On the cooling of the moon by solid convection

If a molten, or partially molten, lunar core exists at present, constraints would be placed on the viscosity of the solid mantle and the distribution of radioactive heat sources. Models in which the heat sources have been concentrated near the surface would rapidly solidify if the effective viscosity was equal to, or less than, 10²² cm² s⁻¹. Retention of most of the heat sources throughout the mantle would permit present day solid convection to occur without cooling the core.     

Magnetism of the moon

The Malkus theory of a precessionally driven magnetoturbulence in a liquid core is applied to the Moon. It is shown that a lunar magnetic field requires the presence of a non-metallic core at at least 2500K or of an iron core at at least 2000K. Within the limits of our present knowledge these requirements may have been satisfied in the past. A new mechanism is proposed which is based on tidal effects in the outer solid and liquid shells whose existence is suggested by measurements of lunar radioactivity. This mechanism could account for the generation of local rather than poloidal fields at low latitudes in agreement with observation.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Thermal evolutions of the terrestrial planets

The thermal evolution of the Moon, Mercury, Mars, Venus and hypothetical minor planets is calculated theoretically, taking into account conduction, solid-state convection, and differentiation. An assortment of geological, geochemical, and geophysical data is used to constrain both the present day temperatures and thermal histories of the planets' interiors. Such data imply that the planets were heated during or shortly after formation and that all the terrestrial planets started their differentiations early in their history. Initial temperatures and core formation play the most important roles in the early differentiation. The size of the planet is the primary factor in determining its present day thermal state. A planetary body with radius less than 1000 km is unlikely to reach melting given heat source concentrations similar to terrestrial values and in the absence of intensive early heating such as short half-life radioactive heating and inductive heating.Studies of individual planets are constrained by varying amounts of data. Most data exist for the Earth and Moon. The Moon is a differentiated body with a crust, a thick solid mantle and an interior region which may be partially molten. It is presently cooling rapidly and is relatively inactive tectonically.Mercury most likely has a large core. Thermal calculations indicate it may have a 500 km thick solid lithosphere, and the core may be partially molten if it contains some heat sources. If this is not the case, the planet's interior temperatures are everywhere below the melting curve for iron. The thermal evolution is dominated by core separation and the high conductivity of iron which makes up the bulk of Mercury.Mars, intermediate in size among the terrestrial planets, is assumed to have differentiated an Fe–FeS core. Differentiation and formation of an early crust is evident from Mariner and Viking observations. Theoretical models suggest that melting and differentiation of the mantle silicates has occurred at least up until 1 billion years ago. Present day temperature profiles indicate a relatively thick (250 km) lithosphere with a possible asthenosphere below. The core is molten.Venus is characterized as a planet similar to the Earth in many respects. Core formation probably occurred during the first billion years after the formation. Present day temperatures indicate a partially molten upper mantle overlain by a 100 km thick lithosphere and a molten Fe–Ni core. If temperature models are good indicators, we can expect that today, Venus has tectonic processes similar to the Earth's.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.     

Stress differences in the moon as an evidence for a cold moon

Assuming that the lateral variations of density in the lunar crust, the crustal density anomalies, are responsible for the lateral undulations of the lunar gravitational potential, we compute these anomalies for four different lunar models, which include an entirely solid Moon and three different solid lunar models with partially molten layers located within 600 km depth. The stress differences created by the density anomalies are determined for these models. It is found that, since the formation of the mascons, the entirely solid lunar model should have supported stress differences of the order of 70 bars while in the case of the other models, the solid layer overlying the partially molten one should have supported stress differences of more than 100 bars. The high stress differences associated with the partially molten models lead us to conclude that these models are not proper ones, and thus the Moon has always been solid since the formation of the mascons. Lunar Science Institute Contribution No. 97. The research in this paper was done while the author was a Visiting Scientist at the Lunar Science Institute, which is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

