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 10^{23} 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, ΔT_{k}. 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, J_{2}, are larger than the hydrostatic contribution [e.g. 2]. The model was applied to 1300 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) [3].
ρ_{m}^{0} (g/cc) | ρ_{k}^{0} (g/cc) | K_{Sm}^{0} (GPa) | K_{Sk}^{0} (GPa) | R_{k} (km) | ΔT_{k} (K) | |
Values | 3.35±0.25 | 6.4 ±1.4 | 180±30 | 170±40 | 2000±400 | 500±500 |
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: Model scenarios with the lowest mass errors (±10^{19} kg) have decompressed densities between 5.19 and 7.38 g/cc. The larger values for decompressed density correspond to larger core radii counterbalanced, to match the total mass, by low core densities, high core bulk moduli and/or hot core adiabats. Restricting the core radius to <2200km (rather than <2400km) results in decompressed density values between 5.19 and 6.38 g/cc.
Conclusions: Due to the uncertainty in the moment of inertia factor, core size, and the core and mantle density for Mercury, accurate calculation of the decompressed density is not possible at this time. Thus the commonly held assumption that, due to its small mass, the decompressed density of Mercury is well constrained at 5.3 g/cc is still open to question. However, application of this model to the Earth indicates that the decompressed density of the Earth is well constrained (±0.1 g/cc), even with variations in the mantle and core density and core size, as long as the total mass, total radius and moment of inertia factor constraints are met. Measurement of the moment of inertia for Mercury would better constrain the decompressed density.
References: [1] Stacey, F.D. 1992. Physics of the Earth. Brookfield Press. [2] Ness, N.F. 1978. Space Sci. Rev. 21:527-553. [3] Harder H. and Shubert G. 2001. Icarus 151:118-122.
Note: This published abstract contains significant errors; a corrected version is available here.
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