Contribution of tidal dissipation to lunar thermal history

The possible contributions of tidal heating to lunar thermal history are investigated. Analytic determinations of tidal dissipation in a homogeneous, incompressible Moon and in a two-layer Moon with a soft core and rigid mantle are given as a function of position in the Moon and as a function of Earth-Moon separation. The most recent information on the historical values of the lunar obliquity is employed, and we present results for the constant values of orbital eccentricity of e = 0.0 and e = 0.055. For a simplified orbital evolution and a dissipation factor Q = 100, the total increase in the mean lunar temperature for the homogeneous case does not exceed several tens of degrees. For the two-layer models the local dissipation may be enhanced over that of the homogeneous Moon by a factor of 5 for a core radius of 0.5 lunar radii and by a factor of 100 for a core radius of 0.95 lunar radii. The corresponding factors for the total dissipation are 3 and 15 for the two values of core radii, respectively. We conclude that tidal contributions to lunar thermal history are probably not important. But under special circumstances the enhanced dissipation in a two-layer Moon could have led to a spectacular thermal event.     

Secular tidal changes in lunar orbit and Earth rotation

Small tidal forces in the Earth–Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = \(-25.97\pm 0.05 ''/\)cent\(^{2}\), da/dt = 38.30 ± 0.08 mm/year, and di/dt = ?0.5 ± 0.1 \(\upmu \)as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives \(\sim \) \(3\times 10^{-12}\)/year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = \((1.50 \pm 0.10)\times 10^{-11}\)/year. For total dn/dt, there is \(\le \)1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is \(-1316 ''\)/cent\(^{2}\) or 87.5 s/cent\(^{2}\) for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 \(\upmu \)as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.     

The tidal loss of satellite-orbiting objects and its implications for the lunar surface

Tidal interactions, by altering spin and orbital parameters, can lead to the destruction of bodies in the solar system. Specifically, tidal interactions can rapidly decay the orbit of an object which revolves around a satellite. Hence, almost any object which once orbited a satellite would have impacted the satellite early in the history of the solar system. This may explain the absence of such objects today.The tidal loss of lunar-orbiting objects offers a solution to the problem of how objects may have been “stored” for ≈0.5 eons prior to impacting the Moon. The craters produced by the impacts of lunar-orbiting objects should have characteristic sizes, shapes, and ages. The Crisium and Serenitatis basins exhibit these characteristics, and, therefore, could have been produced by the impact of a lunar orbiting object. Finally, the possibility that the Imbrium and Crisium basins originated from one object, which fragmented prior to impact, is discussed.     

Duration and extent of lunar volcanism: Comparison of 3D convection models to mare basalt ages

It is widely accepted that lunar volcanism started before the emplacement of the mare fills ( b.p.) and lasted for probably more than 3.0 Ga. While the early volcanic activity is relatively easy to understand from a thermal point of view, the late stages of volcanism are harder to explain, because a relatively small body like the Earth's Moon is expected to cool rapidly and any molten layer in the interior should solidify rather quickly. We present several thermal evolution models, in which we varied the boundary conditions at the model surface in order to evaluate the influence on the extent and lifetime of a molten layer in the lunar interior. To investigate the influence of a top insulating layer we used a fully three-dimensional spherical shell convection code for the modelling of the lunar thermal history. In all our models, a partial melt zone formed nearly immediately after the simulation started (early in lunar history), consistent with the identification of lunar cryptomare and early mare basalt volcanism on the Moon. Due to the characteristic thickening of the Moon's lithosphere the melt zone solidified from above. This suggests that the source regions of volcanic rock material proceeded to increasing depth with time. The rapid growth of a massive lithosphere kept the Moon's interior warm and prevented the melt zone from fast freezing. The lifetimes of the melt zones derived from our models are consistent with basalt ages obtained from crater chronology. We conclude that an insulating megaregolith layer is sufficient to prevent the interior from fast cooling, allowing for the thermal regime necessary for the production and eruption of young lava flows in Oceanus Procellarum.     