Synthesis and stability of iron nanoparticles for lunar environment studies

Abstract– Simulants of lunar dust are needed when researching the lunar environment. However, unlike the true lunar dust, today’s simulants do not contain nanophase iron. Two different processes have been developed to fabricate nanophase iron to be used as part of a lunar dust simulant. (1) The first is to sequentially treat a mixture of ferric chloride, fluorinated carbon, and soda lime glass beads at about 300 °C in nitrogen, at room temperature in air, and then at 1050 °C in nitrogen. The product includes glass beads that are gray in color, can be attracted by a magnet, and contains α‐iron nanoparticles (which seem to slowly lose their lattice structure in ambient air during a period of 12 months). This product may have some similarity to the lunar glassy agglutinate, which contains FeO. (2) The second is to heat a mixture of carbon black and a lunar simulant (a mixed metal oxide that includes iron oxide) at 1050 °C in nitrogen. This process simulates lunar dust reactions with the carbon in a micrometeorite at the time of impact. The product contains a chemically modified simulant that can be attracted by a magnet and has a surface layer whose iron concentration increased during the reaction. The iron was found to be α‐iron and Fe₃O₄ nanoparticles, which appear to grow after the fabrication process. This growth became undetectable after 6 months of ambient air storage, but may last for several years or longer.     

The evolution of the moon

The thermal evolution of the Moon as it can be defined by the available data and theoretical calculations is discussed. A wide assortment of geological, geochemical and geophysical data constrain both the present-day temperatures and the thermal history of the lunar interior. On the basis of these data, the Moon is characterized as a differentiated body with a crust, a 1000-km-thick solid mantle (lithosphere) and an interior region (core) which may be partially molten. The presence of a crust indicates extensive melting and differentiation early in the lunar history. The ages of lunar samples define the chronology of igneous activity on the lunar surface. This covers a time span of about 1.5 billion yr, from the origin to about 3.16 billion yr ago. Most theoretical models require extensive melting early in the lunar history, and the outward differentiation of radioactive heat sources.Thermal history calculations, whether based on conductive or convective computation codes define relatively narrow bounds for the present day temperatures in the lunar mantle. In the inner region of the 700 km radius, the temperature limits are wider and are between about 100 and 1600°C at the center of the Moon. This central region could have a partially or totally molten core.The lunar heat flow values (about 30 ergs/cm²s) restrict the present day average uranium abundance to 60 ± 15 ppb (averaged for the whole Moon) with typical ratios of K/U = 2000 and Th/U = 3.5. This is consistent with an achondritic bulk composition for the Moon.The Moon, because of its smaller size, evolved rapidly as compared to the Earth and Mars. The lunar interior is cooling everywhere at the present and the Moon is tectonically inactive while Mars could be and the Earth is definitely active.     

Temperature gradients at the core-mantle interface

Heat flowing out of the core must flow into the mantle. If the Earth's magnetic field is owing to adiabatic magnetohydrodynamic circulation of the outer core, whole mantle convection or melting at the core mantle boundary is required to keep the inner core from becoming isothermal, thereby preventing adiabatic circulation.Alternatively, the outer core fluid must have some unexpected and exotic property such as an extremely low coefficient of thermal expansion and resultant low Gruneisen's parameter.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973. Publication No. 1046 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Calif., U.S.A.     

Does the Moon Have a Metallic Core?: Constraints from Giant Impact Modeling and Siderophile Elements

The issue of whether the Moon has a small metallic core is reexamined in light of new information: improved dynamical modeling, new constraints on core size, and high temperature and pressure metal-silicate partition coefficients. Addressed specifically is the question of whether the Moon's siderophile element budget can be explained by derivation of the Moon from a differentiated impactor or proto-Earth (stage 1), followed by formation of a small metallic core within the Moon (stage 2). If the Moon is made of mantle material from either a “hot” impactor or a “warm” impactor or proto-Earth, a small metallic core (0.7 to 2 mass%) is predicted. If the Moon is made from mantle material from a “hot” proto-Earth, the lunar mantle would be more depleted in W or Re than is observed. Scenarios in which the Moon is made from impactor or proto-Earth mantle material that has equilibrated with metal at low pressures and temperatures (“cold” scenarios) would yield a much larger metallic core than observed. Finally, the greater depletions of Ni, Mo, and Re in the Moon (relative to the Earth) can be explained by low PT and reduced metal-silicate equilibrium in an impactor without later core formation in the Moon (i.e., no stage 2), but depletions of Co, Ga, and W cannot. Altogether, geochemically unlikely or geophysically inadequate non-metallic core alternatives, substantial geophysical evidence for a metallic core, and the successful models presented here for siderophile element depletions all favor the presence of a small lunar metallic core. Previous geochemical objections to an impactor origin of the Moon are eliminated because siderophile element concentrations in the lunar mantle are consistent with separation of a small core from a bulk Moon derived from impactor mantle material.     

