The Expansion of the Distance Between Two Arbitrary Gravitating Points as Applied to Specific Models of Celestial Bodies

For the complete system of biharmonic functions a suitable representation in spheroidal coordinates is found. It is used for expanding the distance between two arbitrary gravitating points and its inverse quantity in appropriate series. Such expansions can be of interest and useful in a number of problems of celestial mechanics and stellar dynamics.     

Gamma-ray bursts: optical afterglows in the deep Newtonian phase

Gamma-ray burst remnants become trans-relativistic typically in days to tens of days, and they enter the deep Newtonian phase in tens of days to months, during which the majority of shock-accelerated electrons will no longer be highly relativistic. However, a small portion of electrons are still accelerated to ultra-relativistic speeds and are capable of emitting synchrotron radiation. The distribution function for electrons is re-derived here so that synchrotron emission from these relativistic electrons can be calculated. Based on the revised model, optical afterglows from both isotropic fireballs and highly collimated jets are studied numerically, and compared to analytical results. In the beamed cases, it is found that, in addition to the steepening due to the edge effect and the lateral expansion effect, the light curves are universally characterized by a flattening during the deep Newtonian phase.     

Pregalactic Chemistry

The evolution of the universe from times after the recombination of the first atoms is controlled by chemistry. Chemistry can also help us to learn more about the first structures. In this paper we review the chemistry and atomic physics that are important in the time shortly after recombination, including the formation of the first structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Himalayan magmatism and porphyry copper–molybdenum mineralization in the Yulong ore belt, East Tibet

Summary ?The NW–SE-trending Yulong porphyry Cu–Mo ore belt, situated in the Sanjiang0 area of eastern Tibet, is approximately 400 km long and 35 to 70 km wide. Complex tectonic and magmatic processes during the Himalayan epoch have given rise to favorable conditions for porphyry-type Cu–Mo mineralization. Porphyry masses of the Himalayan epoch in the Yulong ore belt are distributed in groups along regional NW–SE striking tectonic lineaments. They were emplaced mainly into Triassic and Lower Permian sedimentary-volcanic rocks. K–Ar und U–Pb isotopic datings give an intrusion age range of 57–26 Ma. The porphyries are mainly of biotite monzogranitic and biotite syenogranitic compositions. Geological and geochemical data indicate that the various porphyritic intrusions in the belt had a common or similar magma source, are metaluminous to peraluminous, Nb–Y–Ba-depleted, I-type granitoids, and belong to the high-K calc-alkaline series. Within the Yulong subvolcanic belt a number of porphyry stocks bear typical porphyry type Cu–Mo alteration and mineralization. The most prominent porphyry Co–Mo deposits include Yulong, Malasongduo, Duoxiasongduo, Mangzong and Zhanaga, of which Yulong is one of the largest porphyry Cu (Mo) deposits in China with approximately 8 × 10⁶ tons of contained Cu metal. Hydrothermal alteration at Yulong developed around a biotite–monzogranitic porphyry stock that was emplaced within Upper Triassic limestone, siltstone and mudstone. The earliest alteration was due to the effects of contact metamorphism of the country rocks and alkali metasomatism (potassic alteration) within and around the porphyry body. The alteration of this stage was accompanied by a small amount of disseminated and veinlet Cu–Mo sulfide mineralization. Later alteration–mineralization zones form more or less concentric shells around the potassic zone, around which are distributed a phyllic or quartz–sericite–pyrite zone, a silicification and argillic zone, and a propylitic zone. Fluid inclusion data indicate that three types of fluids were involved in the alteration–mineralization processes: (1) early high temperature (660–420 °C) and high salinity (30–51 wt% NaCl equiv) fluids responsible for the potassic alteration and the earliest disseminated and/or veinlet Cu–Mo sulfide mineralization; (2) intermediate unmixed fluids corresponding to phyllic alteration and most Cu–Mo sulfide mineralization, with salinities of 30–50 wt% NaCl equiv and homogenization temperatures of 460–280 °C; and (3) late low to moderate temperature (300–160 °C) and low salinity (6–13 wt% NaCl equiv) fluids responsible for argillic and propylitic alteration. Hydrogen and oxygen isotopic studies show that the early hydrothermal fluids are of magmatic origin and were succeeded by increasing amounts of meteoric-derived convective waters. Sulfur isotopes also indicate a magmatic source for the sulfur in the early sulfide mineralization, with the increasing addition of sedimentary sulfur outward from the porphyry stock. Received August 29, 2001; revised version accepted May 1, 2002 Published online: November 29, 2002     

