Hi there! Today I will present you a paper that has recently been accepted for publication in Celestial Mechanics and Dynamical Astronomy, entitled Constraints on dissipation in the deep interiors of Ganymede and Europa from tidal phase-lags. This study has been conducted in Germany, at the DLR, by Hauke Hussmann.
The idea is here to get some clues on the interior of the satellites of Jupiter Ganymede and Europa, from two different signatures of the tides raised by Jupiter.
The tidal Love numbers h2 and k2
I have recently presented the tidal Love number k2 in a post on Mercury. In a nutshell: it represents the amplitude of variation of the gravity field of the satellite, at the orbital frequency. Please note that contrary to Mercury, only the orbital frequency is to be considered in the periodic variations of the gravity field. The reason for that is in the rotational dynamics: the main satellites of Jupiter rotate synchronously, showing the same face to their planet like our Moon, while Mercury is in a 3:2 spin-orbit resonance.
The tidal Love number h2 represents the amplitude of the tidal deformation of the topography of the satellite. Something remarkable on these 2 numbers is that h2 is mostly sensitive to the surface, while k2 is the response of the whole body. The idea of this study is to compare the two numbers, to get clues on the interior.
The satellites of Jupiter
At this time, 67 natural satellites are known for Jupiter. They can be classified into 3 groups:
- The inner satellites Metis, Adrastea, Amalthea and Thebe. These are small bodies, their mean radii being between 8 and 85 km. They orbit at less than 3 Jupiter radii.
- The Galilean satellites Io, Europa, Ganymede and Callisto. These are pretty large bodies, which were discovered in 1610 by Galileo Galileo. They orbit between 6 and 25 Jupiter radii. They contain almost of the mass of the satellites of Jupiter, which make them particularly interesting. For instance, their large masses is responsible for an interesting 3-bodies mean-motion resonance involving Io, Europa, and Ganymede. Basically, Io makes 4 revolutions around Jupiter while Europa makes 2 and Ganymede exactly one. This configuration is known as Laplacian resonance. Moreover the sizes of the 4 Galilean satellites, combined with the tides raised by Jupiter, are also responsible for internal differentiation. In particular, these 4 bodies are all considered to harbor global internal fluid layers.
- The irregular satellites. These are small bodies orbiting far much further from Jupiter. They are probably former asteroids which were trapped by the gravity field of Jupiter. Contrary to the two other groups, which have pretty circular and coplanar orbits, the irregular satellites can have highly eccentric and inclined orbits. Some of them are even retrograde.
The next space missions JUICE and Europa Multiple Flyby
Ganymede and Europa are the main targets of the next two missions to the system of Jupiter. These two missions are the ESA mission JUICE, and the NASA Europa Mission.
JUICE, for JUpiter ICy moons Explorer, is planned to be launched in 2022 and to orbit Jupiter in 2030. Then, it will make flybys of Europa and Callisto, before becoming a satellite of Ganymede. Ganymede is thus the main target. Among the 11 instruments constituting JUICE, let us focus on two of them: GALA and 3GM.
GALA, for GAnymede Laser Altimeter, will measure the topography of the planet, while 3GM, for Gravity and Geophysics of jupiter and the Galilean Moons, is the radioscience experiment. It will in particular measure the gravity field of the body. The connection with the study I am presenting you is that h2 is expected from GALA, while k2 is expected from 3GM. Another connection is that Hauke Hussmann is both the first author of this study, and the principal investigator of GALA.
The NASA Europa Mission, also known as Europa Multiple-Flyby Mission, and previously Europa Clipper, will obviously target Europa. It should be launched in the 2020’s, and the nominal mission plans to perform 45 flybys of Europa.
One of the motivations to explore these bodies is the search for extraterrestrial life. Europa and Ganymede are known to harbor a subsurface ocean, and we wonder whether these oceans contain the ingredients for bacteriological life. These two missions will give us more information on the interior, from gravity data, analysis of the topography, imagery of the surface, measurements of the magnetic field… bringing new constraints on the oceans, like their depths, density, or viscosity…
The idea of these studies is to compare the Love number h2, from the topography, and k2, from the gravity field, to constrain the interior. For that, the authors have considered several models of interior of Europa and Ganymede, and simulated the resulting Love numbers.
These interior models have to be realistic, which means being consistent with our current knowledge of these bodies, i.e. their total mass and their shapes, and being physically relevant. This implies that their densities increase radially, from the surface to the center. So, the surface is assumed to be made of ice coating a water ocean. Below the ocean is another ice layer, which itself surrounds a denser core. The ocean tends to decouple the icy shell from the action of the interior.
The authors particularly focus on the phase difference between h2 and k2. Basically, the Love numbers are complex numbers, the imaginary part representing the dissipation, while the real part is related to a purely elastic tide. From their simulations, they show that these phase differences should be of several degrees. Their possible measurements should constrain the viscosity of the ice shell coating the core of Ganymede, and the temperature of the mantle of Europa.
Of course, the most interesting perspective is the future measurements of these phase differences by JUICE and NASA Europa Mission. The information they will provide will be supplemented by better constraints on the gravity field, on the magnetic field, on the rotation…
The authors assumed the rotations of these satellites to be synchronous, as suggested by the theory. But features at the surface of Europa suggest that the rotation of its surface could be actually slightly super-synchronous. This is something that the dynamical theories still need to understand, but this would probably affect the tidal action of Jupiter on Europa.