The Lyapunov exponents in the dynamics of triple star systems

The dynamics of weakly heirarchical triple stars with equal masses are considered. Full spectra of the Lyapunov exponents are found via numerical integration of the orbits, for various initial configurations of the systemin the planar problem and with initial conditions in the vicinity of the 2 : 1 resonance (i.e., with the initial ratios of the periods of the outer and inner binaries being close to 2 : 1). Dependences between the Lyapunov time and the disruption time of the systemare constructed for initial conditions near and far from resonance. The character of these relationships is different near and far from resonance, corresponding to two kinds of Hamiltonian intermittency. The trajectories “stick” to the regular component in phase space near resonance, while this effect is not dominant far from resonance. Analysis of the distributions of the disruption times of the triple systems for initial conditions near and far from resonance confirm these conclusions.     

Dark halos of wide triple systems of galaxies

A new class of metagalactic system—wide triple systems of galaxies with characteristic scale lengths of ～1 Mpc—are analyzed. Dynamical models of such systems are constructed, and the amount of dark mass contained in them is estimated. In principle, kinematic data for wide triplets allow two types of models: with individual galactic halos and with a common halo for the entire system. A choice between the two models can be made based on X-ray observations of these systems, which can determine whether clustering and hierarchical evolution continues on scales of ～1 Mpc or whether systems with such scale lengths are in a state of virial quasi-equilibrium.     

Trajectories of bodies in triple systems with moderate lifetimes

The general three-body problem with equal masses and zero initial velocities is considered. Sets of initial conditions for which the triple systems decay over comparatively short times, 10T _cr < T < 20T _cr, are distinguished (T _cr is the mean crossing time for a component of the system). These sets form distinct families of structures in the domain of the initial conditions. The properties of trajectories of the bodies within some of these structures are described. It is shown that the set of families is no more than countable. A new classification for families of trajectories in decaying triple systems is proposed. Some problems in classifying trajectories in the three-body problem that must be addressed in the future are formulated.     

Trajectories of bodies in zones of rapidly decaying triple systems

The general three-body problem with equal masses and zero initial velocities is considered. Zones in which the triple systems decay over short times T < 10T _cr are distinguished in the domain of the initial conditions, where T _cr is the mean crossing time for a component of the triple system. These zones form distinct families of structures. Properties of the trajectories of bodies within these structures are described. The structures often display a layered character, with each layer corresponding to triple systems in which a particular body departs during the decay. These layers alternate with zones in which the decay does not occur on such short time scales, and the bodies are flung outward without this leading to a departure, or undergo simple interactions. In the zones of rapid decay, the departure of one of the bodies occurs after one or a few triple encounters between the components.     

Formation of low-mass X-ray novae with black holes from triple systems

We apply a population synthesis technique to study the formation and evolution of low-mass X-ray binaries with black holes, observed as X-ray novae, from hierarchical triple systems. A scenario is suggested in which an inner close binary system evolves into an X-ray system with a large mass ratio. The high rate of accretion onto the neutron star leads to a common envelope stage, which may result in the formation of a Thorne-Zytkow (TZ) object. During its evolution, the envelope of the TZ object expands, encompassing the third star. The recurrent common-envelope stage decreases the size of the orbit of the third star, leading to the formation of a lowmass X-ray nova with a black hole. The dynamical stability of triple systems automatically ensures that only lowmass X-ray novae form. We also consider the possible formation of an X-ray nova from a binary in the case of asymmetrical core collapse during a supernova explosion.     

Criteria for the stability of triple systems and their application to observations of multiple stars

Criteria for stability of triple systems are studied and compared with the results of numerical simulations obtained for model triple systems and observed multiple stars. The results for the stability analyses using two new criteria—those of Aarseth and of Valtonen et al.—agree with the simulation results in 98% of cases. Thus, these criteria can be used to analyze the stability of systems for which direct modeling of their dynamical evolution is difficult (for example, because not all orbital parameters for their subsystems are known). The last published version of the “Multiple-Star Catalog” of Tokovinin is analyzed to search for systems that may be unstable according to the two new criteria. More detailed studies are carried out for the HD 284419 (T Tau) system. The parameters of the apparent motion method is used to obtain new orbital solutions for this system. The regions of dynamical stability of the system as functions of the orbital parameters are estimated. It is not possible to determine a unique solution for the orbit with the available data; for periods shorter than 300 yr and longer than 5500 yr, the probability of decay of the system on time scales less than 107 yr is high. This conclusion is supported by the application of the stability criteria, as well as direct modeling of the system’s dynamical evolution.     

