3.10 Tidal heating explained

Tidal heating happens whenever tides distort the solid interior of a moon. Now, if you bend any solid it gets warm, because the atoms have to slide past each other. You can see this for yourself. Take a piece of wire, bend it to and fro a few times, touch it to your lips, it will actually feel warm.

Now, coming up are extracts from a video we made in 1993 to show where and how tidal heating occurs. Although it’s an old video, the basic science inside it, like my taste in shirts, hasn’t really changed.

I’m a geologist. And of all the worlds in the Solar System, the ones that excite me most are some of the large satellites of the outer planets. The outer layers of most of them are ice rather than ordinary rock. But that doesn’t matter, because in all important respects the ice behaves exactly like rock.

Looking very closely at an image, all you can see are the individual picture elements, or pixels, from which the image is composed. In this example, they represent areas about two km across. These are the basic data recorded by the camera, and represent simply the amount of sunlight reflected from the surface in each square. The brightness of each pixel is proportional to this. As I zoom outwards, you lose sight of the individual pixels, and begin to see the picture itself.

In this case, we’re looking at part of Rhea, one of Saturn’s moons which is about 1,500 km in diameter. This sort of picture is just what most people expected to see on the solid surfaces in the outer Solar System. It indicates a passive world with no signs of geological activity.

The features you can see are craters produced by impacts of meteorites and other debris hitting the surface at speeds of 10 km a second or more. What surprised scientists was that this kind of fairly dull surface turned out to be uncommon. Many of the outer planet satellites are much more exciting looking places.

Great fault troughs were seen cutting through the surfaces of some satellites. Others have regions where ancient impact craters have being buried under recent outpourings of icy lava. Clearly, these are not passive inactive worlds at all.

Now, there’s almost certainly been too little radioactive heating within these bodies to explain the amount of melting that’s evidently occurred. Even Io, which is essentially a rocky body and so it needs much more heat than an icy satellite before melting can begin, turns out to have a young surface.

Io has about the same size and mass as the Earth’s Moon, and should by rights be about equally as densely cratered. But the Voyager images revealed no impact craters at all. Instead, the sulfur rich rock of Io’s surface is covered by lava flows and other volcanic features. Some of the volcanoes were even found to be active, spouting plumes of sulfur and sulfur dioxide 100 km or more into space. Infrared observations from ground based telescopes show that Io continues to be active today.

The amount of heat escaping per square metre of Io’s surface is over a hundred times that escaping from the Moon, and about 25 times that escaping from the Earth. So what’s causing all this heating responsible for resurfacing Io and many of the icy satellites? Well, the answer appears to lie in the orbital interactions of satellites moving around extremely massive planets.

Consider this model of a satellite spinning on its axis. The gravitational pull of the planet will distort the satellite’s shape, raising a tidal bulge on the side facing the planet, and an equal bulge on the opposite side. The size of the tidal bulge has been exaggerated on this model.

In the case of Io, it’s been calculated to be about two kilometres high.

The near side bulge must stay facing the planet, so it has to migrate around the equator to achieve this. This continuously flexes the satellite’s body, and causes an enormous amount of heating by a kind of internal friction. This kind of heat generation is called tidal heating.

But you don’t get something for nothing - the energy comes from a loss of angular momentum from the satellite’s spin. In other words, its rotation gets slowed down. In addition, its orbit will probably evolve, and the spin of the planet may decrease slightly. The slowing down of a satellite’s rotation will cease when it makes exactly one rotation per orbit, because when this happens the satellite always keeps the same face towards the planet.

This means that the tidal bulge no longer has to migrate across the satellite’s surface. So energy is no longer being expended on internal friction, and tidal heating should stop. All large planetary satellites, including our own Moon, are in this state of synchronous rotation. Tidal heating can be an enormous source of energy in the outer Solar System, but there’s a problem.

