Search

This study analyzes the secular dynamics of two extended bodies in Keplerian orbits, focusing on tidal effects. It introduces formulas for energy dissipation within each body in a binary system. The bodies can have a finite number of layers with linear viscoelastic rheology. The layers must be sufficiently coupled so that the rotation of each layer remains close to the average rotation of the body. The body is assumed to be in a "viscous regime" (though it may contain purely elastic layers), meaning that the relaxation times of the rheology are much shorter than the typical despinning time and deviations from sphericity are caused only by tidal and centrifugal stresses. The main contribution of this paper is the decomposition of orbital-averaged equations into a fast–slow system. This reduction allows the slow dynamics to be represented as sliding along a torque-free curve with occasional jumps at folding points. This greatly simplifies the analysis of the dynamics as a function of the rheological parameters. [ABSTRACT FROM AUTHOR]

Understanding of secular evolution of the Earth system is based largely on the rock and mineral archive preserved in the continental lithosphere. Based on the frequency and range of accessible data preserved in this record, we divide the secular evolution into seven phases: (a) "Proto‐Earth" (ca. 4.57–4.45 Ga); (b) "Primordial Earth" (ca. 4.45–3.80 Ga); (c) "Primitive Earth" (ca. 3.8–3.2 Ga); (d) "Juvenile Earth" (ca. 3.2–2.5 Ga); (e) "Youthful Earth" (ca. 2.5–1.8 Ga); (f) "Middle Earth" (ca. 1.8–0.8 Ga); and (g) "Contemporary Earth" (since ca. 0.8 Ga). Integrating this record with knowledge of secular cooling of the mantle and lithospheric rheology constrains the changes in the tectonic modes that operated through Earth history. Initial accretion and the Moon forming impact during the Proto‐Earth phase likely resulted in a magma ocean. The solidification of this magma ocean produced the Primordial Earth lithosphere, which preserves evidence for intra‐lithospheric reworking of a rigid lid, but which also likely experienced partial recycling through mantle overturn and meteorite impacts. Evidence for craton formation and stabilization from ca. 3.8 to 2.5 Ga, during the Primitive and Juvenile Earth phases, likely reflects some degree of coupling between the convecting mantle and a lithosphere initially weak enough to favor an internally deformable, squishy‐lid behavior, which led to a transition to more rigid, plate like, behavior by the end of the early Earth phases. The Youthful to Contemporary phases of Earth, all occurred within a plate tectonic framework with changes between phases linked to lithospheric behavior and the supercontinent cycle. Plain Language Summary: The record of Earth evolution is preserved in the continental rock archive, but is incomplete and our knowledge of it decreases with increasing age and depth of preservation. Based on secular cooling of the mantle and associated changing lithospheric properties, we recognize three dominant tectonic modes that have operated on Earth; stagnant lid, squishy lid, and plate tectonics. After solidification of the Earth's initial magma ocean (>4.45 Ga), the lithosphere was likely dominated by mafic crust that existed until ca. 3.8 Ga. The tectonic mode that operated at this time involved either no lithosphere‐mantle coupling (cf., stagnant lid), or coupling between non‐rigid lithosphere and convecting mantle (cf., squishy lid). The latter mode likely operated through most of the Archean (ca. 3.8–2.5 Ga), and was associated with the formation of the stable interior of continents, called cratons. The stabilization of these cratons in the latter half of the Archean (ca. 3.2–2.5 Ga) is associated with the development of rigid lithosphere and the transition to a plate tectonic mode that continues to the present day. Further changes, likely in response to the supercontinent cycle, lead to subdivisions of the Earth system between ca. 1.8 and 0.8 Ga. Key Points: Long‐term record of Earth evolution preserved in continental lithosphereThree main tectonic modes operated through Earth history: stagnant lid, squishy lid and rigid, active lid (plate tectonics)Stabilization of cratons at end of Archean marks transition to plate tectonics with supercontinent cycle controlling subsequent changes [ABSTRACT FROM AUTHOR]

