Liquid core is cooling due to heat conduction towards the lower mantle. Independently from the absolute liquid core temperature (likely much lower than usually assumed considering pure iron melting temperatures), its radius is continuously reducing. At the same time, the radius of the solid core is increasing. What is the rate of liquid core radius decrease?
Thank you for giving me also appropriare references.
michele
P.S. for "plumologists": it is the lower mantle that is cooling the liquid core, it is not the liquid core that is warming the lower mantle. This difference could be considered as trivial, but it is at the base of the plate-driven tectonics vs. mantle plume theory (i.e., top-down tectonics vs. bottom-up tectonics).
Dear Michele Lustrino ,
In your analysis I am missing the heat production due to nuclear reactions in the inner core. If you may assume validity of Fourier's law, the core temperature will be just proportional to the total of this heat production. This will decay in time as a sum of exponentials (in principle one for each specific reaction). The core radius will be determined by the position where temperature equals the melting temperature of the core. In reality the transport equation determining the temperature profile will be much more complicated, due to e.g. convection, temperature dependence of heat conductivity and latent heat at the border between liquid and solid core. But, if the decay times of the main nuclear reactions are large, the change in radius of the liquid core will be very slow. This is very likely to be the case, since nuclear reactions with a decay time that is short on the lifetime of the earth will have died out since long.
Dear Henk,
thank you for the reply. I do not believe that there is any measurable radiogenic heat produced in the core, giving the neigligible presence of U (1.5 ppb), Th (5 ppb) and K (about 200 ppm). Written in other words, inner (and outer) core is cooling.
Also the melting temperature of the outer core are poorly determined. For sure the temperature requested by plume theory are too much high, considering the several impurities lowering its solidus. Indeed, instead of a classical iron-nickel alloy, Earth's core has about 5 wt% Si, 5 wt% O, 1.8 wt% S, 0.8 wt% C and about 0.3% of both Mn and P. Addtion of all these elements strongly depresses core solidus.
In any case, my question was much easier and direct: is there any idea about the annual radius decrease of liquid core?
Cheers,
Michele
Dear Michele,
I do not think the radiogenetic heat can be negligible. In that case the temperature inside the crust would be almost homogeneous, given the relative smallness of the heat flow through the crust.
I found an article on wikipedia ( https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget#Radiogenic_heat ) stating that about half of the heat flow from the inner earth is radiogenetic and the remainder is from primordial heat. A rough calculation based on earth mass of 6x10^{24} kg, specific heat of 1000J/(kg K), primordial heat flow of 20 TW (wikipedia) and temperature decrease of a few thousand K confirms this may be a reasonable estimate.
Another wikipedia article ( https://en.wikipedia.org/wiki/Core%E2%80%93mantle_boundary ) teaches us that the core consists of iron-nickle and the mantle mostly of silicate. This would mean the core radius is determined primarily by the amount of iron and nickle within the core, which will not change over time. However, there will be a temperature effect on the radius due to thermal expansion, but this will be quite small, as thermal expansion coefficients of metals are small. On top of that, the effect of density increase within the liquid core due to decreasing temperature, will be offset in part by growth of the solid core, which for iron at the melting line has a lower density than the liquid phase.
Henk do not mix radiogenic heat of the mantle with that of the core.
The first wikipediea article is correct (but, as scientists, we should refer to regular peer-reviewed scientific articles, not to popular webistes). About half of the power released from the Earth (~44-47 TW) comes from radiogenic heat (estimates range from ~10 to ~30 TW). I confirm that Earth's core has virtually no 235U, 238U, 232Th and 40K.
As concerns the second wikipedia article I can say that we know for about one century that Earth's core is made up mostly by a Fe-Ni-rich metal alloy. We do not need wikipedia to remind us this feature. I am not questioning if the Fe-Ni amount in the core varies with time.
My original question remains there: what is the rate of liquid core radius decrease per year by cooling (i.e. by heat transfer to the overlying mantle)?
Cheers,
michele
Hi everybody,
I found the answer by myself in the article of Hirose et al. 2013 (Composition and state of the core. Annual Review of Earth and Planetary Sciences, 41, 657-691).
These authors state that a likely growth rate of the inner core is 570 m/Myr (i.e., 570 km/Gyr).
The same article reports that the age of the inner core is quite recent, estimated to about 870 Ma.
Cheers,
michele
P.S. Also these authors consider negligible the radiogenic heat of the core.
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