Dynamical classification of trans-neptunian objects: Probing their origin, evolution, and interrelation

The orbital structure of trans-neptunian objects (TNOs) in the trans-neptunian belt (Edgeworth-Kuiper belt) and scattered disk provides important clues to understand the origin and evolution of the Solar System. To better characterize these populations, we performed computer simulations of currently observed objects using long-arc orbits and several thousands of clones. Our preliminary analysis identified 622 TNOs, and 65 non-resonant objects whose orbits penetrate that of at least one of the giant planets within 1 Myr (the centaurs). In addition, we identified 196 TNOs locked in resonances with Neptune, which, sorted by distance from the Sun, are 1:1 (Neptune trojans), 5:4, 4:3, 11:8, 3:2, 18:11, 5:3, 12:7, 19:11, 7:4, 9:5, 11:6, 2:1, 9:4, 16:7, 7:3, 12:5, 5:2, 8:3, 3:1, 4:1, 11:2, and 27:4. Kozai resonant TNOs are found inside the 3:2, 5:3, 7:4, and 2:1 resonances. We present detailed general features for the resonant populations (i.e., libration amplitude angles, libration centers, Kozai libration amplitudes, etc.). Taking together the simulations of Lykawka and Mukai [Lykawka, P.S., Mukai, T., 2007. Icarus 186, 331-341], an improved classification scheme is presented revealing five main classes: centaurs, resonant, scattered, detached and classical TNOs. Scattered and detached TNOs (non-resonant) have q (perihelion distance) <37 AU and q>40 AU, respectively. TNOs with 37 AU<q<40 AU occupy an intermediate region where both classes coexist. Thus, there are no clear boundaries between the scattered and detached regions. We also securely identified a total of 9 detached TNOs by using 4-5 Gyr orbital integrations. Classical objects are non-resonant TNOs usually divided into cold and hot populations. Their boundaries are as follows: cold classical TNOs (i?5°) are located at 37 AU<a<40 AU (q>37 AU) and 42 AU<a<47.5 AU (q>38 AU), and hot classical TNOs (i>5°) occupy orbits with 37 AU<a<47.5 AU (q>37 AU). However, a more firm classification is found with i>10° for hot classical TNOs. Lastly, we discuss some implications of our classification scheme comparing all TNOs with our model and other past models.     

Long term dynamical evolution and classification of classical TNOs

Classical trans-Neptunian objects (TNOs) are believed to represent the most dynamically pristine population in the trans-Neptunian belt (TNB) offering unprecedented clues about the formation of our Solar System. The long term dynamical evolution of classical TNOs was investigated using extensive simulations. We followed the evolution of more than 17000 particles with a wide range of initial conditions taking into account the perturbations from the four giant planets for 4 Gyr. The evolution of objects in the classical region is dependent on both their inclination and semimajor axes, with the inner (a<45 AU) and outer regions (a>45 AU) evolving differently. The reason is the influence of overlapping secular resonances with Uranus and Neptune (40–42 AU) and the 5:3 (a∼ ∼42.3 AU), 7:4 (a∼ ∼43.7 AU), 9:5 (a∼ ∼44.5 AU) and 11:6 (a∼ ∼ 45.0 AU) mean motion resonances strongly sculpting the inner region, while in the outer region only the 2:1 mean motion resonance (a∼ ∼47.7 AU) causes important perturbations. In particular, we found: (a) A substantial erosion of low-i bodies (i<10°) in the inner region caused by the secular resonances, except those objects that remained protected inside mean motion resonances which survived for billion of years; (b) An optimal stable region located at 45 AU<a<47 AU, q>40 AU and i>5° free of major perturbations; (c) Better defined boundaries for the classical region: 42–47.5 AU (q>38 AU) for cold classical TNOs and 40–47.5 AU (q>35 AU) for hot ones, with i=4.5° as the best threshold to distinguish between both populations; (d) The high inclination TNOs seen in the 40–42 AU region reflect their initial conditions. Therefore they should be classified as hot classical TNOs. Lastly, we report a good match between our results and observations, indicating that the former can provide explanations and predictions for the orbital structure in the classical region.     