• The rutile data record changes in the dominant metamorphic modes. • Earliest rutile age peak aligns with the oldest evidence of low T/P metamorphism. • T/P of Archean rutile forms a tight normal distribution. • Paleoproterozoic rutile T/P distribution is skewed to lower T/P condition. Rutile provides crucial insights into the evolution of plate tectonics and variations in tectonomagmatic modes over Earth's history primarily because rutile predominantly tracks higher-pressure metamorphism (>1.0–1.2 GPa). Comparison of rutile age and compositional data with diverse proxies tracks the presence of low temperature/pressure (T/P) metamorphic conditions, enabling the tracing of plate tectonics onset and evolution. We present a new compilation of rutile U-Pb ages that lag zircon ages by approximately 50 Myr, potentially indicating cooling ages of metamorphic belts. The earliest rutile age peak (ca. 1.8 Ga) aligns with the oldest evidence for low T/P metamorphic conditions. This coincides with a shift in the T/P distribution of rutile whereas the T/P of Archean rutile forms a tight normal distribution. In the Paleoproterozoic, the rutile T/P distribution is skewed to lower T/P, following the broader pattern of the full metamorphic record. The degree of lower T/P skew increases through time until the lower T/P population dominates the rutile record from the Neoproterozoic to the present. These data further highlight shifts in dominant metamorphic modes that can be tied to the evolution of the tectonic system, with early Archean metamorphism being associated with plume-driven vertical tectonics or hot, shallow subduction and post-Archean metamorphism being associated with progressive less plume-driven vertical tectonics and colder, steeper subduction. Although the frequency of rutile is lower during the Mesoproterozoic, the rutile T/P during this time follows the progressive skewing pattern from the Paleoproterozoic to the present and is likely inconsistent with a phase of interrupted tectonics characterized by stagnant lid. [ABSTRACT FROM AUTHOR]

We consider an exoplanetary system consisting of a star and two planets. The masses of the planets are significantly less than the mass of the star. The evolution of the orbital motion of exoplanets is studied within the framework of a double averaged unrestricted three-body problem. The main attention is paid to coplanar configurations, when the star and planets move in a certain plane that preserves a constant position. The possibility of reversing the orbital motion of the inner planet is noted. [ABSTRACT FROM AUTHOR]

Compilation of age and endowment data for deposits that commonly occur on convergent margins (volcanic-hosted massive sulfide, porphyry copper, orogenic gold, granite-related rare metal and pegmatite deposits: over 1000 deposits from 21 mineral provinces) indicate that metallogenic patterns have changed over time. For much of Earth's history, metallogenesis along convergent margins is marked by a relatively systematic temporal progression of deposits succeeding one-another, which we refer to as the convergent margin metallogenic cycle (CMMC): volcanic-hosted massive sulfide (VHMS) and/or calc-alkalic porphyry copper → orogenic gold → alkalic porphyry copper, granite-related rare metals and/or pegmatite. Typically individual CMMCs last for 60–160 Myr, and the progression appears to be related to the convergent margin tectonic cycle. Prior to ca. 3000 Ma, however, CMMCs are not recognized. Rather, these old mineral provinces are characterized by long metallogenic histories (370–500 Myr) with no discernible pattern of deposit types. The Mesoarchean to Paleoproterozoic is characterized mostly by mineral provinces with relatively short (60–155 Myr) metallogenic histories and a single CMMC. Between 1950 Ma and 1700 Ma some convergent margin mineral provinces (e.g. Trans-Hudson and Svecofennian) are characterized by multiple CMMCs, with metallogenic histories that last up to 160 Myr. Between 1250 Ma and 750 Ma, longer-lived yet relatively poorly-constrained metallogenic histories (up to 320 Myr) appear, and after ca. 750 Ma, convergent margins are mostly long-lived (290–450 Myr) and are characterized by multiple CMMCs with complex metallogenic histories. These four periods in the metallogenesis of convergent margins appear to reflect secular changes in tectonic processes. Prior to ca. 3200–3000 Ma, stagnant lid tectonics, which did not involve modern-style subduction, dominated, resulting in non-cyclical mineralization. After the initiation of some early form of subduction between ca. 3200 Ma and ca. 3000 Ma, the metallogenic style changed. The dominance of provinces from 3000 to 1700 Ma with a single CMMC, and a relatively short metallogenic history suggests that convergent margins were shorter-lived. This is consistent with models of shallow-break-off subduction whereby the subducting slab breaks off at shallow levels due to lower plate strength beginning in the later Archean. We suggest that between ca. 3000 and ca. 1700 Ma a propensity for slab break-off could shut down individual subduction systems and produce short-lived metallogenic histories with a single CMMC. The change to longer metallogenic histories and dominant multiple CMMCs begins with Rodinia assembly: the length and complexity of metallogenesis systematically increases thereafter. The lengthening of convergent margin metallogenesis resulted from more stable convergence as continuous ridge push and the stronger density contrasts of the subducting slab causing re-initiation of subduction outboard rather than complete termination of subduction when the convergent margin was perturbed. As consequence of these driving factors, the metallogenic history of young convergent margins involves multiple CMMCs and/or complex temporal interleaving of deposit types. [ABSTRACT FROM AUTHOR]