Coupled convection and tidal dissipation in Europa’s ice shell

We performed 2D numerical simulations of oscillatory tidal flexing to study the interrelationship between tidal dissipation (calculated using the Maxwell model) and a heterogeneous temperature structure in Europa’s ice shell. Our 2D simulations show that, if the temperature is spatially uniform, the tidal dissipation rate peaks when the Maxwell time is close to the tidal period, consistent with previous studies. The tidal dissipation rate in a convective plume encased in a different background temperature depends on both the plume and background temperature. At a fixed background temperature, the dissipation increases strongly with plume temperature at low temperatures, peaks, and then decreases with temperature near the melting point when a melting-temperature viscosity of 10¹³ Pa s is used; however, the peak occurs at significantly higher temperature in this heterogeneous case than in a homogeneous medium for equivalent rheology. For constant plume temperature, the dissipation rate in a plume decreases as the surrounding temperature increases; plumes that are warmer than their surroundings can exhibit enhanced heating not only relative to their surroundings but relative to the Maxwell-model prediction for a homogeneous medium at the plume temperature. These results have important implications for thermal feedbacks in Europa’s ice shell.To self-consistently determine how convection interacts with tidal heating that is correctly calculated from the time-evolving heterogeneous temperature field, we coupled viscoelastic simulations of oscillatory tidal flexing (using Tekton) to long-term simulations of the convective evolution (using ConMan). Our simulations show that the tidal dissipation rate resulting from heterogeneous temperature can have a strong impact on thermal convection in Europa’s ice shell. Temperatures within upwelling plumes are greatly enhanced and can reach the melting temperature under plausible tidal-flexing amplitude for Europa. A pre-existing fracture zone (at least 6 km deep) promotes the concentration of tidal dissipation (up to ∼20 times more than that in the surroundings), leading to lithospheric thinning. This supports the idea that spatially variable tidal dissipation could lead locally to high temperatures, partial melting, and play an important role in the formation of ridges, chaos, or other features.     

A theoretical evaluation of the lunar tidal variations in the ionospheric F2-layer

Time-varying solutions of the full continuity equation for electrons in the F2-region are obtained. The effects of production, loss, diffusion and electrodynamic ‘E × B’ drift are taken into account. The ‘E × B’ drift term consists of a solar and a lunar component. The solar component of drift is assumed diurnal with 14.6m/sec maximum upward speed at mid-day. The lunar component is assumed sinusoidal with period of half lunar day and amplitude one tenth of the solar drift; the phase is assumed to remain constant in lunar time, in accordance with Chapman's phase law.The results show that the lunar variations in the F2-region are markedly dependent on solar time and latitude. It is also shown that the average semi-diurnal lunar variations in N_mF2 and h_mF2 at any particular lunar time are almost opposite in phase to each other (i.e. out of phase by 6 hr) in the magnetic equatorial zone, and out of phase by 2 hr at moderate latitudes. The phase of δh_mF2 is 10 hr at low latitudes and 9 hr at moderate latitudes. The phase of δN_mF2 is 4 hr at low latitudes and 11 lunar hr at moderate latitudes.The results also show that the phase of the lunar semi-monthly oscillations in N_mF2 undergoes a rapid shift of about 5 lunar hr in going from 8 to 12° and the so called phase reversal occurs at about 10° lat at which the amplitude of N_mF2. becomes extremely small.These and other results are in good agreement with observations. Thus it is shown that the main features of the observed lunar tidal variations of the F2-region within 20° of the magnetic equator can be explained satisfactorily by the superposition of a small lunar drift on a large solar drift.     

Age and Metallicity Gradients in the Galactic Bulge

We test for age and metallicity gradients in the Galactic Bulgebetween the two low extinction windows Baade's window (l = 1^° .1b=−4^° .8) and Sagittarius-I (l=1^° .3 b=−2^° .7). We derive ametallicity difference of ≤ 0.2 dex between BW andSGR-I window. This corresponds to a metallicity gradient of 1.3 dexkpc^-1. This steep gradient is reconcilable with the existence of ashort scale length inner component to the Bulge, most likely thatprominent in the NIR, which perhaps forms a separate entitysuperimposed on the larger, optical Bulge. Through number counts incolour-magnitude diagram around the turnoff for several fields andclusters, extending over a range in galactic longitude we find no evidencefor a significant young stellar population in the GalacticBulge. Previous suggestions of the existence of a significant youngstellar population have most likely incorrectly identified theforeground disk stars. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Chemical Evolution of the Galactic Bulge

In this paper we review the chemical evolution models for the Galactic bulge: in particular, we discuss the predictions of models as compared with the available abundance data and infer the mechanism as well as the time scale for the formation of the Galactic bulge. We show that good chemical evolution models reproducing the observed metallicity distribution of stars in the bulge predict that the [α/Fe] >0 over most of the metallicity range. This is a very important constraint indicating that the bulge of our Galaxy formed at the same time and even faster than the inner Galactic halo. We also discuss predictions for the evolution of light elements such as D and ⁷Li and conclude that the D astration should be maximum due to the high star formation rate required for the bulge whereas the evolution of the abundance of Li should be similar to that observed in the solar neighbourhood, but with an higher Li abundance in the interstellar medium at the present time. This revised version was published online in July 2006 with corrections to the Cover Date.     

