The interior structure of Mercury: what we know, what we expect from BepiColombo
Introduction
The BepiColombo mission scheduled for launch to Mercury in 2009 and to arrive at the planet in 2011 will provide a chance to get high-resolution gravity and topography data from Mercury and to measure the tidal Love numbers of the planet. According to the prospected mission scenario outlined in the BepiColombo System and Technology Report (ESA, 2000) the planetary orbiter, a 3 axis stabilised nadir pointing remote sensing spacecraft, will orbit the planet for a nominal mission duration of about one terrestrial year. The orbit will be nearly polar with a period of , a periherm altitude of , where the most accurate measurements can be taken, and an apoherm altitude of . During the nominal mission duration the planet's surface will be covered completely once at periherm altitude.
Among the scientific goals of the mission are a better exploration of the interior structure and chemistry of the planet which in part motivates the inclusion of a radio science experiment and a laser altimeter in the strawman payload. Other science goals of the radio science experiment are related to general relativity and the time rate of change of the gravitational constant G. In this paper, we review the present knowledge of the interior structure of Mercury and show how the data expected from BepiColombo can be used to significantly improve on our knowledge. In particular, we will address the possible estimates of the core radius and density, the state of the core and the radius of a possible solid inner core. In addition, we will discuss whether or not an undulation of the core–mantle boundary could be seen in the gravity field data.
During the two encounters of the Mariner 10 spacecraft with Mercury in March 1974 and March 1975 measurements of the planet's mass and the two second degree gravitational coefficients, J2 and C22, were obtained from radio Doppler and range data. The planet's radius of was inferred from radio occultation observations. The determinations of the mass and radius gave a mean density of , the largest density of the terrestrial planets. A combined least-squares fit to the Doppler data provided values of J2=(6.0±2.0)×10−5 and C22=(1.0±0.5)×10−5 (Anderson et al., 1987 with Guiseppe Colombo, by the way). The large value of J2 in spite of the planet's slow rotation period of 58.6462 days has been interpreted to be due to non-hydrostatic contributions to the polar oblateness of the gravity field, whereas the value of C22 indicates that the equatorial principal moment of inertia (MOI) are different from each other. Since a correction of J2 for non-hydrostatic contributions to the gravity field is not possible at the present time, its value cannot be used to estimate the moment of inertia or the first moment of the density distribution, a useful quantity for interior structure models. To determine its value is one of the primary targets of most space missions to Mercury proposed to date including BepiColombo. A rough estimate from J2 places its value at , where M is the mass and R is the planet's (volume) average surface radius.
The interior structure of Mercury can thus at present only be modelled on the basis of the known mass of the planet and its radius. Simple models of Mercury's interior structure have been presented by e.g., BVSP (1981) and most recently by Harder and Schubert (2001). (An example of a simple two-layer model with a core and a silicate shell that we will use as a basis for our discussion in the next section is shown in Fig. 1.) In addition to the mass and radius, general perceptions about the chemistry and structure of terrestrial planets and the likely densities of prime chemical reservoirs such as a basaltic crust, a chemically more primitive mantle and an iron-rich core have been invoked.
Ground-based radar ranging data have recently been used to determine the equatorial elliptical shape of Mercury and to discuss implications for the internal structure (Anderson et al., 1996). The centre of figure (CF) has been concluded to be shifted with respect to the planet's centre of mass (CM) by in the equatorial plane. The equatorial CF–CM offset has been interpreted to indicate a hemispheric asymmetry in crustal thickness. Assuming a representative density contrast between crust and mantle, the hemispherically averaged excess crustal thickness has been estimated to be about which is comparable to that of the Moon. An average crustal thickness of has been calculated by comparison of Mercury's equatorial ellipticity to the gravitational coefficient C22 and assuming that the equatorial ellipticity is isostatically compensated due to Airy isostasy (Anderson et al., 1996).
Mercury's average density is exceptionally large for a body of its size. Reduced to standard conditions, and room temperature, to account for self compression and temperature, it is at much larger than that of any other terrestrial planet. For example, the corresponding value for the Earth is only and that of Mars is . This peculiarity indicates that the mass concentration of iron, calculated to be in Mercury (Wasson, 1988), should be about twice that in the Earth, , and suggests an extremely large iron core of 1800– radius that comprises roughly half of the planetary mass. If Mercury formed by condensation from the solar nebula at its present position then it should be strongly depleted in volatiles such as sulphur (e.g., Lewis 1972, Lewis 1988; Goettel, 1988) and the core should be composed of almost pure iron. Only small amounts of a light alloying constituent in the core are then expected.