Exploring weakly perturbed Keplerian motion within the restricted three-body problem, Lidov (Planet Space Sci 9:719-759, 1962) and, independently, Kozai (Astron J 67:591-598, 1962) discovered coupled oscillations of eccentricity and inclination (the KL cycles). Their classical studies were based on an integrable model of the secular evolution, obtained by double averaging of the disturbing function approximated with its first non-trivial term. This was the quadrupole term in the series expansion with respect to the ratio of the semimajor axis of the disturbed body to that of the disturbing body. If the next (octupole) term is kept in the expression for the disturbing function, long-term modulation of the KL cycles can be established (Ford et al. in Astrophys J 535:385-401, 2000; Naoz et al. in Nature 473:187-189, 2011; Katz et al. in Phys Rev Lett 107:181101, 2011). Specifically, flips between the prograde and retrograde orbits become possible. Since such flips are observed only when the perturber has a nonzero eccentricity, the term 'eccentric Kozai-Lidov effect' (or EKL effect) was proposed by Lithwick and Naoz (Astrophys J 742:94, 2011) to specify such behavior. We demonstrate that the EKL effect can be interpreted as a resonance phenomenon. To this end, we write down the equations of motion in terms of 'action-angle' variables emerging in the integrable Kozai-Lidov model. It turns out that for some initial values the resonance is degenerate and the usual 'pendulum' approximation is insufficient to describe the evolution of the resonance phase. Analysis of the related bifurcations allows us to estimate the typical time between the successive flips for different parts of the phase space. [ABSTRACT FROM AUTHOR]

• Anorthosites are far more common than previously thought. • Anorthosites have mostly formed in subduction zones throughout the Earth's history. • Anorthosites have crystallised from tholeiitic or high-Al tholeiitic magmas. • A marked change in the geochemistry of anorthosites occurred in the Proterozoic. • The petrogenesis of anorthosites reflects the secular evolution of the Earth. Petrologists are still trying to solve the 'anorthosite problem', which was first identified by N.L. Bowen in 1917 and revolves around the uncertainty surrounding the petrogenesis, tectonic setting, emplacement, and parental magma compositions of anorthosites. Anorthosites are volumetrically minor to significant, occur worldwide and have implications for upper mantle depletion, oceanic and continental crust growth and evolution, the longevity of plate tectonic processes on Earth, and magma chamber processes. Anorthosites have formed throughout Earth history from 3950 Ma to the Present. Anorthosites are far more common than previously thought as there are at least 2,126 known preserved anorthosite occurrences worldwide. Anorthosites are closely associated with gabbros and leucogabbros and spatially associated with pillow-bearing mafic volcanic rocks in ophiolites and layered intrusions, except for Proterozoic anorthosites that are closely associated with intermediate to felsic intrusives. Archean anorthosites often contain near-spherical calcic plagioclase (An 70-100) megacrysts up to 45 cm in diameter and magmatic amphibole, Proterozoic anorthosites have elongate (≤1 m) andesine (An 30-50) megacrysts, and Phanerozoic anorthosites contain calcic plagioclase (An 70-100). The plagioclase anorthite contents of anorthosites vary throughout Earth history, troughing in the Proterozoic. This corroborates the whole-rock geochemistry of anorthosites, which also varies throughout Earth history and indicates that crustal contamination played a significant role in the petrogenesis of Proterozoic anorthosites. Relatively high mantle heat flow and partial melting and the thermal blanketing of Proterozoic supercontinents led to the generation of large anorthosite massifs. Archean, Proterozoic and Phanerozoic anorthosites crystallised from tholeiitic or high-Al tholeiitic parental magmas that were derived from depleted mantle sources and significantly assimilated continental crust in the Proterozoic. Archean anorthosites crystallised from hydrous Ca- and Al-rich tholeiitic parental magmas derived by partial melting of hydrated sub-arc depleted mantle sources. Anorthosites have predominantly formed in subduction-related settings throughout Earth history, indicating that plate tectonic processes have operated since the beginning of the Eoarchean. The proportion of subduction-related anorthosites significantly declined in the Proterozoic following supercontinent amalgamation. Calcic megacrystic anorthosites and massif-type anorthosites are largely restricted to the Archean and Proterozoic, respectively, yet they occur throughout Earth history. The petrogenesis of anorthosites reflects the secular evolution of the Earth. [ABSTRACT FROM AUTHOR]