The structure of non-hierarchical triple system stability regions

A detailed study of the two-dimensional initial conditions region section in the planar three-body problem is performed. The initial conditions for the three well-known stable periodic orbits (the Schubart’s orbit, the Broucke’s orbit and the eight-like orbit) belong to this section. Continuous stability regions (for the fixed integration interval) generated by these periodic orbits are found. Zones of the quick stability violation are outlined. The analysis of some concrete trajectories coming from various stability regions is performed. In particular, trajectories possessing varying number of “eights” formed by moving triple system components are discovered. Orbits with librations are also found. The new periodic orbit originated from the zone siding with the Schubart’s orbit region is discovered. This orbit has reversibility points (each of the outer bodies possess a reversibility point) and two points of close double approach of the central body to each of the outer bodies. The influence of the numerical integration accuracy on the results is studied. The stability regions structure is preserved during calculations with different values of the precision parameter, numerical integration methods and regularization algorithms of the equations of motion.     

The initial fast decay phase of stellar flares

The initial fast decay phase of a stellar flare is shown to be caused by the rapid cooling of the flare plasma, which radiates as a perfect blackbody at the flare brightness maximum.     

The triple isotopic composition of oxygen in leaf water

The isotopic composition of atmospheric O₂ depends on the rates of oxygen cycling in photosynthesis, respiration, photochemical reactions in the stratosphere and on δ¹⁷O and δ¹⁸O of ocean and leaf water. While most of the factors affecting δ¹⁷O and δ¹⁸O of air O₂ have been studied extensively in recent years, δ¹⁷O of leaf water—the substrate for all terrestrial photosynthesis—remained unknown. In order to understand the isotopic composition of atmospheric O₂ at present and in fossil air in ice cores, we studied leaf water in field experiments in Israel and in a European survey. We measured the difference in δ¹⁷O and δ¹⁸O between stem and leaf water, which is the result of isotope enrichment during transpiration. We calculated the slopes of the lines linking the isotopic compositions of stem and leaf water. The obtained slopes in ln(δ¹⁷O + 1) vs. ln(δ¹⁸O + 1) plots are characterized by very high precision (∼0.001) despite of relatively large differences between duplicates in both δ¹⁷O and δ¹⁸O (0.02-0.05‰). This is so because the errors in δ¹⁸O and δ¹⁷O are mass-dependent. The slope of the leaf transpiration process varied between 0.5111 ± 0.0013 and 0.5204 ± 0.0005, which is considerably smaller than the slope linking liquid water and vapor at equilibrium (0.529). We further found that the slope of the transpiration process decreases with atmospheric relative humidity (h) as 0.522-0.008 × h, for h in the range 0.3-1. This slope is neither influenced by the plant species, nor by the environmental conditions where plants grow nor does it show strong variations along long leaves.     

The triple multimineral barrier for hazardous waste encapsulation

According to the present state of science and technology, the ultimate disposal of critical substances such as chemotoxic wastes, metal slurries, radioactive substances, etc., as well as houshold waste, necessitates enclosure within a multi-barrier system. The geology of the disposal site plays an important role. The site itself defines the geological barrier which has to fulfill at least two requirements: namely low permeability and retention, respectively retardation qualities. These can be achieved to a certain degree either by clay minerals, zeolites or an artificial product such as active coal. In order to increase the imperviousness and retardation potentials of e.g. clayey geological barriers, technical barriers have to be added. One of them and the most important is the mineralogic barrier. It consists of clay dominated layers and according to the multimineral barrier concept the different layers have to meet different functions.     

The decay products of rn in etched track radon detection

Precipitation of decay products of atmospheric ²²²Rn in small containers and the effects of their precipitation on alpha-particle-track-measurements of radon activities were studied. From decay curves of decay product activities on surfaces exposed to radon-containing air the ratios ²¹⁴Pb/²¹⁸Po (=r) in the precipitates were determined. From r average ages of precipitating decay products were calculated. Average ages and r were low, indicating rapid precipitation of decay products, and decreased with container size. Activities on exposed surfaces were approximately those expected if decay products precipitate completely and uniformly on the internal surfaces of containers.Decay products precipitated on foils of correct thickness covering cellulose nitrate (CN) track detectors produce tracks. Therefore track densities produced by given radon activities are increased by such covers to extents predictable from the decay product activities on the overlays. Tracks formed under overlays may etch to larger, more vertical-sided, more easily counted forms. When suspended, uncovered, in air at distances from surfaces greater than the ranges of the alpha particles, three types of CN recorded tracks at the rate (ρ′) of 0.12 tracks cm⁻² (pCi Rn)⁻¹ 1⁻¹ hr⁻¹ as predicted by a theoretical expression. In small containers (ρ′) varied with position and container size.     