It’s been estimated that it should take tidal forces no more than about 10 million years to bring the satellite into synchronous rotation. So although it explains how tidal heating have been an important heat source for satellites in the distant past, we haven’t explained how it continues today. To do this, we have to consider a satellite’s orbit. When we do so, we find that tidal heating for a synchronously rotating satellite ceases completely only if the orbit’s circular.

Conservation of angular momentum means that a satellite spins on its axis at a uniform rate. On the other hand, orbital motion is dictated by Kepler’s laws, so that while the satellite’s spin continues at a uniform rate, its speed round an elliptical orbit will vary.

Well, let’s begin by dividing a single orbit into four. Each position is reached after a quarter of the orbital period. The satellite travels fastest when closest to the planet, in accordance with Kepler’s second law.

Now, the satellite must be rotating at a uniform speed because there’s no way for significant amounts of angular momentum to be swapped from satellite to planet during the time taken for a single orbit. This means that at each position it will have rotated through exactly a quarter turn, which we can mark by adding blue arrows indicating a point on the satellite’s surface.

At the same time, the tidal bulge must always face the planet. We can mark this bulge in each case with a red arrow. At each stage in the orbit, the relative position of the arrows is different, so the bulge must still be moving relative to the surface of the satellite as it orbits the planet. The bulge is now oscillating about a mean position, and not migrating right round the globe as before.

From the planet, if an observer could watch the satellite all the way around its orbit, its surface would seem to wobble left and right, a phenomenon known as libration. As the satellite moves closer to and further from the planet, it moves back and forth within the planet’s gravitational field. This will force the tidal bulge to expand and contract in height, as well as shifting its position. Both these modes of deformation cause internal friction, which heats the interior of the satellite.

So, even in a synchronously rotating satellite tidal heating can continue, though at a much slower rate than for a rapidly rotating satellite. The rate of tidal heating’s negligible within the Moon, but it does account for the geological activity in most of the satellites of the outer planets. Given enough time, tidal forces tend to drag a satellite into a circular orbit, upon which tidal heating would cease. This will be the eventual fate of a single satellite influenced only by a much larger and spherical planet. In the outer Solar System, things aren’t so simple

Jupiter, for instance, has four large satellites - the three inner ones are in orbital resonance. For every orbit that Ganymede makes, Europa completes two, and Io, four. This means that each satellite passes closest to its neighbour at the same point in every orbit. And a repeated gravitational tug each time pulls the orbit out of shape. These gravitational interactions within families of satellites force their orbits to remain elliptical, and allow tidal heating to remain an important heat source.

Apart from present day activity on Io, tidal heating has caused recent and probably continuing activity on Europa, which has a cracked and deformed icy surface. Tidal heating has also kept Ganymede active for far longer than the outermost of Jupiter’s large satellites, Callisto. Episodes of orbital resonance have probably also been responsible for signs of geological activity on the satellites of Saturn and Uranus, too.

So, geological activity on the satellites of the outer planets can be explained by tidal heating. Is it all cut and dried then? Well, no, it isn’t. There are still many unanswered problems.

For example, some models suggest that the present rate of tidal heating of Io is not sufficient to account for its large number of active volcanoes. There are several possible explanations. We could have underestimated the rate of tidal heating, or overestimated the heat released by volcanoes, or perhaps Io’s undergoing a temporary pulse of volcanic activity. Or else we just don’t adequately understand the evolution of what are, after all, very complex orbital interactions within Jupiter’s large family of satellites.

Nowadays we know a lot more about Enceladus, the moon of Saturn, because of orbital studies made by a mission called Cassini. For example, we know that it’s not been resurfaced by vast outpourings of icy lava like I said in that old video. The surface has been broken up by a network of very closely spaced faults. But also, we’ve seen jets of ice crystals being vented out into space from below the surface of Enceladus, and these must be coming from an internal liquid zone. And this internal liquid zone could only be kept warm and liquid because of tidal heating.