Riner, M. A., C. R. Bina, and M. S. Robinson, Revisiting the decompressed density of Mercury, Meteoritics and Planetary Science, 41, Supplement, Proceedings of 69th Annual Meeting of the Meteoritical Society, Zurich, A149, 5377, 2006.
Introduction: Mercury is unique among the terrestrial planets in terms of its low mass (3.302 x 1023 kg) and high average density (5.427 g/cc) that together imply an iron-rich composition relative to Venus, Earth, Mars and the Moon. Typically planetary bulk density is converted to decompressed density to allow meaningful interplanetary comparisons. The methodology used to calculate planetary decompressed density is not well documented in the scientific literature. Meaningful interpretations of decompressed density values require a clear elucidation of assumptions and methodology. In this abstract we present a detailed calculation of decompressed density for Mercury along with an analysis of the sensitivity of the method and implications for scientific interpretations of Mercury's decompressed density.
Method: The model uses a second-order Birch-Murnaghan equation of state to calculate Mercury's self compression, assuming an adiabatic temperature profile within the mantle and core [e.g. 1]. The temperature difference at the core mantle boundary is represented by the difference between the mantle and core adiabats extrapolated to zero pressure, ΔTk. We assume a constant thermal expansion coefficient (α = 2.5 x 10-5 K-1).
The model is constrained by the observed total mass and total radius. Unfortunately the moment of inertia of Mercury is poorly constrained because Mercury rotates so slowly that non-hydrostatic contributions to the second degree gravitational potential coefficient, J2, are larger than the hydrostatic contribution [e.g. 2]. The model was applied to over 8000 random scenarios using the range of values shown in Table 1. The parameter values for the core are selected to cover a range of compositions (Fe and FeS) and phase (liquid and solid) . The effect of light alloying elements on the bulk modulus of iron is poorly understood; the endmembers of the range used here are published experimental values [4-5].
|ρm0 (g/cc)||ρk0 (g/cc)||KSm0 (GPa)||KSk0 (GPa)||Rk (km)||ΔTk (K)|
Table 1 – From left to right the columns indicate the range of values for mantle density, core density, bulk moduli of mantle and core, (all at zero-pressure and 300K) core radius, and the temperature difference between the mantle and core adiabats extrapolated to zero pressure.
Results: The model estimates the decompressed density of Mercury is 5.1±0.1 (1σ). The full range of plausible values is 4.84 to 5.27 g/cc. For reasonable mantle and thermal inputs a pure iron core (8.2 g/cc, 210GPa) is 1770km while a iron with 10 wt% sulfur core (5.4 g/cc, 60GPa) is 2190km.
Conclusions: The most probable value for Mercury's decompressed density is 5.1 g/cc. Our model is most sensitive to the bulk modulus of the core due to the wide range of plausible values reflecting uncertainty in the effect of light alloying elements on the compressibility of iron. Improved knowledge of the moment of inertia of Mercury may not improve decompressed density estimates without a better understanding of the compressibility of iron and iron alloys.
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