Anisotropic distribution functions for spherical galaxies

A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular momentum. It requires the density to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the angular momentum. The products of the density and its radial and transverse velocity dispersions can be also expressed as a sum of products of functions of the potential and of the radial coordinate. Several examples are given, including some of new anisotropic distribution functions. This device can be extended further to the related problem of finding two-integral distribution functions for axisymmetric galaxies.     

A comprehensive study of distribution laws for the fragments of Košice meteorite

In this study, we conduct a detailed analysis of the Ko?ice meteorite fall (February 28, 2010), to derive a reliable law describing the mass distribution among the recovered fragments. In total, 218 fragments of the Ko?ice meteorite, with a total mass of 11.285 kg, were analyzed. Bimodal Weibull, bimodal Grady, and bimodal lognormal distributions are found to be the most appropriate for describing the Ko?ice fragmentation process. Based on the assumption of bimodal lognormal, bimodal Grady, bimodal sequential, and bimodal Weibull fragmentation distributions, we suggest that, prior to further extensive fragmentation in the lower atmosphere, the Ko?ice meteoroid was initially represented by two independent pieces with cumulative residual masses of approximately 2 and 9 kg, respectively. The smaller piece produced about 2 kg of multiple lightweight meteorite fragments with the mean around 12 g. The larger one resulted in 9 kg of meteorite fragments, recovered on the ground, including the two heaviest pieces of 2.374 kg and 2.167 kg with the mean around 140 g. Based on our investigations, we conclude that two to three larger fragments of 500–1000 g each should exist, but were either not recovered or not reported by illegal meteorite hunters.     

On the Nature of Neutral-Line-Associated Radio Sources

A number of authors claimed that radio sources above the neutral line of the magnetic field in solar active regions are due to non-thermal emission. This study shows that the thermal mechanism explains the radio emission from such sources. Models similar to those used for interpreting cyclotron lines were used in this study. Such models account for a steep decline in the spectrum at high frequencies and a low degree of polarization. The magnetic field between the two sunspots with an anti-parallel magnetic field has a lower gradient than the field above the sunspots. This, combined with the possibly high temperature in coronal loops connecting the sunspots, leads to the following conclusions. The optical thickness of the gyroresonance layers is increased and leads to more effective radiation at a harmonic number of 4 or 5. The lower gradient of the field between the sunspots also results in more rapid growth of emission intensity with increasing wavelength in this region than in the regions immediately above the sunspots. Additionally, the spatial averaging of the source structure due to the antenna beam pattern leads to a decrease in the degree of polarization in the region between the sunspots.     

Oxygen abundances in the most oxygen-rich spiral galaxies

Oxygen abundances in the spiral galaxies expected to be richest in oxygen are estimated. The new abundance determinations are based on the recently discovered ff relation between auroral and nebular oxygen-line fluxes in high-metallicity H  ii regions. We find that the maximum gas-phase oxygen abundance in the central regions of spiral galaxies is 12+log(O/H) ∼ 8.75. This value is significantly lower (by a factor of ≳5) than the previously accepted value. The central oxygen abundance in the Milky Way is similar to that in other large spirals.     

Evolution of the Oort cloud angular momentum: Numerical simulation

This paper considers the evolution of a flat svarm of cometary bodies (under the effect of the passage of stars), initially moving in one direction along the circular orbits with radii 1.4×10⁴<r<2×10⁴ AU and along elliptic orbits with semi-major axes 5×10³<a<1×10⁴ AU and with perihelia within 50<q<100 AU. Numerical simulation shows that the original flat belt of comets is thermalizing. Its root-mean-squarez-coordinate grows withr. A cometary cloud forms with a dense flattened inner core and a rarefied halo (the Oort cloud proper). The value =N _core/N _halo varies within a wide range (up to the order of magnitude) depending on the model used (N _core andN _halo are the numbers of comets in the core and the halo, respectively).The hypothesis of a massive Oort cloud (Marochniket al., 1988) implies that the Oort cloud should have a large angular momentum. This paper employs numerical simulation to calculate Oort cloud models to which the initially flat located at the periphery of the solar nebula rotating cometary swarms is evolving in time. The loss of the initial angular momentum over the time of the Oort cloud evolution is not large.     

Crustal origin for coupled 'ultra-depleted' and 'plagioclase' signatures in MORB olivine-hosted melt inclusions: evidence from the Siqueiros Transform Fault,East Pacific Rise