Melting of iron–silicon alloy up to the core–mantle boundary pressure: implications to the thermal structure of the Earth’s core

The melting temperature of Fe–18 wt% Si alloy was determined up to 119 GPa based on a change of laser heating efficiency and the texture of the recovered samples in the laser-heated diamond anvil cell experiments. We have also investigated the subsolidus phase relations of Fe–18 wt% Si alloy by the in-situ X-ray diffraction method and confirmed that the bcc phase is stable at least up to 57 GPa and high temperature. The melting curve of the alloy was fitted by the Simon’s equation, P(GPa)/a = (T _m(K)/T ₀) ^c , with parameters, T ₀ = 1,473 K, a = 3.5 ± 1.1 GPa, and c = 4.5 ± 0.4. The melting temperature of bcc Fe–18 wt% Si alloy is comparable with that of pure iron in the pressure range of this work. The melting temperature of Fe–18 wt% Si alloy is estimated to be 3,300–3,500 K at 135 GPa, and 4,000–4,200 K at around 330 GPa, which may provide the lower bound of the temperatures at the core–mantle boundary and the inner core–outer core boundary if the light element in the core is silicon.     

Seismic response controlled structure with Active Variable Stiffness system

The Active Variable Stiffness (AVS) system is proposed as a seismic response control system. It actively controls structural characteristics, such as stiffness of a building, to establish a non-resonant state against earthquake excitations, thus suppressing the building's response. It consumes a relatively small amount of energy and maintains the safety of the building in moderate to severe earthquakes. In order to accumulate practical data and investigate them, a building has been constructed as a trial. This paper describes the applied system, the control algorithm, verification of stiffness selection, results of tests for verifying system characteristics, some observed earthquake records and simulation analyses. Responses in controlled and uncontrolled states have been compared to show the effectiveness of the proposed system.     

Localized rheological weakening by grain-size reduction during lithospheric extension

Grain-size reduction may be a possible mechanism for the origin of localized deformation in the ductile regime. I investigated the effects of grain-size reduction due to dynamic recrystallization, cataclasis, and syntectonic metamorphic reaction on the stress envelope in the lithospheric mantle during extension by using a simple one-dimensional model. In this model, the lithosphere extends uniformly with a constant strain rate, and a fall in rock strength appears as a decrease in stress. Because grain-size distribution at the onset of extension is unknown, I regarded the steady state grain-size due to dynamic recrystallization as the initial size. Then, I evaluated the maximum effects of grain-size reduction by dynamic recrystallization during extension, and consequently examined the effects of grain-size reduction by cataclasis and metamorphic reaction under conditions when dynamic recrystallization occurs significantly. I find that it is difficult to bring about localized rheological weakening by grain-size reduction owing to dynamic recrystallization. In contrast, grain-size reduction by cataclasis can cause localized weakening during extension. There is a wide-ranging rate of grain-size reduction by means of cataclasis that causes localized weakening just below the Moho. I specified the reaction from spinel-lherzolite to plagioclase-lherzolite that plays a role in grain-size reduction by syntectonic metamorphism. The reaction occurs at depths less than 35 km, which is independent of the initial thermal state of the lithosphere. Localized rheological weakening can occur if the following conditions are satisfied: (1) grain-size before the reaction is greater than 0.7 mm under dry conditions and greater than 0.5 mm under wet conditions, and it decreases down to those values by the reaction; (2) grain-size decreases down to less than initial grain-size, when the dominant deformation mechanism is GSS creep at the onset of extension. It is also noted that dry conditions are more favourable for localized weakening.     

Shaking table tests on seismic response of steel braced frames with column uplift

Previous studies have suggested that rocking vibration accompanied by uplift motion might reduce the seismic damage to buildings subjected to severe earthquake motions. This paper reports on the use of shaking table tests and numerical analyses to evaluate and compare the seismic response of base‐plate‐yielding rocking systems with columns allowed to uplift with that of fixed‐base systems. The study is performed using half‐scale three‐storey, 1 × 2 bay braced steel frames with a total height of 5.3 m. Base plates that yield due to column tension were installed at the base of each column. Two types of base plates with different thicknesses are investigated. The earthquake ground motion used for the tests and analyses is the record of the 1940 El Centro NS component with the time scale shortened by a factor of 1/√2. The maximum input acceleration is scaled to examine the structural response at various earthquake intensities. The column base shears in the rocking frames with column uplift are reduced by up to 52% as compared to the fixed‐base frames. Conversely, the maximum roof displacements of the fixed and rocking frames are about the same. It is also noted that the effect of the vertical impact on the column associated with touchdown of the base plate is small because the difference in tensile and compressive forces is primarily due to the self‐limiting tensile force in the column caused by yielding of the base plate. Copyright © 2006 John Wiley & Sons, Ltd.     