Frozen fields

Magnetic fields due to permanent magnetization of planetary crusts and interiors have been clearly detected only for the Earth and Moon. However, they are likely to be a ubiquitous property of silicate and partially silicate objects in the solar system. An indication that this is true is the recent indirect evidence from the Galileo flybys that the asteroids Gaspra and Ida have intrinsic magnetic fields. Lunar paleomagnetism differs substantially from terrestrial paleomagnetism in part because the dominant ferromagnetic carriers are metallic Fe-Ni grains rather than iron oxides such as magnetite. The distribution of metallic iron remanence carriers on the Moon is influenced strongly by impact processes. In addition, large-scale lunar impacts may have produced transient magnetic fields capable of imparting magnetization with or without a former core dynamo. An unresolved issue of lunar paleomagnetism is the origin of swirl-like albedo markings associated with the strongest magnetic anomalies detected from orbit. The interpretation of solar wind magnetic field perturbations during the Gaspra and Ida flybys as due to intrinsic asteroidal magnetic fields has been supported by detailed magnetohydrodynamic simulations. The inferred magnetization limits for Gaspra are consistent with a wide variety of meteorite types and do not allow firm constraints to be imposed on Gaspra's bulk composition.     

Post-imbrian global lunar tectonism: Evidence for an initially totally molten Moon

Evaluation of all reasonable sources of stress in the lunar crust indicates that compressional thermoelastic stresses are the only ones which have been tectonically significant on the global scale during the last 3.5×10⁹ yr of lunar history — i.e., the post-Imbrian. However, the thermoelastic stresses calculated for lunar models which have accretional heating profiles at the beginning of lunar history; i.e., a molten zone only a few hundred kilometers deep and a cool deep interior, are less than 1 kbar in the crust. Such stresses are lower than the more than 1 to 7 kbar needed to initiate thrust faulting in the outer crust according to Anderson's theory of thrust faulting. Thus such accretional models predict that no significant global thrust faulting has occurred during the post-Imbrian and that the crust should currently be seismically quiet on the global scale.In contrast, the compressional thermoelastic stresses generated in a Moon which was initially totally molten, as is the case if the Moon formed by fission, are up to 3.5 kbar in the outer few km of the crust at present. These stresses are well within the range needed to cause thrust faulting in the outer 4 km of the crust. According to this model there should be modest scale (10 km), young ( 0.5 to 1×10⁹ yr old) thrust fault scarps in the highlands.Photoselenological investigations confirm that scarps with the expected age and geometric characteristics are found in the highlands. Thus the currently available photoselenological data support the stress model derived for an initially totally molten Moon, but not one which was molten only in the outer few hundreds of km.     

New Trends in the Development of the Lunar Physical Libration Theory

A review of the modern state of the lunar libration theory is presented. A significant progress in the lunar investigation is achieved due to the simultaneous processing of results of the satellite Doppler tracing and of the lunar laser ranging. The data evidencing existence of a small iron core in the Moon are discussed. In this connection, the further development of the theory of rotation of the Moon presents the study of internal structure and dynamics of a lunar body. A model of a two-layer Moon can have a very advanced application to explain some observed phenomena and to be as a first approach in the modelling of internal processes determining the lunar rotation.     

