System.

As most of the satellites of Saturn, our knowledge of Iapetus made invaluable progress since 2004 thanks to the Cassini spacecraft, which imaged it. It confirmed the two-tone coloration, and detected a mountainous equatorial ridge.

Iapetus seen by the Cassini spacecraft. © NASA
Iapetus seen by the Cassini spacecraft. © NASA

The equatorial ridge

The Cassini images showed a 20 km-wide mountainous ridge, which is very close to the equator. So close that it is hard to believe it appeared there by chance. It is present on the dark hemisphere, while isolated equatorial mountains can be seen on the bright side. Some peaks reach 20 km.

Since its discovery late 2004, this ridge is a matter of investigation, and several competing explanations can be found in the literature:

  1. A signature of its past, fast rotation (the measured oblateness of Iapetus is consistent with a rotation period of 16 hours)
  2. A signature of a past critical spin state, i.e. close to provoke disruption of Iapetus,
  3. Upwarping of the lithosphere from below,
  4. Cryovolcanism,
  5. Planetary contraction,
  6. Material from an ancient ring system,
  7. Material from impact generated debris.

We can see that some of these scenarios propose an inner (endogenic) cause, while others propose an outer (exogenic) one. Almost all of them suggest an early formation of the ridge, except the last one.
One way to date a geological feature is to count its craters, and this is where this study intervenes. Its first product is a database of 7,748 craters ranging from 0.83 to 591 km in diameter.

Counting the craters

When an impactor reaches a planetary surface, it creates a crater. If one day geological processes are strong enough to create a tectonic feature, then it may at least alter the crater, or even hide it. If we see an uncraterized geological feature, that means that it is pretty young. We could even try to give it an age in estimating the evolution of the cratering rates over the evolution of the Solar System. By the way, the early Solar System was very intensively bombarded, with an episode of Late Heavy Bombardment occurring between 4.1 and 3.8 billions years ago. Bombardments still happen nowadays, but are much less frequent.

In this study the authors worked from Cassini and Voyager images of the surface of Iapetus, and considered different zones: central ridge, peripheral ridge, and off ridge. Moreover they classified the craters following their diameters, so as to estimate a distribution law: number of craters vs. size. They also catalogued the orientation of the deformations of the craters, since it could tell us something on the geological evolution of Iapetus (how did it alter the surface?)

This systematic search for craters was assisted by the commercial software Esri’s ArcGIS, supplemented by the dedicated add-on Crater Helper Tools.

Results

The first result is a database of 7,748 craters. But the main question is: what can we say about the ridge? The authors observe a depletion of large craters, i.e. with a diameter bigger than 16 km, in the ridge, which would be consistent with a pretty recent formation, and thus would favor the scenario of a ridge created by the debris of an impact. Nevertheless, the authors are prudent with this conclusion, they seem to suggest that the resolution of the images and the risk of saturation of small craters (when you are heavily bombarded, new craters destroyed ancient ones, and the overall number does not increase) do not permit to discard a scenario of early formation of the ridge. Further studies will probably be needed to reach an agreement on the origin of this mountainous equator.

The study and its authors

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

The fate of the Alkyonides

Hello everybody! Today, I will tell you on the dynamics of the Alkyonides. You know the Alkyonides? No? OK… There are very small satellites of Saturn, i.e. kilometer-sized, which orbit pretty close to the rings, but outside. These very small bodies are known to us thanks to the Cassini spacecraft, and a recent study, which I present you today, has investigated their long-term evolution, in particular their stability. Are they doomed or not? How long can they survive? You will know this and more after reading this presentation of Long-term evolution and stability of Saturnian small satellites: Aegaeon, Methone, Anthe, and Pallene, by Marco Muñoz-Gutiérrez and Silvia Giuliatti Winter. This study has recently been accepted for publication in The Monthly Notices of the Royal Astronomical Society.

The Alkyonides

As usually in planetary sciences, bodies are named after the Greek mythology, which is the case of the four satellites discussed today. But I must admit that I cheat a little: I present them as Alkyonides, while Aegeon is actually a Hecatoncheires. The Alkyonides are the 7 daughters of Alcyoneus, among them are Anthe, Pallene, and Methone.