Sensitive high-resolution ion microprobe U-Pb ages of the Latest Oligocene-Early Miocene rift-related Hidaka high-temperature metamorphism in Hokkaido, northern Japan

Abstract   In order to define the timing of granulite facies metamorphism, sensitive high-resolution ion microprobe (SHRIMP) U-Pb analyses were performed on zircons of three pelitic granulites from the lower metamorphic sequence of the Hidaka Metamorphic Belt, southern central Hokkaido, Japan. Both rounded and prismatic zircons were found in the granulite samples. The rounded zircons had thin (10–20 µm) concentric overgrowth rims on detrital cores, while the prismatic zircons did not have detrital cores. Both the overgrowth rims on the rounded zircons and the entire prismatic zircons were formed under granulite facies metamorphism and consistently yield Latest Oligocene–Early Miocene ages (23.7 ± 0.4 Ma to 17.2 ± 0.5 Ma; ²⁰⁶Pb/ ²³⁸U ages ( n  = 31) with low Th/U ratios, mostly <0.1). The internal structure of zircons and their SHRIMP U-Pb ages provide strong evidence in support of the granulite facies event occurring during the Latest Oligocene-Early Miocene. The detrital cores of rounded zircons show a huge variety of ages; Mesoarchean to Paleoproterozoic, Paleozoic to Mesozoic and Paleogene. The interior and marginal portions of the Eurasian continent including cratonic areas are suggested for their source provenances. These wide variations in age suggest that the protolith of the granulites of the lower metamorphic sequence were deposited near the trench of the Eurasian continental margin during Paleogene. The protolith of the lower metamorphic sequence of the Hidaka metamorphic belt was thrust under the upper metamorphic sequence, which had already been metamorphosed in early Paleogene. The Latest Oligocene-Early Miocene Hidaka high-temperature metamorphic event is presumed to have been caused by asthenospheric upwelling during back-arc rifting of the Kuril and Japan basins.     

Paleoseismic events and the 1596 Keicho-Fushimi large earthquake produced by a slip on the Gosukebashi fault at the eastern Rokko Mountains,Japan

Field surveys and trench excavation investigations revealed that there were at least four large seismic events produced by slips on the Gosukebashi fault in the Holocene in the southeastern Rokko Mountains of Japan. The characteristics of deformed topographies and three-dimensionally excavated exposures show that this fault is a right-lateral strike–slip fault having an average slip rate of 1.0 mm/year, with a reverse displacement component. The principle indicators of past faulting events are: (i) termination of secondary faults; (ii) sedimentary deposits related to faulting; and (iii) injection veins of fault gouge related to seismic faulting in the fractured zone. Radiocarbon dates indicate that the events occurred pre-1660 BC , 1660 BC –220 AD , from ～ 30–220 to 600 AD and 15th century AD . The youngest event is probably associated with the large 1596 AD Keicho-Fushimi earthquake which occurred in the area around Kyoto and Kobe Cities. The second younger event is probably correlated with the 416 AD Yamato earthquake, which is the oldest historic earthquake in Japanese historic records. The results of trench surveys show that the horizontal displacement produced by an individual event is ～ 1.5 m, and the recurrence of seismic event intervals is ～ 1200 years in the Gosukebashi fault.     

Center to limb variation of the intensity of the photospheric faculae

Center to limb variation of the excess brightness of photospheric facular granules was observed at 530 nm with a balloon-borne telescope of 10 cm aperture. Facular granules are found to be 9.2% and 16.2% brighter than the adjacent quiet region at cos = 0.65 and 0.50 respectively, being the angle between the Sun's normal and the line of sight. This observation, together with our earlier result (Hirayama, 1978), leads to facular models which are 600 K hotter than the photosphere if the diameter of facular granules is assumed to be 600 km, and 1000 K hotter if 150 km is assumed instead. It was also found that the soft X-ray bright points as observed with the Skylab do not correspond spatially to the photospheric facular granules near the polar region.