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.

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…

• The study, here: http://www.sciencedirect.com/science/article/pii/S0019103516304250, shared by the authors here. They present there study here.
• The web site of Marc Neveu,
• The web page of Alyssa Rose Rhoden. You can also follow her on Twitter here.
• The code used by the authors. Thanks to them for sharing!

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.