The moon after Apollo

The Apollo missions have gradually increased our knowledge of the Moon's chemistry, age, and mode of formation of its surface features and materials Apollo 11 and 12 landings proved that mare materials are volcanic rocks that were derived from deep-seated basaltic melts about 3.7 and 3.2 billion years ago, respectively. Later missions provided additional information on lunar mare basalts as well as the older, anorthositic, highland rocks. Data on the chemical make-up of returned samples were extended to larger areas of the Moon by orbiting geochemical experiments. These have also mapped inhomogeneities in lunar surface chemistry, including radioactive anomalies on both the near and far sides.Lunar samples and photographs indicate that the moon is a well-preserved museum of ancient impact scars. The crust of the Moon, which was formed about 4.6 billion years ago, was subjected to intensive metamorphism by large impacts. Although bombardment continues to the present day, the rate and size of impacting bodies were much greater in the first 0.7 billion years of the Moon's history. The last of the large, circular, multiringed basins occurred about 3.9 billion years ago. These basins, many of which show positive gravity anomalies (mascons), were flooded by volcanic basalts during a period of at least 600 million years. In addition to filling the circular basins, more so on the near side than on the far side, the basalts also covered lowlands and circum-basin troughs.Profiles of the outer lunar skin were constructed from the mapping camera system, including the laser altimeter, and the radar sounder data. Materials of the crust, according to the lunar seismic data, extend to the depth of about 65 km on the near side, probably more on the far side. The mantle which underlies the crust probably extends to about 1100 km depth. It is also probable that a molten or partially molten zone or core underlies the mantle, where interactions between both may cause the deep-seated moonquakes.The three basic theories of lunar origin—capture, fission, and binary accretion—are still competing for first place. The last seems to be the most popular of the three at this time; it requires the least number of assumptions in placing the Moon in Earth orbit, and simply accounts for the chemical differences between the two bodies. Although the question of origin has not yet been resolved, we are beginning to see the value of interdisciplinary synthesis of Apollo scientific returns. During the next few years we should begin to reap the fruits of attempts at this synthesis. Then, we may be fortunate enough to take another look at the Moon from the proposed Lunar Polar Orbit (LPO) mission in about 1979.     

Properties of the hermean regolith: iii. disk-resolved vis-NIR reflectance spectra and implications for the abundance of iron

Disk-resolved reflectance spectra of the surface of Mercury (longitudes 240-300°), obtained in the visual (vis) and near-infrared (NIR) spectral region, are presented and analyzed. The observations were made at the 2.6-m Nordic Optical Telescope with the ALFOSC low-resolution spectrograph on 20 and 22 June 1999 in the wavelength range 520-970 nm with a footprint size of 700 km on the mid-disk of Mercury. A method which enables more accurate correction for telluric line absorptions and atmospheric extinction than that applied on previously published vis-NIR spectra of Mercury is introduced. The resulting reflectance spectra are remarkably linear, lack significant absorption features, and have optical slopes comparable to remotely sensed lunar pure anorthosites. The relation between spectral slope and photometric geometry found by Warell (2002, Icarus 156, 313-317) is confirmed and is explained as caused by strongly backscattering particles with embedded submicroscopic metallic iron in a mature regolith. With the theoretical maturation model of Hapke (2001, J. Geophys. Res. 106 (E5), 10039-10073) an abundance of 0.05-0.3 wt% submicroscopic metallic iron in the regolith for silicate grain sizes in the range 10-80 μm is determined, implying a ferrous iron content in mafic minerals intrinsically lower than that of the lunar highlands. A binary crustal composition model with anorthite linearly mixed with pyroxene provides better spectral fits than a pure anorthitic composition. Comparison with mature lunar pure anorthosite spectra yields a confident upper limit to the FeO content of 3 wt% under the assumption that the surfaces are similarly matured, but this figure probably represents a considerable overestimate. The average mercurian regolith does not seem to be substantially more weathered than the most mature lunar highland soils in terms of abundance of submicroscopic metallic iron, indicating that a steady-state maturation level has been reached. However, the strong relation between optical spectral slope and photometric geometry may imply that the majority of regolith particles are more fine-grained than their lunar counterparts and that the regolith is admixed with complex agglutinate weathering products which are more abundant and more transparent than those of the lunar highlands. This is consistent with more energetic impacts and a higher rate of impact melt production in an iron-poor regolith. An observed relation between the spectral slope and latitude provides evidence that the Ostwald ripening process may be operating at equatorial latitudes on Mercury.     

