PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history · The solid Earth: structure, fields and thermal history
The Solid Earth, Ch Dating, heat flow and the thermal history of the Earth
Problem
Mars can only be read from outside, the way we have read the Earth so far. Its mean radius is RMars=3390km, and seismic records from the InSight lander, together with its moment of inertia, put its core radius near rc≈1830km. Mars presently shows no global magnetic field, only patches of crustal remanent magnetism, and its dynamo is thought to have shut down by about 4Gyr ago. Gravity at Mars's core-mantle boundary is close to its surface value, g≈3.7ms−2, and the core temperature there is estimated at T≈1900K. Take αV=1×10−5K−1 and cp=750Jkg−1K−1, the same order as used for Earth's core in section 3.8, and consider the same bracket of core conductivity used there, kcore=40 and 150Wm−1K−1. Models of Mars's overall thermal budget put the heat presently leaving its core at somewhere between 3 and 8mWm−2, averaged over the core-mantle boundary.
((a)) Find the adiabatic temperature gradient at Mars's core-mantle boundary.
((b)) Find the adiabatic heat flux qad for each of the two conductivities.
((c)) For each conductivity, say whether there is a surplus left over for thermal convection, and hence whether the core could presently be driving a thermal dynamo.
((d)) The half-space cooling and plate cooling models, derived in section 3.6 for sea floor spreading away from a ridge, do not directly describe Mars, which has no plate tectonics. Name the one assumption of that derivation Mars does not supply.
((e)) Assume that a mantle which convects more vigorously draws heat out of the core faster, so that the core heat flow qc rises with the mantle's convective vigour. Using the lesson of section 3.7, that convective heat loss rises steeply with mantle temperature, explain why an early, hotter Mars could have had a surplus over its adiabat, even though qad, which is proportional to the core temperature, was then somewhat larger too.