F stars, metallicity and the ages of red galaxies at z > 1

We explore whether the rest-frame near-ultraviolet spectral region, observable in high-redshift galaxies via optical spectroscopy, contains sufficient information to allow the degeneracy between age and metallicity to be lifted. We do this by first testing the ability of evolutionary synthesis models to reclaim the correct metallicity when fitted to the near-ultraviolet spectra of F stars of known (subsolar and supersolar) metallicity. F stars are of particular interest because the rest-frame near-ultraviolet spectra of the oldest known elliptical galaxies at   z > 1  appear to be dominated by F stars near to the main-sequence turn-off.
We find that, in the case of the F stars, where the Hubble Space Telescope ultraviolet spectra have a high signal-to-noise ratio, fitting models in which the metallicity is allowed to vary as a free parameter is rather successful at deriving the correct metallicity. As a result, the estimated turn-off ages of these stars yielded by model-fitting are well constrained. Encouraged by this we have fitted these same variable-metallicity models to the deep, optical spectra of the   z ≃ 1.5 mJy  radio galaxies 53W091 and 53W069 obtained with the Keck telescope. While the age and metallicity are not so easily constrained for these galaxies, we find that even when metallicity is allowed as a free parameter, the best estimates of their ages are still ≥3 Gyr, with ages younger than 2 Gyr now strongly excluded. Furthermore, we find that a search of the entire parameter space of metallicity and star formation history using MOPED leads to the same conclusion. Our results therefore continue to argue strongly against an Einstein–de Sitter universe, and favour a Λ-dominated universe in which star formation in at least these particular elliptical galaxies was completed somewhere in the redshift range   z = 3–5  .     

Collisional instability of the drift wave in multi-component plasmas

The collisional instability of the drift wave in a multi-component plasma is investigated. It is shown that when the electron and ion density gradients are different, e.g., due to the presence of a static third component or due to neutral drag effects, the drift mode becomes unstable. The instability is caused by the simultaneous action of the electron collisions with all other plasma species and the spatial difference of the density of the plasma components. This instability may be expected as a natural consequence of the stratification of a multi-component plasma placed in an external gravity field where it can operate for any amount of charge on heavy particles. Therefore it could develop in weakly ionized cold interstellar regions for example, when the heavy particles, i.e. charged grains, are a few tens of Å in size, and carry typically ±1,±2 charge. In the solar atmosphere, it may appear in the weakly ionized photospheric layers due to the convective motion of the neutral component.     

Polar Ring Currents on the sun During a Polar Magnetic Field Reversal

We have studied the variations of the height of polar crown prominences according to daily observations of the Sun at the Kodaikanal Observatory (India) during 1905–1975. Polar ring filaments at latitudes 60°–80° are related to the polar magnetic field reversal. A double decrease of the height of polar ring filaments was found in the course of their migration from 40°to the poles. We estimated the limiting height of the equilibrium of polar ring filaments from the stability condition of a strong electric current. We found that the transition from large-scale to small-scale ring filaments reduces the critical height of the stability for the prominences. A model of an inverse-polarity filament was used.     

Investigation of Failure Mechanisms and Migration of Organic Chemicals at Wilsonville, Illinois

Ground water contamination was discovered in 1981 in a monitoring well at the Earthline disposal facility near Wilsonville, Illinois. Organic chemicals had migrated at a rate 100 to 1000 times greater than predicted when the site received its permit to operate in 1978. Postulated failure mechanisms included migration through previously unmapped permeable zones, subsidence of an underground mine, organic-chemical and clay-mineral interactions, acid-mine drainage and clay interactions, trench-cover settlement, and erosion.
In this investigation, the Illinois State Geological Survey found the primary reason for the rapid migration: the presence of previously undetermined fractures and joints in glacial till. The inaccurate predictions of hydraulic conductivity were based on laboratory-determined values that did not adequately measure the effects of fractures and joints on the transit time calculations. Field-measured hydraulic conductivity values were generally 10 to 1000 times greater than their laboratory-measured counterparts, thus largely accounting for the discrepancy between predicted and actual migration rates in the transit time calculations. The problem was compounded, however, by the burial of liquid wastes and by trench covers that allowed excess surface runoff to enter the trenches. Organic-chemical and clay-mineral interactions may also have exacerbated the problem in areas where liquid organic wastes were buried.