The G-dwarf problem: A tentative analytical approach,relaxing instantaneous recycling

Starting from a general solution for the birth functionB(m, t) of stars described in detail in Casusoet al. (1989), we have obtained a first-order analytical approximation to this function as a function of metallicityZ. Using this, we obtained a fit to the observational curve compiled by Tinsley (1980) for the cumulative function of stars with metallicity lower than a given value in the solar neighbourhood. In addition, using the same expression, with its numerical fit to previous data, we obtain a good fit to the differential distributions of stars at low metallicity given in the review by Pagel (1987), given a bifurcation in the birth function at low values ofZ, which would correspond to two distinct epochs of onset of star formation. The analysis gives an infall of gas towards the solar neighbourhood up to the epoch of metallicityZ=6.7×10^–3 with a correspondingly increased star formation rate, which subsequently stabilized, and another similar inflow up toZ=1.2×10^–3, followed again by a steady star formation rate for largerZ. Although the assumptions made are still relatively crude, and the numbers should be considered tentative, the flexibility of the model in handling the problem is that we wish to show here.     

Surviving Metal in Meteoritic Iron Oxide from The Wolf Creek,Western Australia,Meteorite Crater

Abstract. Some very small particles of metal, revealed by polishing a chunk of Wolf Creek meteoritic iron oxide, appear to consist entirely of moderately shocked kamacite. The apparent lack of surviving taenite tentatively suggests that the Wolf Creek crater was formed by a hexahedrite, although medium octahedrites have recently been found within 4000 meters of the crater. Macrosegregation of nickel within the Wolf Creek meteoroid could account for the discrepancy. Further research on surviving metal is indicated.     

Fusion cross sections for nucleonic-halo systems in solar systems

The behavior of total fusion cross sections for proton and neutron-halo systems at near and sub-barrier energies have been studied using coupled-channel calculations. We have done the fusion distribution by considering phonon excitations and rotational deformation. Comparing with available experimental data represents a good agreement for neutron halo systems. A comparison between the reduced fusion cross sections of these systems shows different behavior in sub-barrier energies.     

Predictability in dynamical systems

The problem has basically three aspects: A mathematical, a physical and thirdly, an epistemological one. Even though the state of a dynamical system as a function of time may be perfectly and unambiguously determined in principle, do we at this time have the means to find out what this state is?     

Quasi-equilibrium in collisional systems

Quasi-equilibrium states, in which collisional systems do not show the usually observed rapid decrease or increase in orbital eccentricities and inclinations, consist of two major types. In the first type (linear systems) the coefficient of restitution must depend on the velocity of impact to maintain the equilibrium. In the second type (non-linear systems) this is not necessary, but an appropriate perturbation is needed. Drag in a co-moving medium leads to this type, for instance. Two other types (degenerate systems and stochastic systems) can be defined, but they are not studied in this paper. Quasi-equilibrium systems are bimodal. Stable configurations are not possible between certain values of the optical thickness. The accretion of matter in a proto-planet may trigger a jump from one stable region to another in the surrounding medium. If this happens, a dense zone is produced at the distance of 16/9 planetary radii. This phenomenon seems to explain the origin of planetary rings. The distance of 16/9 radii (127 000 km for Jupiter, 107 000 km for Saturn and 44 000 km for Uranus) agrees remarkably well with the observations. In this model the ring is maintained by the pressure of an extremely rarefied medium.     

The Hill stability of inclined small mass binary systems in three-body systems with special application to triple star systems, extrasolar planetary systems and Binary Kuiper Belt systems

The dynamical stability of a bound triple system composed of a small binary or minor planetary system moving on a orbit inclined to a central third body is discussed in terms of Hill stability for the full three-body problem. The situation arises in the determination of stability of triple star systems against disruption and component exchange and the determination of stability of extrasolar planetary systems and minor planetary systems against disruption, component exchange or capture. The Hill stability criterion is applied to triple star systems and extrasolar planetary systems, the Sun-Earth-Moon system and Kuiper Belt binary systems to determine the critical distances for stable orbits. It is found that increasing the inclination of the third body decreases the Hill regions of stability. Increasing the eccentricity of the binary also produces similar effects.These type of changes make exchange or disruption of the component masses more likely. Increasing the eccentricity of the binary orbit relative to the third body substantially decreases stability regions as the eccentricity reaches higher values. The Kuiper Belt binaries were found to be stable if they move on circular orbits. Taking into account the eccentricity, it is less clear that all the systems are stable.     

Evolution in semi-detached binary systems

The evolutionary process of semi-detached binary systems is examined on the basis of non-conservation of orbital angular momentum. We conclude that the semi-detached binary systems follow Type B evolution.     

Tidal interactions in multi-planet systems

We study systems of close orbiting planets evolving under the influence of tidal circularization. It is supposed that a commensurability forms through the action of disk induced migration and orbital circularization. After the system enters an inner cavity or the disk disperses the evolution continues under the influence of tides due to the central star which induce orbital circularization. We derive approximate analytic models that describe the evolution away from a general first order resonance that results from tidal circularization in a two planet system and which can be shown to be a direct consequence of the conservation of energy and angular momentum. We consider the situation when the system is initially very close to resonance and also when the system is between resonances. We also perform numerical simulations which confirm these models and then apply them to two and four planet systems chosen to have parameters related to the GJ 581 and HD 10180 systems. We also estimate the tidal dissipation rates through effective quality factors that could result in evolution to observed period ratios within the lifetimes of the systems. Thus the survival of, or degree of departure from, close commensurabilities in observed systems may be indicative of the effectiveness of tidal disipation, a feature which in turn may be related to the internal structure of the planets involved.     