Lunar heat flow and regolith structure inferred from interferometric observations at a wavelength of 49.3 cm

We discuss observations of the Moon at a wavelength of 49.3 cm made with the Owens Valley Radio Observatory Interferometer. These observations have been fit to models in order to estimate the lunar dielectric constant, the equatorial subsurface temperature, the latitude dependence of the subsurface temperature, and the subsurface temperature gradient. The models are most consistent with a dielectric constant of 2.52 ± 0.01 (formal errors), an equatorial subsurface temperature of 249_?5⁺⁸K, and a change in the subsurface temperature with latitude (ψ), which is proportional to cos^0.38ψ. Since the temperature of the Moon has been measured by the Apollo Lunar Heat Flow Experiment, we have been able to use our determination of the equatorial temperature to estimate the error in the flux density calibration scale at 49.3cm (608 MHz). This results in a correction factor of 1.03 ± 0.04, which must be applied to the flux density scale. This factor is much different from 1.21 ± 0.09 estimated by Muhleman et al. (1973) from the brightness temperature of Venus and apparently indicates that the observed decrease in the brightness temperature of Venus at long wavelengths is a real effect.The estimates of the temperature gradient, which are based on the measurement of limb darkening, are small and negative (temperature decreases with depth) and may be insignificantly different from zero since they are only as large as their formal errors. We estimate that a temperature gradient in excess of 0.6K/m at 10m depth would have been observed. Thus, a temperature gradient like that measured in situ at the Apollo 15 and 17 landing sites in the upper 2m of the regolith is not typical of the entire lunar frontside at the 10m depths where the 49.3 cm wavelength emission originates. This result may indicate that the mean lunar heat flow is lower than that measured at the Apollo landing sites, that the thermal conductivity is greater at 10m depth than it is at 2m depth, or that the radio opacity is greater at 10m depth than at 2m depth. The negative estimates of the temperature gradient indicate that the Moon appeared limb bright and might be explained by scattering of the emission from boulders or an interface with solid rock. The presence of solid rock at 10m depths will probably cause heat flows like those measured by Apollo to be unobservable by our interferometric method at long wavelengths, since it will cause both the thermal conductivity and radio opacity of the regolith to increase. Thus, our data may be most consistent with a change in the physical properties of the regolith to those of solid rock or a mixture of rock and soil at depths of 7 to 16m. Our results show that future radio measurements for heat flow determinations must utilize wavelengths considerably shorter than 50 cm (25 cm or less) to avoid the rock regions below the regolith.     

Planck mean efficiency factors for six material candidates as interstellar grains

Planck mean absorption cross-sections have been computed for spherical grains composed of graphite, iron, ice, olivine, amorphous quartz and a lunar silicate. Experimentally determined infrared optical constants have been used for all these materials. Ice mantle particles and planetesimal particles (iron core and olivine mantle) have also been considered with values of outer and inner radii covering a wide range of astrophysical conditions.The results given both graphically and in a tabular form are discussed and compared with those of other authors. The relationships of mantle and core properties are also critically discussed.     

The significance of observed rotational magnetic hysteresis in lunar samples

Rotational Magnetic hysteresis (W _R ) curves for lunar soils 10084, 12070, 14259, and rock 14053, have been published. There is no adequate explanation to date for the observed largeW _R at high fields. Lunar rock magnetism researchers consider fine particle iron to be the primary source of stable magnetic remanence in lunar samples. Iron has cubic anisotropy with added shape anisotropy for extreme particle shapes. The observed high fieldW _R must have its source in uniaxial or unidirectional anisotropy. This implies the existence of minerals with uniaxial anisotropy or exchange coupled spin states. Therefore, the source of this observed high fieldW _R must be identified and understood before serious paleointensity studies are made. It is probable that the exchange coupled spin states and/or the source of uniaxial anisotropy responsible for the high fieldW _R might be influenced by the lunar surface diurnal temperature cycling. The possible sources of high fieldW _R in lunar samples are presented and considered.     

