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Abstract
Abstract By plotting empirical chemical element abundances on Earth relative to the Sun and normalized to silicon versus their first ionization potentials, we confirm the existence of a correlation reported earlier. To explain this, we develop a model based on principles of statistical physics that predicts differentiated relative abundances for any planetary body in a solar system as a function of its orbital distance. This simple model is successfully tested against available chemical composition data from CI chondrites and surface compositional data of Mars, Earth, the Moon, Venus, and Mercury. We show, moreover, that deviations from the proposed law for a given planet correspond to later surface segregation of elements driven both by gravity and chemical reactions. We thus provide a new picture for the distribution of elements in the solar system and inside planets, with important consequences for their chemical composition. Particularly, a 4 wt% initial hydrogen content is predicted for bulk early Earth. This converges with other works suggesting that the interior of the Earth could be enriched with hydrogen.
Highlights
According to the most widely accepted model, the solar system formed from the gravitational collapse of a fragment of a giant molecular cloud (Brahic 2006)
The elemental composition of the most primitive accreting material before condensation is supposed to be similar to the carbonaceous Ivuna- (CI) chondrites, meteorites that are considered the least chemically fractionated when relative abundances are compared to the photosphere (McSween & Huss 2010)
We show in the Appendix A (Figures A4 and A5) that temperatures of condensation of 50% of the mass into the most stable mineral, 50% Tc, are very poorly correlated to differentiation factors (R2 = 0.4 and 0.2 with and without noble gases, respectively) as well as to ionization potential (IP)
Summary
According to the most widely accepted model, the solar system formed from the gravitational collapse of a fragment of a giant molecular cloud (Brahic 2006). For very large distances, the ratio of ionized over neutral atoms approaches 1, even for the elements with the higher IPs, the flux of highly energetic photons received by any atom from the hot central body decreases as d−2 This apparent paradox can be solved considering that if the ionization probability of an atom per unit time decreases, being proportional to the flux of photons, the timescale to reach thermal equilibrium with the cosmic background, i.e., heat the cold and dilute ions up to TCB by transfer of energy from the hot electrons, may increase indefinitely. Equation (1) implies that all elements will become fully ionized at a large distance from the proto-Sun, while this translates from Equation (6) into differentiation factors approaching 1 for all elements, i.e., all atoms stay trapped in orbit by Lorenz forces able to sustain gravitational attraction We can infer that for d < 1 au, electrons excited in the plasma are close to gravitational equilibrium, while they have an excess of kinetic energy for d 1 au
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