Here are some of there characteristics:

Methone Pallene Anthe Aegaeon
Semimajor axis 194,402 km 212,282 km 196,888 km 167,425 km
Eccentricity 0 0.004 0.0011 0.0002
Inclination 0.013° 0.001° 0.015° 0.001°
Diameter 2.9 km 4.4 km 2 km 0.66 km
Orbital period 24h14m 27h42m 24h52m 19h24m
Discovery 2004 2004 2007 2009

For comparison, Mimas orbits Saturn at 185,000 km, and the outer edge of the A Ring, i.e. of the main rings of Saturn, is at 137,000 km. So, we are in the close system of Saturn, but exterior to the rings.

Discovery of Anthe, aka S/2007 S4. Copyright: NASA.
Discovery of Anthe, aka S/2007 S4. Copyright: NASA.

These bodies are in mean-motion resonances with main satellites of Saturn, more specifically:

  • Methone orbits near the 15:14 MMR with Mimas,
  • Pallene is close to the 19:16 MMR with Enceladus,
  • Anthe orbits near the 11:10 MMR with Mimas,
  • Aegaeon is in the 7:6 MMR with Mimas.

As we will see, these resonances have a critical influence on the long-term stability.

Rings and arcs

Beside the main and well-known rings of Saturn, rings and arcs of dusty material orbit at other locations, but mostly in the inner system (with the exception of the Phoebe ring). In particular, the G Ring is a 9,000 km wide faint ring, which inner edge is at 166,000 km… Yep, you got it: Aegaeon is inside. Some even consider it is a G Ring object.

Methone and Anthe have dusty arcs associated with them. The difference between an arc and a ring is that an arc is longitudinally bounded, i.e. it is not extended enough to constitute a ring. The Methone arc extends over some 10°, against 20° for the Anthe arc. The material composing them is assumed to be ejecta from Methone and Anthe, respectively.

However, Pallene has a whole ring, constituted from ejecta as well.

Why sometimes a ring, and sometimes an arc? Well, it tell us something on the orbital stability of small particles in these areas. Imagine you are a particle: you are kicked from home, i.e. your satellite, but you remain close to it… for some time. Actually you drift slowly. While you drift, you are somehow shaken by the gravitational action of the other satellites, which disturb your Keplerian orbit around the planet. If you are shaken enough, then you may leave the system of Saturn. If you are not, then you can finally be anywhere on the orbit of your satellite, and since you are not the only one to have been ejected (you feel better, don’t you?), then you and your colleagues will constitute a whole ring. If you are lucky enough, you can end up on the satellite.

The longer the arc (a ring is a 360° arc), the more stable the region.

Frequency diffusion

The authors studied

  1. the stability of the dusty particles over 18 years
  2. the stability of the satellites in the system of Saturn over several hundreds of kilo-years (kyr).

For the stability of the particles, they computed the frequency diffusion index. It consists in:

  1. Simulating the motion of the particles over 18 years,
  2. Determining the main frequency of the dynamics over the first 9 years, and over the last 9 ones,
  3. Comparing these two numbers. The smaller the difference, the more stable you are.

The numerical simulations is something I have addressed in previous posts: you use a numerical integrator to simulate the motion of the particle, in considering an oblate Saturn, the oblateness being mostly due to the rings, and several satellites. Our four guys, and Janus, Epimetheus, Mimas, Enceladus, and Tethys.

How resonances destabilize an orbit

When a planetary body is trapped in a mean-motion resonance, there is an angle, which is an integer combination of angles present in its dynamics and in the dynamics of the other body, which librates. An example is the MMR Aegaeon-Mimas, which causes the angle 7λMimas-6λAegaeonMimas to librate. λ is the mean longitude, and ϖ is the longitude of the pericentre. Such a resonance is supposed to affect the dynamics of the two satellites but, given their huge mass ratio (Mimas is between 300 and 500 millions times heavier than Aegaeon), only Aegaeon is affected. The resonance is at a given location, and Aegaeon stays there.
But a given resonance has some width, and several resonant angles (we say arguments) are associated with a resonance ratio. As a consequence, several resonances may overlap, and in that case … my my my…
The small body is shaken between different locations, its eccentricity and / or inclination can be raised, until being dynamically unstable…
And in this particular region of the system of Saturn, there are many resonances, which means that the stability of the discovered body is not obvious. This is why the authors studied it.