We investigate the secular dynamics of two-planet coplanar systems evolving under mutual gravitational interactions and dissipative forces. We consider two mechanisms responsible for the planetary migration: star-planet (or planet-satellite) tidal interactions and interactions of a planet with a gaseous disc. We show that each migration mechanism is characterized by a specific law of orbital angular momentum exchange. Calculating stationary solutions of the conservative secular problem and taking into account the orbital angular momentum leakage, we trace the evolutionary routes followed by the planet pairs during the migration process. This procedure allows us to recover the dynamical history of two-planet systems and constrain parameters of the involved physical processes. [ABSTRACT FROM AUTHOR]

The author of this paper examines the influence of time variation of the gravitational constant on the evolution of the orbital elements of binary stars. The theoretical results show that the semimajor axis, eccentricity and mean longitude exhibit periodic, secular and mixed periodic variation, but the longitude of the periastron exists in periodic and mixed periodic variation, but not secular variation. The inclination and ascending node exhibit no variation. In addition, the limits of the secular evolution of the orbit of six binary stars due to time variation of the gravitational constant are estimated. The numerical results are given. The theoretical results are discussed and conclusions drawn. [ABSTRACT FROM AUTHOR]

Abstract: Most of the East European Craton lacks surface relief; however, the amplitude of topography at the top of the basement exceeds 20 km, the amplitude of topography undulations at the crustal base reaches almost 30 km with an amazing amplitude of ca. 50 km in variation in the thickness of the crystalline crust, and the amplitude of topography variations at the lithosphere–asthenosphere boundary exceeds 200 km. This paper examines the relative contributions of the crust, the subcrustal lithosphere, and the dynamic support of the sublithospheric mantle to maintain surface topography, using regional seismic data on the structure of the crystalline crust and the sedimentary cover, and thermal and large-scale P- and S-wave seismic tomography data on the structure of the lithospheric mantle. For the Precambrian lithosphere, an analysis of Vp/Vs ratio at 100, 150, 200, and 250 km depths does not show any age-dependence, suggesting that while Vp/Vs ratio can be effectively used to outline the cratonic margins, it is not sensitive to compositional variations within the cratonic lithosphere. Statistical analysis of age-dependence of velocity, density, and thermal structure of the continental crust and subcrustal lithosphere in the study area (0–62E, 45–72N) allows to link lithospheric structure with the tectonic evolution of the region since the Archean. Crustal thickness decreases systematically with age from 42–44 km in regions older than 1.6 Ga to 37–40 km in the Paleozoic–Mesoproterozoic structures, and to ca. 31 km in the Meso-Cenozoic regions. However, the isostatic contribution of the crust to the surface topography of the East European Craton is almost independent of age (ca. 4.5 km) due to an interplay of age-dependent crustal and sedimentary thicknesses and lithospheric temperatures. On the contrary, the contribution of the subcrustal lithosphere to the surface topography strongly depends on the age, being slightly positive (+0.3+0.7 km) for the regions older than 1.6 Ga and negative (−0.5–1 km) for younger structures. This leads to age-dependent variations in the residual topography, i.e. the topography which cannot be explained by the assumed thermal and density structure of the lithosphere, and which can (at least partly) originate from the dynamic component caused by the mantle flow. Positive dynamic topography at the cratonic margins, which exceeds 2 km in the Norwegian Caledonides and in the Urals, clearly links their on-going uplift with deep mantle processes. Negative residual topography beneath the Archean-Paleoproterozoic cratons (−1–2 km) indicates either a smaller density deficit (ca. 0.9%) in their subcrustal lithosphere than predicted by global petrologic data on mantle-derived xenoliths or the presence of a strong convective downwelling in the mantle. Such mantle downflows can effectively divert heat from the lithospheric base, leading to a long-term survival of the Archean-Paleoproterozoic lithosphere. [Copyright &y& Elsevier]

