Recently, I've been working on 3D tidal heating and convection models for icy satellites. In particular, I've been focusing on Enceladus (en-SEH-la-dus), a small-to-medium size moon of Saturn. The satellite is named after a giant in ancient Greek mythology, believed to be buried under Mt. Aetna. If you use the Italian pronunciation, you get "en-che-LA-dus", hence the image to the right. Enceladus is a particularly interesting target, given the south polar thermal anomaly, showing massive heat flux and vapor escape from a world thought to be dead. The popular idea at the moment is that orbital energy from Enceladus' eccentric orbit about Saturn is being dissipated as heat in the ice shell. But is tidal heating sufficient to explain the observations? And are there other ways of doing it? That's what I'm testing.
Enceladus is a small moon, only 500 km in diameter. For comparison, that's roughly the size of Great Britain as shown in this NASA Image. Small bodies tend to cool quickly, so it was quite exciting when Cassini found the vapor plume and heat flow anomaly at the south pole.
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Below is a cartoon of the interior of Enceladus. If Enceladus is differentiated, it consists of a rocky core with radius 160 km, overlain by a shell of ice and water with combined thickness of 90 km. The depth to the ocean (if it exists at all) is not known as was treated as a free parameter in my models.
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I modeled tidal heating in both the ice shell and the silicate core. Below is a plot of the axisymmetrically averaged tidal heating, that is averaged over all longitudes (Imagine taking a segment of an orange). The outer colored region is the ice shell and the inner colored region is the rocky core. Red signifies regions of high tidal dissipation, blue indicates areas of low dissipation. The heating is expressed in terms of power per unit volume. The actual values vary depending on the specific model parameters, but the pattern is the same in general. The tick marks on the left denote radial position in meters. The marks along the right edge denote the latitude.
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There are two key features in the plot above. First, the maximum dissipation occurs near the base of the ice shell in the polar regions. Second, while the same color scheme is used for the ice shell and the core, the core heating has been scaled up by a factor of 10,000 to make it show up. Tidal heating is negligible in the core and is not considered further here. The white zone in between the core and the ice shell is the ocean. It is excluded from the model, because no heat is dissipated in a liquid layer, assuming a Maxwellian response.
Tidal dissipation varies with longitude as well. Below is a map view of the tidal dissipation at the base of the ice shell. Counter-intuitively, the tidal dissipation is highest at the poles, and lowest on the equator at the points facing and opposite Saturn.
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