Results

Stability of the dusty particles

The authors find that Pallene cannot clear its ring efficiently, despite its size. Actually, this zone is the most stable, wrt the dynamical environments of Anthe, Methone and Aegaeon. However, 25% of the particles constituting the G Ring should collide with Aegaeon in 18 years. This probably means that there is a mechanism, which refills the G Ring.

Stability of the satellites

From long-term numerical simulations over 400 kyr, i.e. more than one hundred millions of orbits, these 4 satellites are stable. For Pallene, the authors guarantee its stability over 64 Myr. Among the 4, this is the furthest satellite from Saturn, which makes it less affected by the resonances.

A perspective

The authors mention as a possible perspective the action of the non-gravitational forces, such as the solar radiation pressure and the plasma drag, which could affect the dynamics of such small bodies. I would like to add another one: the secular tides with Saturn, and the pull of the rings. They would induce drifts of the satellites, and of the resonances associated. The expected order of magnitude of these drifts would be an expansion of the orbits of a few km / tens of km per Myr. This seems pretty small, but not that small if we keep in mind that two resonances affecting Methone are separated by 4 km only.

This means that further results are to be expected in the upcoming years. The Cassini mission is close to its end, scheduled for 15 Sep 2017, but we are not done with exploiting its results!

To know more…

That’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter and Facebook.

On the interior of Mimas, aka the Death Star

Hi there! Today I will tell you on the interior of Mimas. You know, Mimas, this pretty small, actually the smallest of the mid-sized, satellite of Saturn, which has a big crater, like Star Wars’ Death Star. Despite an inactive appearance, it presents confusing orbital quantities, which could suggest interesting characteristics. This is the topic of the study I present you today, by Marc Neveu and Alyssa Rhoden, entitled The origin and evolution of a differentiated Mimas, which has recently been published in Icarus.

Mimas’ facts

The system of Saturn is composed of different groups of satellites. You have

  • Very small satellites embedded into the rings,
  • Mid-sized satellites orbiting between the rings and the orbit of Titan
  • The well-known Titan, which is very large,
  • Small irregular satellites, which orbit very far from Saturn and are probably former asteroids, which had been trapped by Saturn,
  • Others (to make sure I do not forget anybody, including the coorbital satellites of Tethys and Dione, Hyperion, the Alkyonides, Phoebe…).

Discovered in 1789 by William Herschel, Mimas is the innermost of the mid-sized satellites of Saturn. It orbits it in less than one day, and has strong interactions with the rings.

Semimajor axis 185,520 km
Eccentricity 0.0196
Inclination 1.57°
Diameter 396.4 km
Orbital period 22 h 36 min

As we can see, Mimas has a significant eccentricity and a significant inclination. This inclination could be explained by a mean-motion resonance with Tethys (see here). However, we see no obvious cause for its present eccentricity. It could be due to a past gravitational excitation by another satellite.

Mimas, seen by Cassini. We can the crater Herschel, which makes Mimas look like Star Wars' Death Star. Credit: NASA
Mimas, seen by Cassini. We can the crater Herschel, which makes Mimas look like Star Wars’ Death Star. Credit: NASA

The literature is not unanimous on the formation of Mimas. It was long thought that the satellites of Saturn formed simultaneously with the planet and the rings, in the proto-Saturn nebula. The Cassini space mission changed our view of this system, and other scenarios were proposed. For instance, the mid-sized satellites of Saturn could form from the collisions between 4 big progenitors, Titan being the last survivor of them. The most popular explanation seems to be that a very large body impacted Saturn, its debris coalesced into the rings, and then particles in the rings accreted, forming satellites which then migrated outward… these satellites being the mid-sized satellites, i.e. Rhea, Dione, Tethys, Enceladus, and Mimas. This scenario would mean that Mimas would be the youngest of them, and that it formed differentiated, i.e. that the proto-Mimas was made of pretty heavy elements, on which lighter elements accreted. Combining observations of Mimas with theoretical studies of its long-term evolution could help to determine which of these scenarios is the right one… if there is a right one. Such studies can of course involve other satellites, but this one is essentially on Mimas, with a discussion on Enceladus at the end.

