Plate tectonics on Europa?

Hi there! Jupiter has 4 large satellites, known as Galilean satellites since they were discovered by Galileo Galilei in 1610. Among them is Europa, which ocean is a priority target for the search for extraterrestrial life. Many clues have given us the certainty that this satellite has a global ocean under its icy surface, and it should be the target of a future NASA mission, Europa Clipper. Meanwhile it will also be visited by the European mission JUICE, before orbital insertion around Ganymede. Since Europa presents evidences of tectonic activity, the study I present you today, i.e. Porosity and salt content determine if subduction can occur in Europa’s ice shell, by Brandon Johnson et al., wonders whether subduction is possible when two plates meet. This study has been conducted at Brown University, Providence, RI (USA).

Subduction on Earth

I guess you know about place tectonics on Earth. The crust of the Earth is made of several blocks, which drift. As a consequence, they collide, and this may be responsible for the creation of mountains, for earthquakes… Subduction is a peculiar kind of collision, in which one plate goes under the one it meets, just because their densities are significantly different. The lighter plate goes up, while the heavier one goes down. This is what happens on the west coast of South America, where the subduction of the oceanic Nazca Plate and the Antarctic Plate have created the Andean mountains on the South America plate, which is a continental one.

Even if our Earth is unique in the Solar System by many aspects, it is highly tempting to use our knowledge of it to try to understand the other bodies. This is why the authors simulated the conditions favorable to subduction on Europa.

The satellite Europa

Europa is the smallest of the four Galilean satellites of Jupiter. It orbits Jupiter in 3.55 days at a mean distance of 670,000 km, on an almost circular and planar orbit. It has been visited by the spacecraft Pioneer 10 & 11 in 1973-1974, then by Voyager 1 & 2 in 1979. But our knowledge of Europa is mostly due to the spacecraft Galileo, which orbited Jupiter between 1995 and 2003. It revealed long, linear cracks and ridges, interrupted by disrupted terrains. The presence of these structures indicates a weakness of the surface, and argues for the presence of a subsurface ocean below the icy crust. Another argument is the tidal heating of Jupiter, which means that Europa should be hot enough to sustain this ocean.
This active surface shows extensional tectonic feature, which suggests plate motion, and raises the question: is subduction possible?

Numerical simulations of the phenomenon

To determine whether subduction is possible, the authors performed one-dimensional finite-elements simulations of the evolution of a subducted slab, to determine whether it would remain below another plate or not. The equation is: would the ocean be buoyant? If yes, then the slab cannot subduct, because it would be too light for that.

The author considered the time and spatial evolution of the slab, i.e. over its length and over the ages. They tested the effect of

  1. The porosity: Planetary ices are porous material, but we do not know to what extent. In particular, at some depth the material is more compressed, i.e. less porous than at the surface, but it is not easy to put numbers behind this phenomenon. Which means that the porosity is a parameter. The porosity is defined as a fraction of the volume of voids over the total volume investigated. Here, total volume should not be understood as the total volume of Europa, but as a volume of material enshrouding the material element you consider. This allows you to define a local porosity, which thus varies in Europa. Only the porosity of the icy crust is addressed here.
  2. The salt content: the subsurface ocean and the icy crust are not pure ice, but are salty, which affects their densities. The authors assumed that the salt of Europa is mostly natron, which is a mixture essentially made of sodium carbonate decahydrate and sodium bicarbonate. Importantly, the icy shell has probably some lateral density variations, i.e. the fraction of salt is probably not homogeneous, which gives room for local phenomenons.
  3. The crust thickness: barely constrained, it could be larger than 100 km.
  4. The viscosity: how does the material react to a subducting slab? This behavior depends on the temperature, which is modeled here with the Fourier law of heat,
  5. The spreading rate, i.e. the velocity of the phenomenon,
  6. The geometry of the slab, in particular the bending radius, and the dip angle.

And once you have modeled and simulated all this, the computer tells you under which conditions subduction is possible.

Yes, it is possible

The first result is that the two critical parameters are the porosity and the salt content, which means that the conditions for subduction can be expressed with respect to these two quantities.
Regarding the conditions for subduction, let me quote the abstract of the paper: If salt contents are laterally homogeneous, and Europa has a reasonable surface porosity of 0.1, the conductive portion of Europa’s shell must have salt contents exceeding ~22% for subduction to occur. However, if salt contents are laterally heterogeneous, with salt contents varying by a few percent, subduction may occur for a surface porosity of 0.1 and overall salt contents of ~5%.

A possible subduction does not mean that subduction happens. For that, you need a cause, which would trigger activity in the satellite.

Triggering the subduction

The authors propose the following two causes for subduction to happen:

  1. Tidal interaction with Jupiter, enhanced by non-synchronous rotation: Surface features revealed by Galileo are consistent with a crust which would not rotate synchronously, as expected for the natural satellites, but slightly faster, the departure from supersynchronicity inducing a full rotation with respect to the Jupiter-Europa direction between 12,000 and 250,000 years… to be compared with an orbital period of 3.55 days. So, this is a very small departure, which would enhance the tidal torque of Jupiter, and trigger some activity. This interpretation of the surface features as a super-synchronous rotation is controversial.
  2. Convection, i.e. fluid motion in the ocean, due to the variations of temperature.

No doubt Europa Clipper and maybe JUICE will tell us more!

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.