The decay products of 222rn in etched track radon detection

Precipitation of decay products of atmospheric ²²²Rn in small containers and the effects of their precipitation on alpha-particle-track-measurements of radon activities were studied. From decay curves of decay product activities on surfaces exposed to radon-containing air the ratios ²¹⁴Pb/²¹⁸Po (=r) in the precipitates were determined. From r average ages of precipitating decay products were calculated. Average ages and r were low, indicating rapid precipitation of decay products, and decreased with container size. Activities on exposed surfaces were approximately those expected if decay products precipitate completely and uniformly on the internal surfaces of containers.Decay products precipitated on foils of correct thickness covering cellulose nitrate (CN) track detectors produce tracks. Therefore track densities produced by given radon activities are increased by such covers to extents predictable from the decay product activities on the overlays. Tracks formed under overlays may etch to larger, more vertical-sided, more easily counted forms. When suspended, uncovered, in air at distances from surfaces greater than the ranges of the alpha particles, three types of CN recorded tracks at the rate (ρ′) of 0.12 tracks cm^?2 (pCi Rn)^?1 1^?1 hr^?1 as predicted by a theoretical expression. In small containers (ρ′) varied with position and container size.     

Assessment of the Re decay constant by cross calibration of Re-Os molybdenite and U-Pb zircon chronometers in magmatic ore systems

The past decade has seen renewed interest in ¹⁸⁷Re-¹⁸⁷Os geochronology using a variety of matrices including sulfide minerals, shales and meteorites. The most widely used value of the ¹⁸⁷Re decay constant (λ¹⁸⁷Re) is 1.666 ± 0.005 × 10⁻¹¹ a⁻¹ (±0.31%), which is based on cross calibration of Re-Os and Pb-Pb chronometers for certain meteorites [Smoliar M. I., Walker R. J., and Morgan J. W. (1996) Re-Os isotope constraints on the age of Group IIA, IIIA, IVA, and IVB iron meteorites. Science271, 1099-1102]. However, other recent studies have yielded alternate values of λ¹⁸⁷Re, based upon either direct counting experiments or analysis of meteorites. Here, we provide an independent assessment of λ¹⁸⁷Re, using methodology, sample materials, and preparation of Os standard solutions different from those of Smoliar et al. (1996). Combining Re-Os age data for molybdenite formed in magmatic ore deposits, with the U-Pb zircon age of the magmatic rocks, a refined λ¹⁸⁷Re value is determined by averaging 11 individual cross-calibration experiments spanning ca. 2700 Ma of Earth history. Using the U decay constants of Jaffey [Jaffey A. H., Flynn K. F., Glendenin L. E., Bentley W. C., and Essling A. M. (1971) Precision measurement of half-lives and specific activities of 235U and 238U. Phys. Rev.4, 1889-1906], a value for λ¹⁸⁷Re of 1.6668 ± 0.0034 × 10⁻¹¹ a⁻¹ is determined. Using the λ²³⁸U value of Jaffey et al. (1971) and λ²³⁵U value of Schoene [Schoene B., Crowley J. L., Condon D. J., Schmitz M. D., and Bowring S. A. (2006) Reassessing the uranium decay constants for geochronology using ID-TIMS U-Pb data. Geochim. Cosmochim. Acta70, 426-445], a value for λ¹⁸⁷Re of 1.6689 ± 0.0031 × 10⁻¹¹ a⁻¹ is determined. These values are nominally higher (ca. 0.1 and ca. 0.2%) than the value determined by Smoliar et al. [Smoliar M. I., Walker R. J., and Morgan J. W. (1996) Re-Os isotope constraints on the age of Group IIA, IIIA, IVA, and IVB iron meteorites. Science271, 1099-1102], but within calculated uncertainty. Further refinement of λ¹⁸⁷Re by cross calibrating the molybdenite and U-Pb zircon chronometers should be possible by utilizing high precision, single-grain, chemical abrasion zircon U-Pb analyses.     

The influence of the decay of OB associations on the evolution of dwarf galaxies

The ejection of stars from spheroidal and disk dwarf galaxies resulting from the decay of OB associations is studied. This has substantial observational consequences for disk galaxies with escape velocities up to 20 km/s, or dynamical masses up to 10⁸ M _⊙. The ejection of stars can (i) reduce the abundances of the products of Type Ia supernovae and, to a lesser degree, Type II supernovae, in disk stars, (ii) chemically enrich the galactic halo and intergalactic medium, (iii) lead to the loss of 50% of the stellar mass in galaxies with masses ∼10⁷ M _⊙ and the loss of all stars in systems with masses ≲10⁵ M _⊙, (iv) increase the mass-to-luminosity ratio of the galaxy.     

