| MadSci Network: Earth Sciences |
There are several ways to look for an answer to this. One way is to look at how quickly the rocks underground heat up in deep mines or boreholes. If we look around the world at average thermal gradients, a figure like 35%C/Km is typical. Given a figure of 6371 Km for the Earth’s radius, that implies 223,000 degrees Centigrade at the centre of the Earth! Obviously, we’re extrapolating a bit here and there are a few problems with this figure. If it were correct, the Earth would be totally liquid below a few hundred km depth and the surface plates and crust of the Earth would be wildly unstable on top of a sea of boiling magma. We believe Venus is a little like this and every few hundred million years its entire crust is swallowed up into the mantle and destroyed. Fortunately, the Earth is more stable (even Venus isn’t as bad as it sounds, the mantle is far from liquid, just a bit on the soft sticky side of solid)
We know that the Earth is composed of layers of different composition (from actual samples in the crust and in tectonically emplaced units from the Mantle, and from studies of deep volcanic rocks and of meteorites). A lot of the radioactive minerals that generate the heat in the Earth are concentrated near the surface, so the gradient couldn’t be that steep all the way to the core anyway.
The main constraint on the internal temperature is, as mentioned above, that the Earth’s Mantle (the thick layer between core and crust) should not melt significantly at any depth. We know this should be so because seismic energy (sound/shock waves) travels through the Mantle as both Pressure waves (like sound in air) and Shear waves - a more complex ‘wriggly’ sort of sideways motion. Shear waves cannot travel in liquids and are rapidly attenuated (die away) in soft solids. The only significant soft zones are at the base of the Lithosphere (crust + uppermost mantle) at a depth of 120 to 200 km. This is where the geothermal gradient calculated from the surface reaches close to the melting point of the Mantle. Below this depth, the Mantle temperature is self-regulated by large-scale thermal convection. If any part of the Mantle gets too warm it softens, expands, and rises upwards, either as a Mantle Plume, or as part of a larger-scale, slower convection cell. cool Mantle material from above descends to replace the rising material, and cool the Earth. This convection has been going on for essentially the whole age of the Earth, at velocities of the order of 10cm per year, and is the ultimate driving force of Plate Tectonics, although the details are difficult to understand - many scientists argue about the exact mechanisms driving the Plates. This leads us to a temperature of "only" 3000 degrees Centigrade at the Mantle/Outer Core boundary (2900 km depth)
The outer core is liquid (no Shear waves). It convects much more vigorously than the Mantle, and is composed largely of Iron and Nickel. Some other lighter elements are also in there. We can’t get samples so aren’t sure but Sulphur and Oxygen are likely candidates. The convection in the outer core is believed to be responsible for the Earth’s magnetic field. Again, scientists disagree about the details of how it is generated - basically, we don’t know for sure but have a lot of good hints.
The central 1300km (radius) of the Earth contains a solid Inner Core. The composition seems to be mostly the same as the liquid Outer Core. The temperature of this inner core calculates out at about 4100 to 4200 Centigrade, based on models of how the outer core convects, and measurements of the physical properties of iron at high temperature and pressure. The pressure at the Centre of the Earth is around 14.2 Million times atmospheric pressure. Not a nice place for a visit, but quite mild compared to the centre of a star.
So the Answer is 4150 Centigrade, but there’s a lot of work involved to prove it. My main Reference was "Physics of the Earth" by Frank D. Stacey. Published 1977 by John Wiley & Sons. ISBN 0-471-81956-5, but any good geophysics text dealing with the structure and composition of the Earth should cover this. Note that some ideas may have changed in the 20-odd years since this book was written, but the general details will stay valid.
Nick