## Info

Conduction

Convection"

Venus

Probably unimportant

Perhaps dominant

Perhaps significant

Earth

Minor contribution

Dominant

Minor contribution

Mars

Dominant

Negligible

Minor contribution?

Moon

Dominant

Negligible

Negligible

Io

Minor contribution

Negligible

Dominant

Jupiter

Negligible

Dominant

Negligible

Neptune

Negligible

Dominant

Negligible

a Including any solid state convection and any large-scale lithospheric recycling.

a Including any solid state convection and any large-scale lithospheric recycling.

(a) Explain why it is likely that the only way in which energy is being transferred up to the surface layer is by conduction.

(b) What can you deduce about the heat transfer coefficient of the thin surface layer compared with that of the rest of the body?

4.5.3 Observational Indicators of Interior Temperatures

If planetary modellers only had the various types of energy gains and losses that might be present, then models of the interior temperatures of planetary bodies would be very poorly constrained. Fortunately, there are observational data that are direct indicators of the thermal state. These include

• energy flow from the interior;

• seismic waves and the level of seismic activity;

• the degree of departure from isostatic equilibrium;

• the level and nature of geological activity at the surface, today and in the past;

• the magnetic field today, and evidence for its nature in the past.

The energy flow from the interior of a planetary body gives an indication of present-day interior temperatures. In principle the flow can be measured via the IR radiation to space to which it gives rise, this being the way that the energy is ultimately lost by the body. If there is flow from the interior then the rate at which IR radiation is emitted to space would exceed the rate at which radiation is absorbed from the Sun. In practice only for Jupiter, Saturn, and Neptune is this IR excess large enough to have been measured accurately. For some other bodies the present energy flow from the interior has been obtained by estimating the outward energy flow at the surface by conduction, convection, and advection. Values for energy outflows from the interiors of some planetary bodies are given in Table 4.2.

Seismic wave speeds can provide an indirect indication of interior temperatures. □ If there is a zone in which S waves do not travel, what can you conclude about the physical conditions in the zone?

A zone free of S waves must have negligible shear strength, so it could be a liquid or be highly plastic. Departures from isostatic equilibrium indicate lower plasticity, and changes in isostasy can give an indication of how dynamic the interior is, as can the level of seismic activity.

Geological activity is another indicator of interior temperatures, which will be elaborated in later chapters. By examining the geological activity on surfaces of different ages it is possible to gain insight into interior temperatures not only today but in the distant past. The present-day magnetic field indicates whether there are liquids in convection, and past magnetic fields leave an imprint in the rocks, enabling us to infer the nature of the field in the past, and hence gain further insight into interior temperatures throughout the history of the body.

### 4.5.4 Interior Temperatures

It has been noted that the temperatures inside a planetary body at any time t depend on the energy gains and losses at all earlier times. But the gains and losses themselves depend on the temperatures. For example, at time t the temperature profile T(t, r) will help determine whether there is any convection. If there is, then this will increase the energy loss rate at t, which will influence subsequent temperatures. We thus have a complicated interplay, represented in

Interior temperatures at time t

Figure 4.16 The interplay between interior temperatures and the rates of energy gains and losses in a planetary body.

the simplest manner by Figure 4.16. Planetary modellers have to grapple with this interplay until there is self-consistency.

Though the modelling process required to obtain the interior temperatures of a planetary body is intricate, there are three broad features that are readily appreciated. First, energy losses tend to win in the end. Energy sources can slow down the rate of decline of interior temperatures, and can hold interior temperatures steady, even for long periods, by producing energy at the same rate at which energy is lost to space. But most sources of energy either have died already, or are implanting less power as time passes. Sooner or later, interior temperatures will fall, and ultimately all bodies will come to have internal temperatures determined by the balance between solar radiation absorbed and IR radiation emitted to space.

Second, if sufficient time has passed since all energy sources at various depths became active, the temperature decreases monotonically as we move outwards from the centre to the surface. This is because the ultimate energy loss from the body is from its surface. The details of the temperature profile depend on the radial distribution of energy sources and on the heat transfer coefficients at each radius. Only if all energy sources have long been concentrated at the surface will the interior temperature be the same everywhere. □ What can give this outcome?

This is the outcome if, for a long time, the only active source has been solar energy. Another way is through the concentration of all radioactive isotopes into the surface.

Finally, a planetary body will lose internal energy faster per unit mass than a larger planetary body, provided that the two bodies have similar heat transfer coefficients, similar interior energy sources per unit mass, and similar spatial distributions of energy sources. This is because the global rate of energy loss increases with the surface area A of the body, whereas the global rate at which energy is released in the interior increases with the mass M of a body. A/M is thus a measure of the rate of loss of internal energy per unit mass, and A/M increases as the size of the body decreases. For a spherical body of radius R

M 4^R3pm/3

where pm is the mean density. This simplifies to

0 0