Geochemical data from melt inclusions in olivine phenocrysts in a picritic basalt from the Siqueiros Transform Fault on the northern East Pacific Rise provide insights into the petrogenesis of mid-ocean ridge basalts (MORB). The fresh lava contains ~10% of olivine phenocrysts (Fo_89.3-91.2) and rare, small (<1 mm) plagioclase phenocrysts with subhedral to irregular shapes with a range of compositions (An_80-90, An_57-63). Melt inclusions in olivine phenocrysts are glassy, generally rounded in shape and vary in size from a few to ~200 µm. Although most of the inclusions have compositions that are generally consistent with being representative of parental melts for the pillow-rim glasses, several inclusions are clearly different. One inclusion, which contains a euhedral grain of high-Al, low-Ti spinel, has a composition unlike any melt inclusions previously described from primitive phenocrysts in MORB. It has a very high Al₂O₃ (~20 wt%), very low TiO₂ (~0.04 wt%) and Na₂O (~1 wt%) contents, and a very high CaO/Na₂O value (~14). The glass inclusion is strongly depleted in all incompatible elements (La =0.052 ppm; Yb =0.34; La/Sm(n) ~0.27), but it has large positive Sr and Eu anomalies (Sr/Sr* ~30; Eu/Eu* ~3) and a negative Zr anomaly. It also has low S (0.015 wt%) and relatively high Cl (180 ppm). We suggest that this unusual composition is a consequence of olivine trapping plagioclase in a hot, strongly plagioclase-undersaturated magma and subsequent reaction between plagioclase and the host olivine producing melt and residual spinel. Two other melt inclusions in a different olivine phenocryst have compositions that are generally intermediate between 'normal' inclusions and the aluminous inclusion, but have even higher CaO and Sr contents. They are also depleted in incompatible elements, but to a lesser degree than the aluminous inclusion, and have smaller Sr and Eu anomalies. Similar inclusions have also been described in high-Fo olivine phenocrysts from Iceland and northern Mid-Atlantic Ridge. We suggest that the compositions of these inclusions represent assimilation of gabbroic material into the hot primitive magma. The localised nature of this assimilation is consistent with it occurring within a crystal mush zone where the porosity is high as primitive magmas pass through earlier formed gabbroic 'cumulates'. In such an environment the contaminants are expected to have quite diverse compositions. Although the interaction of primitive melts with gabbroic material may not affect the compositions of erupted MORB melts on a large scale, this process may be important in some MORB suites and should be accounted for in petrogenetic models. Another important implication is that the observed variability in melt inclusion compositions in primitive MORB phenocrysts need not always to reflect processes occurring in the mantle. In particular, inferences on fractional melting processes based on geochemistry of ultra-depleted melt inclusions may not always be valid.     

The Composition of Near-solidus Partial Melts of Fertile Peridotite at 1 and 1{middle dot}5 GPa: Implications for the Petrogenesis of MORB

We have determined the near-solidus melt compositions for peridotiteMM-3, a suitable composition for the production of mid-oceanridge basalt (MORB) by decompression partial melting, at 1 and1·5 GPa. At 1 GPa the MM-3 composition has a subsolidusplagioclase-bearing spinel lherzolite assemblage, and a solidusat 1270°C. At only 5°C above the solidus, 4% meltis present as a result of almost complete melting of plagioclase.This melting behaviour in plagioclase lherzolite is predictedfrom simple systems and previous experimental work. The persistenceof plagioclase to > 0·8 GPa is strongly dependenton bulk-rock CaO/Na₂O and normative plagioclase content in theperidotite. At 1·5 GPa the MM-3 composition has a subsolidusspinel lherzolite assemblage, and a solidus at 1350°C.We have determined a near-solidus melt composition at 2% meltingwithin 10°C of the solidus. Near-solidus melts at both 1and 1·5 GPa are nepheline normative, and have low normativediopside contents; also they have the highest TiO₂, Al₂O₃ andNa₂O, and the lowest FeO and Cr₂O₃ contents compared with higherdegree partial melts. Comparison of these near-solidus meltswith primitive MORB glasses, which lie in the olivine-only fieldof crystallization at low pressure, indicate that petrogeneticmodels involving aggregation of near-fractional melts formedduring melting at pressures of 1·5 GPa or less are unlikelyto be correct. In this study we use an experimental approachthat utilizes sintered oxide mix starting materials and peridotitereaction experiments. We also examine some recent studies usingan alternative approach of melt migration into, and entrapmentwithin ‘melt traps’ (olivine, diamond, vitreouscarbon) and discuss optimal procedures for this method. KEY WORDS: experimental petrology; mantle melting; near-solidus; fertile peridotite; MORB     

Multi‐block finite‐difference method for 3D elastodynamic simulations in anisotropic subhorizontally layered media

Prediction of elastic full wavefields is required for reverse time migration, full waveform inversion, borehole seismology, seismic modelling, etc. We propose a novel algorithm to solve the Navier wave equation, which is based on multi‐block methodology for high‐order finite‐difference schemes on curvilinear grids. In the current implementation, the blocks are subhorizontal layers. Smooth anisotropic heterogeneous media in each layer can have strong discontinuities at the interfaces. A curvilinear adaptive hexahedral grid in blocks is generated by mapping the original 3D physical domain onto a parametric cube with horizontal layers and interfaces. These interfaces correspond to the main curvilinear physical contrast interfaces of a subhorizontally layered formation. The top boundary of the parametric cube handles the land surface with smooth topography. Free‐surface and solid–solid transmission boundary conditions at interfaces are approximated with the second‐order accuracy. Smooth media in the layers are approximated up to sixth‐order spatial schemes. All expected properties of the developed algorithm are demonstrated in numerical tests using corresponding parallel message passing interface code.     

Technogenic hydrogeochemical anomalies of tungsten deposits in Kykylbey ore region

Peculiarities of the tungsten deposits drainage flow chemical composition formation, the development of which was ceased almost 40 years ago, have been considered. Migration peculiarities of ore components have been covered, and forms of their migration have been calculated. Inertial characteristics of the surface flow contamination are shown.