The salt decay of medieval bricks at a vault in Brarup Church,Denmark

This paper presents an investigation of the decay of bricks in the chancel vault of Brarup Church located close to the Baltic Sea at the island of Falster in Denmark. The aim of the work was to study a peculiar phenomenon in order to prescribe appropriate treatment. Although protected by a lime plaster, some bricks were pulverized up to 50 mm deep from the topside. The decay occurred in a random pattern over the structure, with undamaged bricks positioned next to deteriorated bricks. The brick structure was investigated by Mercury Intrusion Porosiometry. All bricks had a majority of pores in the range 1–10 μm, but the decayed bricks also had a fraction of pores with a diameter less than 100 nm. The difference may be due to a lower firing temperature, or it may be a consequence of the salt decay. Salt analysis proved that the deteriorated bricks were contaminated with sodium chloride, which could have degraded the brick structure. However, the powdering of the bricks may be caused by the precipitation of gypsum, which was found in the brick powder but not in the deteriorated brick itself. According to calculations with the computer program RUNSALT, the precipitation of gypsum is much influenced by the presence of sodium chloride. The gypsum precipitates due to changes in temperature between 0 and 30°C and variations in relative humidity between 75 and 95%. Seasonal climatic changes in the attic were measured to cover this interval. Perhaps sodium chloride acted as a catalyst that facilitated the accumulation and precipitation of gypsum at the topside of the bricks. A sacrificial plaster, which is the traditional treatment for salt contaminated structures, would not prevent such decay.     

Geochemical test for branching decay of Lu

Two different groups of values for the ¹⁷⁶Lu decay constant have been determined by recent high-precision experiments. The λ¹⁷⁶Lu values of 1.86-1.87 × 10⁻¹¹ a⁻¹ were determined by age comparisons using terrestrial minerals of Proterozoic and late Archean age, whereas values of ∼1.94 × 10⁻¹¹ a⁻¹ were determined in age comparison studies of meteorites.A possible branched decay of ¹⁷⁶Lu could be the cause of this discrepancy. The β⁺ decay of ¹⁷⁶Lu to ¹⁷⁶Yb was detected in the early studies of radioactivity of ¹⁷⁶Lu, with reported values of λβ⁺/(λβ⁺ + λβ⁻) in the total ¹⁷⁶Lu ranging from less than 0.03 to 0.67. If the β⁺ decay fraction is close to the upper limit of the reported values, it can explain the 4%-6% difference between the apparent λ¹⁷⁶Lu values.To get a reliable estimate for the β⁺ decay of ¹⁷⁶Lu, we have measured Yb isotopic composition in 2.7 Ga zircons with Lu/Yb_N (chondrite-normalized) ratios of 1.40 and 1.45, in 1.0 Ga xenotime with Lu/Yb_N = 1.23, using Yb from the 28.4 Ma Fish Canyon Tuff (FCT) zircon and titanite as the modern reference value. Multiple analyses yielded the following weighted mean values (± 2σ) for the ¹⁷⁶Yb/¹⁷⁴Yb ratio: 0.4022134 ± 0.0000017 for the FCT zircon and titanite, 0.4022134 ± 0.0000019 for the 1.0 Ga xenotime, and 0.4022124 ± 0.0000033 for the 2.7 Ga zircons. These data yield λβ⁺/(λβ⁺ + λβ⁻) = −0.005 ± 0.015 (2σ) and establish an upper limit of 0.9% of total decays for the β⁺ decay branch. Branching decay can therefore be eliminated as the cause of the discrepancy in ¹⁷⁶Lu decay constant estimates. We discuss other possible causes of the λ¹⁷⁶Lu terrestrial vs. meteorite discrepancy.     

Numerical simulation of permafrost growth and decay

A series of numerical models on permafrost growth and decay are presented with special emphasis on the climatic conditions in western Europe during the last glacial stage. Numerical modelling of growth and decay of the active layer suggests penetration depths in the range between 0.6 to 1.4 m. Permafrost is estimated to have grown, depending on the sediment type, to a thickness of 90 m to 140 m in northern Germany and The Netherlands within 10 000 y during the peak period of the last glacial stage. Permafrost continued to exist at depth for about 2000 y after the climatic improvement following the Younger Dryas. Permafrost growth under rivers and lakes is shown to be unlikely under the climatic conditions of the last glacial stage in northern Germany. A time period of 10 000 to 42 000 years and a massive climatic excursion (of the order of > 11°C) is required to remove the thick permafrost layers in Siberia and Alaska of today. © 1998 John Wiley & Sons, Ltd.