Rough terrains spin up asteroids

Hi there! If you follow me, you have already heard of the Yarkovsky effect, or even of the YORP, which are non-gravitational forces affecting the dynamics of Near-Earth Asteroids. Today I tell you about the TYORP, i.e. the Tangential YORP. This is the opportunity for me to present you Analytic model for Tangential YORP, by Oleksiy Golubov. This study has recently been published in The Astronomical Journal. The author meets the challenge to derive an analytical formula for the thermal pressure acting on the irregular regolith of an asteroid. Doing it requires to master the physics and make some sound approximations, following him tells us many things on the Tangential YORP.

From Yarkovsky to TYORP

When we address the dynamics of Near-Earth Asteroids, we must consider the proximity of the Sun. This proximity involves thermal effects, which significantly affect the dynamics of such small bodies. In other words, the dynamics is not ruled by the gravitation only. The main effect is the Yarkovsky effects, and its derivatives.


The Sun heats the surface of the asteroid which faces it. When this surface element does not face the Sun anymore, because of the rotation of the asteroid, it cools, and radiates some energy. This effect translates into a secular drift in the orbit, which is known as the Yarkovsky effect. This Yarkovsky effect has been directly measured for some asteroids, in comparing the simulated orbit from a purely gravitational simulation, with the astrometric observations of the objects. Moreover, long-term studies have shown that the Yarkovsky effect explains the spreading of some dynamical families, i.e. asteroids originating from a single progenitor. In that sense, observing their current locations proves the reality of the Yarkovsky effect.
When the asteroid has an irregular shape, which is common, the thermal effect affects the rotation as well.


Cooling a surface element which has been previously heated by the Sun involves a loss of energy, which depends on the surface itself. This loss of energy affects the rotational dynamics, which is also affected by the heating of some surface. But for an irregular shaped body, the loss and gain of energy does not exactly balance, and the result is an asteroid which spins up, like a windmill. In some cases, it can even fission the body (see here). This effect is called YORP, for Yarkovsky-O’Keefe–Radzievskii–Paddack.

This is a large-scale effect, in the sense that it depends on the shape of the asteroid as a whole. Actually, the surface of an asteroid is regolith, it can have boulders… i.e. high-frequency irregularities, which thus will be heated differently, and contribute to YORP… This contribution is known as Tangential YORP, or TYORP.

Modeling the physics

When you heat a boulder from the Sun, you create an inhomogeneous elevation of temperature, which can be modeled numerically, with finite elements. For an analytical treatment, you cannot be that accurate. This drove the author to split the boulder into two sides, the eastern and the western sides, both being assumed to have an homogeneous temperature. Hence, two temperatures for the boulder. Then the author wrote down a heat conduction equation, which says that the total heat energy increase in a given volume is equal to the sum of the heat conduction into this volume, the direct solar heat absorbed by its open surface, and the negative heat emitted by the open surface (which radiates).

These numbers depend on

  • the heat capacity of the asteroid,
  • its density,
  • its heat conductivity,
  • its albedo, i.e. its capacity to reflect the incident Solar light,
  • its emissivity, which characterizes the radiated energy,
  • the incident Solar light,
  • the time.

The time is critical since a surface will heat as long it is exposed to the Sun. In the calculations, it involves the spin frequency. After manipulation of these equations, the author obtains an analytical formula for the TYORP pressure, which depends on these parameters.

A perturbative treatment

In the process of solving the equations, the author wrote the eastern and western temperatures as sums of periodic sinusoidal solutions. The basic assumption, which seems to make sense, is that these two quantities are periodic, the period being the rotation period, P, of the asteroid. This implicitly assumes that the asteroid rotates around only one axis, which is a reasonable assumption for a general treatment of the problem.
As a result, the author expects these two temperatures to be the sum of sines and cosines of periods P/n, P being an integer. For n=1, you have a variation of period P, i.e. a diurnal variation. For n = 2, you have a semi-diurnal one, etc.

The perturbative treatment of the problem consists in improving the solution in iterating it, first in expressing only one term, i.e. the diurnal one, then in using the result to derive the second term, etc. This assumes that these different terms have amplitudes, which efficiently converge to 0, i.e. the semi-diurnal effect is supposed to be negligible with respect to the diurnal one, but very large with respect to the third-diurnal, etc. Writing down the solution under such a form is called Fourier decomposition.

The author says honestly that he did not check this convergence while solving the equation. However, he successfully tested the validity of his obtained solution, which means that the resolution method is appropriate.


The author is active since many years on the (T)YORP issue, and has modeled it numerically in a recent past. So, validating his analytical formula consisted in confronting it with his numerical results.

He particularly confronted the two results in the cases of a wall, a half buried spherical boulder, and a wave in the regolith, with respect to physical characteristics of the material, i.e. dimension and thermic properties. Even though visible differences, the approximation is pretty good, validating the methodology.

This allowed then the author to derive an analytical formula of the TYORP pressure on a while regolith, which is composed of boulders, which sizes are distributed following a power law.


This is the first analytical formula for the TYORP, and I am impressed by the author’s achievement. We can expect in the future that this law (should we call it the Golubov law?) would be a reference to characterize the thermic properties of an asteroid. In other words, future measurements of the TYORP effect could give the thermic properties, thanks to this law. This is just a possibility, which depends on the reception of this study by the scientific community, and on future studies as well.

The study and its author

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.