Globular Clusters and field stars in the Bulge

In this paper we discuss the characteristics of the stellar content of the galactic bulge excluding the stars within a few parsec from the galactic center. The bulge clusters and the field stars are comparedto the disk population. A scenario with a flattened bulge extending toabout 3–4 Kpc from the galactic center is presented. There is evidencefor an old bulge stellar population, decoupled from the disk. This revised version was published online in July 2006 with corrections to the Cover Date.     

Photometry of the lunar surface during lunar eclipses

The photometric observations of the lunar surface during lunar eclipses were carried out on four nights between 1972 to 1978, using the 91 cm reflector of the Dodaira Station of the Tokyo Astronomical Observatory. The photometry was performed in B-, V-, and R-colours, and arranged in accordance with the angular distance from the centre of the Earth's shadow. The results do not show any large systematic differences between the four nights, showing no support for Danjon's proposition.     

Morphology of lunar craters: A test of lunar erosional models

This paper is a test of published theoretical and experimental studies of crater erosion by micrometeorite bombardment which predict systematic variations in the morphology of lunar craters as a function of crater diameter and crater age. Numerical, ranking-type degradation classifications indicate that the craters on Mare Imbrium and Mare Tranquillitatus confirm these predictions by showing a systematic increase in degradation with decreasing diameter for craters smaller than a few kilometers in diameter but larger than the equilibrium diameter, and by showing fixed proportions of fresh, moderately degraded and very degraded craters under equilibrium conditions. Furthermore, the relative ages of the two mare surfaces may be determined using a diameter/mean-degradation-number curve. These determinations of relative age and process of crater erosion are both essentially independent of the traditionally studied crater diameter/frequency relationships. Morphologies of terra craters near Mare Humorum suggest a young, non-equilibrium crater population superposed on a perimordial population with about equilibrium proportions of fresh, moderately degraded and very degraded craters. The primordial population has been modified by pre-Imbrian or early Imbrian deposition of blanketing deposits. A comparative study of several crater degradation classifications indicates that all are essentially interchangeable.     

On the accuracy of lunar ephemerides using the data provided by the future Russian lunar laser ranging system

The potential effect of the future Russian lunar laser ranging system (LLRS) on the accuracy of lunar ephemerides is discussed. In addition to the LLRS in Altai, several other observatories suitable for the LLRS installation are considered. The variation of accuracy of lunar ephemerides in the process of commissioning of new LLRS stations is estimated by mathematical modeling. It is demonstrated that the error in the determination of certain lunar ephemeris parameters may be reduced by up to 16% after seven years of operation of the Altai LLRS with a nearly optimal observational program.     

Abundances in Individual Stars of the Galactic Bulge

Element ratios in two stars of NGC 6553 and one star in NGC 6528 reveal that α-elements are enhanced relative to Fe. The metallicity [Fe/H] ≈ −0.6, but taking into account the overabundances of several elements, the overall metallicity is close to solar. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dark matter in the Galactic Bulge: a Microlensing point of view

Microlensing is one of the most promising technique to probe the densityof dark matter in the Galactic Bulge. We review briefly the history ofmicrolensing and comment on the discovery of high optical depthin the direction of the Bulge. This optical depth is several timeslarger than the first theoretical predictions. We will show that someof the discrepancy can be resolved by taking into account the effectof self amplification of stars into the Galactic Bar. We will alsoexplain that the optical depth is contaminated with the contributionof faint unresolved stars. However, we emphasize that a categoryof sources, the bulge giants are bright enough to escape the biasdue to unresolved sources. Finallywe show that even if self amplification in the bar is taken into account, the optical depth to giants is hard to reproduce. We concludeby saying that in the near future this excess in the bulge opticaldepth should be clarified and measured with good accuracy. In particulargood progress should be made when the analyze of the last observationsof Bulge giants will be completed by the MACHO group. The futureimplementation of the image subtraction technique in the data pipelinesshould also help to overcome the bias in the measurement of the opticaldepth to turnoff stars. This revised version was published online in July 2006 with corrections to the Cover Date.     

The negative polarization parameters of the light scattered by the lunar surface: Mapping

The images of the southwestern part of the lunar disk showing the distributions of the negative polarization parameters of the light scattered by the lunar surface are presented. The distributions of the negative polarization minimum P _min, the inversion angle α_inv, and the polarization slope at the inversion point h significantly differ from the albedo image. This testifies to the fact that polarimetry yields independent information on the structure and optical properties of the lunar regolith.     