The optical effects of small iron particles that darken but do not redden: Evidence of intense space weathering on Mercury

Submicroscopic iron particles larger than about 50 nm, infused throughout mineral grains or glasses, are abundant in planetary materials altered by their environment such as shocked meteorites and lunar agglutinate glasses. Such particles darken their host material but do not redden their spectra but to date there has been no theoretical treatment of their optical effects. Using Mie theory, we modify the Hapke (2001) radiative transfer model of the effects of space weathering to include these effects. Comparison with laboratory measurements shows that the new treatment reproduces the relationship between submicroscopic iron size, abundance and reflectance. We apply this new model to near-IR spectra of Mercury recently obtained by the MESSENGER spacecraft and find that submicroscopic iron is much more abundant on Mercury than in lunar soils, with typical total submicroscopic iron abundances near 3.5 wt.% compared to about 0.5 wt.% for lunar soils We also find that the ratio of iron particles that darken but do not redden to the abundance of very small iron particles that impart the red slope to space weathered material is much larger than lunar (6 vs. 2). Both the total submicroscopic iron abundance and ratio of particle size fractions are consistent with the higher production of melt and vapor in micrometeorite impact on Mercury relative to the Moon (Cintala, 1992) that enables more accumulation of space weathering products before sequestration by regolith overturn. The radiative transfer model cannot directly constrain the abundance of opaque minerals on Mercury because of ambiguities between the darkening effects of opaques and submicroscopic iron particles larger than 50 nm, but assuming the opaques are the ultimate source of the submicroscopic iron, our results place a lower limit of 4-20 wt.% on opaque abundance on Mercury depending on the composition of the opaque phase and whether titanium metal also contributes to the space weathering effect.     

Precession of the lunar core

Goldreich (Goldreich, P. [1967]. J. Geophys. Res. 72, 3135) showed that a lunar core of low viscosity would not precess with the mantle. We show that this is also the case for much of lunar history. But when the Moon was close to the Earth, the Moon’s core was forced to follow closely the precessing mantle, in that the rotation axis of the core remained nearly aligned with the symmetry axis of the mantle. The transition from locked to unlocked core precession occurred between 26.0 and 29.0 Earth radii, thus it is likely that the lunar core did not follow the mantle during the Cassini transition. Dwyer and Stevenson (Dwyer, C.A., Stevenson, D.J. [2005]. An Early Nutation-Driven Lunar Dynamo. AGU Fall Meeting Abstracts GP42A-06) suggested that the lunar dynamo needs mechanical stirring to power it. The stirring is caused by the lack of locked precession of the lunar core. So, we do not expect a lunar dynamo powered by mechanical stirring when the Moon was closer to the Earth than 26.0-29.0 Earth radii. A lunar dynamo powered by mechanical stirring might have been strongest near the Cassini transition.     

Properties of the solar nebula and the origin of the moon

The basic geochemical model of the structure of the Moon proposed by Anderson, in which the Moon is formed by differentiation of the calcium, aluminium, titanium-rich inclusions in the Allende meteorite, is accepted, and the conditions for formation of this Moon within the solar nebula models of Cameron and Pine are discussed. The basic material condenses while iron remains in the gaseous phase, which places the formation of the Moon slightly inside the orbit of Mercury. Some condensed metallic iron is likely to enter the Moon in this position, and since the Moon is assembled at a very high temperature, it is likely to have been fully molten, so that the iron can remove the iridium from the silicate material and carry it down to form a small core. Interactions between the Moon and Mercury lead to the present rather eccentric Mercury orbit and to a much more eccentric orbit for the Moon, reaching past the orbit of the Earth, establishing conditions which are necessary for capture of the Moon by the Earth. In this orbit the Moon, no longer fully molten, will sweep up additional material containing iron oxide. This history accounts in principle for the two major ways in which the bulk composition of the Moon differs from that of the Allende inclusions.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

A magnetic dynamo in the moon?

The existence of fossil lunar magnetism has caused speculation that the Moon had, at one time, an internally produced dynamo magnetic field. Quantitative analysis of this idea, constrained by the largest iron lunar core compatible with observations, implies that the Moon would have had to rotate faster than its breakup angular velocity in order to support a dynamo magnetic field.A paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.