Abstract: The lower part of the Pilbara Supergroup records 300 million years of voluminous basaltic magmatism from ca. 3.515 to 3.24 Ga. The basalts are divided into two compositionally distinct but contemporaneous and interbedded types. Compared to low-Ti basalts, high-Ti basalts (TiO2 >0.8 wt.%) have relatively high concentrations of HFSE and REE, are generally more Fe-rich, have very low Al2O3/TiO2 (18.7–8.9) and high Gd/Yb ratios (1.12–2.23). The composition of the high-Ti basalts, and their source, did not change significantly throughout the 300 m.y. period of basalt eruption. In contrast, low-Ti basalts show distinct secular trends to lower concentrations of incompatible trace elements and to lower ratios of La/Sm, La/Gd, La/Yb and Gd/Yb that reflect a source progressively more depleted than N-MORB source. Gd/Yb ratios in the younger low-Ti basalts are as low as 0.67, well below estimates for modern depleted mantle (0.98). These values reflect a strongly depleted source, and possibly also a contribution from a low Gd/Yb source component representing the garnet-bearing residue of previous high-pressure melting events. The source for the low-Ti basalts comprised the accumulated residues of plumes that produced the earliest high-Ti basalts and of plumes that produced subsequent high-Ti basalts, and was periodically modified through melt extraction. It remained isolated from the convecting asthenosphere throughout the 300 m.y. period of basaltic magmatism, but parts of it remelted each time one of a series of plumes impinged on the lithospheric mantle. It progressively formed the thick, depleted, and buoyant sub-continental lithospheric mantle (SCLM) that is complimentary to the thick pile of interbedded high- and low-Ti basalt that comprises the bulk of the Pilbara Supergroup. These interpretations support models for Palaeoarchaean protocrust formation through extensive mantle plume magmatic events, and models that suggest that the Archaean SCLM formed at the same time as early voluminous mafic magmatism. [Copyright &y& Elsevier]

The ca. 2 Ga retrogressed eclogites in the Usagaran Belt in central Tanzania are among the oldest documented eclogites in the world. As such, they have been used to pinpoint the thermal conditions of the onset of modern style subduction on Earth. Two samples of retrogressed mafic eclogite have been interrogated to reconstruct the metamorphic history of the subducted crust. The samples are several kilometres apart, separated by a mylonitic upper amphibolite-transitional granulite foliation. Lu--Hf garnet geochronology pinpoints eclogite metamorphism at 1994 ± 9 Ma, supported by rutile U--Pb geochronology. Zircon U--Pb geochronology supports subduction metamorphism at ca. 2000 Ma. Mineral equilibria modelling and Zr in rutile thermometry suggests the retrogressed eclogites reached a minimum pressure of 18 kbar at approximately 800 °C, consistent with a warm subduction thermal gradient. These conditions were followed by amphibolite-granulite-facies overprinting. Proposed tectonic models for the formation of the eclogites involve either east-dipping subduction of the Tanzanian Craton margin, or west-dipping subduction of oceanic crust under the Tanzanian Craton. The retrogressed eclogites were likely exhumed via slab breakoff driven buoyancy of the oceanic crust and transferred to shallow crustal levels in a back arc position. This data, combined with data from eclogites from the Eburnian-Transamazonian and Ubende orogens, demonstrate the possible existence of a large subduction system on the margin of west Africa from ca. 2.1–1.9 Ga. This system has led to the preservation of several eclogitic rocks, which suggests that modern style subduction was operating on significant geographic and temporal scales at this time. • Eclogite-facies metamorphism in the Usagaran Belt occurred at ca. 1994 Ma as dated by garnet Lu--Hf. • Peak conditions were at least 18 kbar at ~ 800 °C, pointing to warm subduction thermal gradients in the Palaeoproterozoic. • Tectonic scenarios for formation of the eclogites involve E- or W-dipping subduction followed by buoyancy driven exhumation [ABSTRACT FROM AUTHOR]

Stellar bars are important internal drivers of the secular evolution of disk galaxies. Using a sample of nearby barred galaxies with weak and strong bars, we evaluate the correlations between star formation properties in different galactic structures and their associated bars, and try to interpret the complex process of bar-driven secular evolution. We find that weaker bars tend to associate with lower concentrical star formation activities, while stronger bars appear to have large scatter in the distribution of the global star formation activities. In general, the star formation activities in early- and late-type galaxies have different behavior, with similar star formation rate density distributions. In addition, there are only weak trends toward increased star formation activities in bulges and galaxies with stronger bars, which is consistent with previous works. Our results suggest that the different stages of the evolutionary sequence and many factors besides bars may contribute to the complexity of this process. Furthermore, significant correlations are found between the star formation activities in different galactic structures, in which barred galaxies with intense star formation in bulges tend to also have active star formation in their bars and disks. Most bulges have higher star formation densities than their associated bars and disks, indicating the presence of bar-driven evolution. Therefore, we derived a possible criterion (Figure 1) to quantify the different stages of a bar-driven evolutionary sequence. Future work is needed to improve on the uncertainties of this study. [ABSTRACT FROM PUBLISHER]