Structural disturbances of the lunar surface caused by spacecraft

From the lunar surface survey performed with a narrow-angle camera of the Lunar Reconnaissance Orbiter (LRO) spacecraft, the distributions of the phase ratios of the Apollo 11 and 12 landing sites and the Ranger 9 impact site were mapped. In the acquired images, the traces of the structural disturbances of the lunar regolith layer caused by the jet flows are seen. In the Ranger 9 impact site, one can see the crater of about 15 m across with a ray system, which is hardly noticeable in the brightness picture, but has a high contract in the phase ratio picture. The character of the photometric anomaly of the rays of this crater shows that they are formed by the ejected stones composing the rugged relief, which induces a strong shadow effect. At the same time, the influence of jet flows from the rocket engines smooths the relief and leads to the photometric anomaly of the opposite sign. The estimate of the maturity degree of the lunar regolith in the Apollo 11 and 12 landing sites obtained from the SELENE spectral survey suggests that the depth of the influence of the rocket engines on the soil is small, and the surface of the impact crater formed by the Ranger 9 spacecraft contains a large amount of the immature soil.     

“New” lunar meteorites: Implications for composition of the global lunar surface,lunar crust,and the bulk Moon

Abstract— New data for lunar meteorites and a synthesis of literature data have significant implications for the interpretation of global Th data and for the Moon's bulk composition. As presently calibrated (Prettyman et al. 2002), the Lunar Prospector gamma‐ray data imply that the average global surface Th = 1.58 μg/g. However, that calibration yields implausibly high concentrations for the three most Th‐poor documented sampling sites, it extrapolates to a nonzero Lunar Prospector Th, ?0.7 μg/g, at zero sample Th, and it results in a misfit toward too‐high Th when compared with the global regolith Th spectrum as constrained using mainly lunaite regolith breccias. Another problem is manifested by Th versus K systematics. Ground truth data plot consistently to the high‐Th/K side of the Prospector data trend, offset by a factor of 1.2. A new calibration is proposed that represents a compromise between the Th levels indicated by ground truth constraints and the Prettyman et al. (2002) calibration. Conservatively assuming that the Th versus K issue is mostly a K problem, the average global surface Th is estimated to be ?1.35 μg/g. The Moon's remarkable global asymmetry in KREEP abundance is even more pronounced than previously supposed. The surface Th concentration ratio between the hemisphere antipodal to the Procellarum basin and the hemisphere centered on Procellarum is reduced to 0.24 in the new calibration. This extreme disparity is most simply interpreted as a consequence of Procellarum's origin at a time when the Moon still contained at least a thin residual layer of a global magma ocean. Allowing for diminution of Th with depth, the extrapolated bulk crustal Th is ?0.73 μg/g. Further extrapolation to bulk Moon Th yields ?0.07 μg/g, which is nearly identical to the consensus estimate for Earth's primitive mantle. Assuming chondritic proportionality among refractory lithophile elements implies Al₂O₃ of approximately 3.8 wt%. The Moon's bulk mantle mg ratio is only weakly constrained by seismic and mare‐basaltic data. KREEP‐and mare‐free lunaite regolith samples, other thoroughly polymict lunar meteorites, and a few KREEP‐free Apollo highland samples manifest a remarkable anticorrelation on a plot of Al₂O₃ versus mg. This trend implies that an important component of the Moon is highly magnesian. The bulk Moon is inferred to have an Earth‐like oxide mg ratio of ?87–88 mol%. The close resemblance between the bulk Moon and Earth's primitive mantle extends to moderately volatile elements, most clearly Mn. Unless major proportions of Cr and V are sequestered into deep mantle spinel, remarkably Earth‐like depletions (versus chondrites) are also inferred for bulk Moon Cr and V.     

Chemistry of the Calcalong Creek lunar meteorite and its relationship to lunar terranes

Abstract— The Calcalong Creek lunar meteorite is a polymict breccia that contains clasts of both highlands and mare affinity. Reported here is a compilation of major, minor, and trace element data for bulk, clast, and matrix samples determined by instrumental neutron activation analysis (INAA). Petrographic information and results of electron microprobe analyses are included. The relationship of Calcalong Creek to lunar terranes, especially the Procellarum KREEP Terrane and Feldspathic Highlands Terrane, is established by the abundance of thorium, incompatible elements and their KREEP‐like CI chondrite normalized pattern, FeO, and TiO₂. The highlands component is associated with Apollo 15 KREEP basalt but represents a variant of the KREEP‐derived material widely found on the moon. Sources of Calcalong Creek's mare basalt components may be related to low‐titanium (LT) and very low‐titanium (VLT) basalts seen in other lunar meteorites but do not sample the same source. The content of some components of Calcalong Creek are found to display similarities to the composition of the South Pole‐Aitken Terrane. What appear to be VLT relationships could represent new high aluminum, low titanium basalt types.