The rotation of Mimas

As most of the natural satellites of the giant planets, Mimas is synchronous, i.e. it shows the same face to Saturn, its rotational (spin) period being on average equal to its orbital one. “On average” means that there are some variations. These are actually a sum of periodic oscillations, which are due to the variations of the distance Mimas-Saturn. And from the amplitude and phase of these variations, you can deduce something on the interior, i.e. how the mass is distributed. This could for instance reveal an internal ocean, or something else…

This rotation has been measured in 2014 (see this press release). The mean rotation is indeed synchronous, and here are its oscillations:

Period Measured
amplitude (arcmin)
Theoretical
amplitude (arcmin)
70.56 y 2,616.6 2,631.6±3.0
23.52 y 43.26 44.5±1.1
22.4 h 26.07 50.3±1.0
225.04 d 7.82 7.5±0.8
227.02 d 3.65 2.9±0.9
223.09 d 3.53 3.3±0.8

The most striking discrepancy is at the period 22.4 h, which is the orbital period of Mimas. These oscillations are named diurnal librations, and their amplitude is very sensitive to the interior. Moreover, the amplitude associated is twice the predicted one. This means that the interior, which was hypothesized for the theoretical study, is not a right one, and this detection of an error is a scientific information. It means that Mimas is not exactly how we believed it is.

The authors of the 2014 study, led by Radwan Tajeddine, investigated 5 interior models, which could explain this high amplitude. One of these models considered the influence of the large impact crater Herschel. In all of these models, only 2 could explain this high amplitude: either an internal ocean, or an elongated core of pretty heavy elements. Herschel is not responsible for anything in this amplitude.

The presence of an elongated core would support the formation from the rings. However, the internal ocean would need a source of heating to survive.

Heating Mimas

There are at least three main to heat a planetary body:

  1. hit it to heat it, i.e. an impact could partly melt Mimas, but that would be a very intense and short heating, which would have renewed the surface…nope
  2. decay of radiogenic elements. This would require Mimas to be young enough
  3. tides: i.e. internal friction due to the differential attraction of Saturn. This would be enforced by the variations of the distance Saturn-Mimas, i.e. the eccentricity.

And this is how we arrive to the study: the authors simulated the evolution of the composition of Mimas under radiogenic and tidal heating, in also considering the variations of the orbital elements. Because when a satellite heats, its eccentricity diminishes. Its semimajor axis varies as well, balanced between the dissipation in the satellite and the one in Saturn.

The problems

For a study to be trusted by the scientific community, it should reproduce the observations. This means that the resulting Mimas should be the Mimas we observe. The authors gave themselves 3 observational constraints, i.e. Mimas must

  1. have the right orbital eccentricity,
  2. have the right amplitude of diurnal librations,
  3. keep a cold surface.

and they modeled the time evolution of the structure and the orbital elements using a numerical code, IcyDwarf, which simulates the evolution of the differentiation, i.e. separation between rock and water, porosity, heating, freezing of the ocean if it exists…

Results

The authors show that in any case, the ocean cannot survive. If there would be a source of heating sustaining it, then the eccentricity of Mimas would have damped. In other words, you cannot have the ocean and the eccentricity simultaneously. Depending on the past (unknown) eccentricity of Mimas and the dissipation in Saturn, which is barely known, an ocean could have existed, but not anymore.
As a consequence, Mimas must have an elongated core, coated by an icy shell. The eccentricity could be sustained by the interaction with Saturn. This elongated core could have two origins: either a very early formation of Mimas, which would have given enough time for the differentiation, or a formation from the rings, which would have formed Mimas differentiated.

Finally the authors say that there model does not explain the internal ocean of Enceladus, but Marc Neveu announces on his blog that they have found another explanation, which should be published pretty soon. Stay tuned!

Another mystery

The 2014 study measured a phase shift of 6° in the diurnal librations. This is barely mentioned in the literature, probably because it bothers many people… This is huge, and could be more easily, or less hardly, explained with an internal ocean. I do not mean that Mimas has an internal ocean, because the doubts regarding its survival persist. So, this does not put the conclusions of the authors into question. Anyway, if one day an explanation would be given for this phase lag, that would be warmly welcome!

To know more…

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