The silicate shell, the mantle and the crust, must be thin (Fig. 1), 500– in total, with possibly important consequences for tectonics and volcanism. Convection in a planetary mantle depends on the ratio between the planet and core radii. For a thin shell such as the mantle of Mercury, it is expected that the convection pattern will feature a comparative large number of small scale cells (Fig. 2) since the width of the cells should be a few times the thickness of the mantle. This will tend to homogenise the tectonic patterns on the surface. Indeed, the tectonic pattern on the known part of the surface of the planet looks relatively smooth, albeit scarred by impacts, similar to that of the Moon and quite different from that of Mars. As a caveat, however, we note that there is some indication in terrestrial radar data of a possible giant volcanic dome in the unmapped area (Harmon, 1997). A confirmation of the existence of this dome, if it exists, and its subsequent mapping by high resolution imaging will be extremely valuable and will provide interesting constraints on mantle heterogeneity.
Pressure, density, temperature and elastic moduli should vary relatively little through the thin crust and mantle. A discontinuity is expected at the crust–mantle boundary, where the density would jump from around to about . Major phase transition boundaries in the mantle are unlikely because of the small pressure. The pressure at the core–mantle boundary is only about . Chemical layering and an asthenosphere, a partially molten (upper) mantle layer, are however possible. The latter is suggested by recent thermal history calculations (Conzelmann, 1999; Conzelmann and Spohn, 1999). If detected, these layers would provide interesting clues to the accretion, differentiation, and volcanic and tectonic histories of the planet. If the above estimates of the crust thickness of are correct then this would imply the most voluminous crust relative to the mantle among the terrestrial planets and could only be due to substantial partial melting in the mantle over its thermal history.
Perhaps the most important unknowns are related to the size, composition and physical state of the unusually large core. Since it is most likely that the magnetic field observed by Mariner is generated by a hydromagnetic dynamo or, alternatively, a thermoelectric dynamo in the core (Stevenson, 1987), at least an outer shell of the core of perhaps should be liquid. The liquid shell would have formed as a result of planetary cooling and core freezing from a hot initial state with an entirely molten core (e.g., Stevenson et al., 1983; Schubert et al., 1988). The core cannot consist of pure iron under these circumstances because it would be difficult to keep an iron core from completely freezing, as cooling models suggest. A small concentration of sulphur has been postulated (Stevenson et al., 1983) to account for a molten shell because sulphur is well known to depress the freezing point of a core alloy. Moreover, a small amount of sulphur can be reconciled with cosmochemical models that usually take Mercury's composition to be refractory because of its assumed formation close to the sun where temperatures were likely to be high in the early history of the solar nebula. Due to solid inner core growth, the sulphur concentration would become enriched in the outer core shell and the increasing depression of the freezing point would keep an outer layer liquid in spite of planet cooling. The inner core is almost pure iron in this model. Older thermal history models (e.g., Stevenson et al., 1983; Schubert et al., 1988; Spohn, 1991) based on a parameterisation of convective heat transport through the mantle invoked sulphur concentrations in the core between 1% and 5% to keep the core from freezing over the planet's lifetime. Tidal heating in the inner core has also been demonstrated to help in keeping a liquid outer core shell (Schubert et al., 1988). Recent calculations based on a more complete description of mantle convection and incorporating pressure and temperature dependent rheology (Conzelmann and Spohn, 1999) suggest that a terrestrial planet cools mostly by thickening its lithosphere (the outer rigid shell of the planet) while the deep interior stays relatively hot (Fig. 2). These models, in principle, confirm the findings of the older models but predict thicker outer core layers at the same sulphur concentration. The models have little difficulty in keeping a liquid layer in the core, even for sulphur concentrations as small as 0.1%.
The thermo-electric dynamo of Stevenson (1987) requires topographic variations of the core–mantle boundary of the order of a few kilometres in addition of a liquid outer core layer. These variations may perhaps be detected by gravity sounding of the planet.
Section snippets
Modelling the interior structure
Gravity sounding is, at present, the prime method for the exploration of the interior of Mercury and other terrestrial planets in the absence of seismic data. As we will show below, these interpretations will not be unique and self-consistent but will rely on additional information, in particular from chemistry. The BepiColombo mission will measure the components of the spherical harmonic expansion of the gravity field with an accuracy of 10−9 for degree l=2 decreasing to 10−8 for l=20. The
Discussion and conclusions
We have discussed the use of the gravity data expected from the BepiColombo mission to improve on our knowledge about the interior structure and composition of Mercury. The confidence we can have in our present models of Mercury depends mainly on the confidence we have in the values of the silicate shell density and core average densities. Cosmochemical considerations are essential here. For instance, it almost goes without saying that the core should be composed mostly of iron. Moreover, the
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