Nonlinear oscillations in star-forming systems

A number of analytically formulated models of star-forming systems which include nonlinear interactions of stars and interstellar medium are considered. It is shown that two conditions are essential for the development of nonlinear oscillations: namely, the induced star formation and the presence of time-delay or strong nonlinearity in interacting star-cloud systems. The three component model with time-delay reproducing the temporal behaviour obtained in numerical simulations by Seidenet al. (1982) is proposed.     

Relative chaos in stellar systems

Statistical properties of many-dimensional dynamical systems-stellar systems of different types, are investigated by means of new definition of relative chaos based on the estimation of the Ricci curvature in the direction of the velocity of geodesics. Numerical experiment is performed to calculate the Ricci and scalar curvatures for systems with equal total energy. The results of calculations enable one to obtain schematic classification of stellar systems by increasing degree of chaos.     

First-order resonances in three-degrees-of-freedom systems

Hamiltonian systems with three degrees of freedom which have a resonance-ratio 1∶2∶ω with ω=1, 2, 3, or 4 are studied here. The periodic orbits are determined together with their stability characteristics. Furthermore we shall study the fundamental question of asymptotic integrability of these systems.     

Binary evolution in Stellar systems

Three new star cluster models containing 250 members and one case with 500 particles have been studied by numerical methods of direct integration. The evolution is dominated by one central binary in all systems with a realistic mass spectrum and more than 50% of the total energy is absorbed by one heavy pair after only 6–18 mean crossing times. General conditions for binary formation and disruption are discussed and a qualitative explanation is given for the energy sink behaviour. Strong interactions with close binaries lead to increased relaxation and the ejection of energetic escapers. At the same time the corresponding recoil kinetic energy is transferred to the other central members by two-body encounters which prevent a secondary phase of central contraction.     

Multiple-mirror telescope systems in astronomy

The function of a telescope is to optimize the transfer of the information of interest from a source of finite angular size to the analytical device which is going to extract it. It is far from obvious that the conventional large telescope is the optimum fore-optical system for looking through a turbulent atmosphere. There are considerable scientific and financial advantages in going to multiple-imaging-elements and several groups in different parts of the world are working in this direction.Presented at Primars-1 Conference, held at University of Manchester, June 26–30, 1979.     

On arch-filament systems in spotgroups

Systems of arch-shaped filaments (AFS) occurring in the interspot region of young bipolar groups are studied. Their main characteristics are: Average length: 30000km, average width 20000km, width of individual filaments 1000–3000 km, height of arches 4–15000 km. A typical lifetime of the filaments 30 min; appreciable changes of the system occur within several hours; the lifetime of a system is about three days. - The arch-filament systems bridge the neutral line and connect the regions of the innermost spots of opposite polarity. Material moves along the filaments (v 25–50 km/sec) following the direction of the magnetic field, and sometimes arches are observed rising at a rate of 20 km/sec. They are very dark on the inner disk and appear either in emission or in absorption close to the solar limb. - The occurrence of bright points (moustaches) is found to be closely associated with AFS in young spotgroups. - The possible nature of AFS and their relation to other types of filamentary structures is discussed.     

Tidal flows in binary systems

The expressions of the tidal velocity in not very close binaries (double stars, the Sun and a planet, a planet and a satellite) are derived and applied in particular to white dwarfs and the giant planets of the solar system. The magnitude of the velocity on the surface of Jupiter is estimated to be about 0.5 cm s^?1. In white dwarfs the velocities of the order of tens m s^?1 may be encountered, and they can influence their evolution. The symmetry of the tidal flows is noted to be suitable for the magnetic field generation.     

Stability criteria in many-body systems

Celestial Mechanics and Dynamical Astronomy - In previous papers of this series the stability of hierarchical many-body dynamical systems has been considered in terms of parameters which are a...     

Stability criteria in many-body systems

The analytical stability criterion applicable to coplanar hierarchical three-body systems described in the first paper of this series, Walkeret al. (1980), is modified to give an exact representation ofHill-type stability in all such cases. The dependence of the stability on all orbital parameters (in the coplanar case) is taken into account. The criterion for stability is now dependant upon the participating masses, the elements of the initial osculating Keplerian orbits of the system (viz. the orbits ofm ₂ aboutm ₁ andm ₃ about the mass-centre of the (m ₁,m ₂) system) and the positions within these orbits.The behaviour of the stability of such systems is demonstrated (both analytically and numerically) with respect to certain of the parameters involved to consider effects not dealt with in the above-mentioned paper. In particular two interesting real cases of triple systems in the Solar System are discussed, namely Sun-Jupiter-Saturn and Earth-Moon-Sun. The results of the present paper are compared with those of past authors who considered the same systems.Finally some general features arising out of our analysis are discussed.     

Angular momenta in binary systems

The correlations angular momentaL to massesM are studied for different types of spectroscopic binaries. The functionsL=AM ^b have the coefficientb with the values expected from a Keplerian mechanics, but the valuesA(q, T), A(q, a), A(q, v), associated tob=5/3, 3/2, and 2, respectively, are given (statistically speaking) by multiples or submultiples of discrete values of: the mass ratiosq, the semi-major axesa, periodsT, and velocitiesv of the reduced mass. This indicates the existence of a discrete unit of actionL=(1/2)×potential energy xperiod. Postulates about equivalent states of angular momenta for different orbital parameters are introduced, being this coherent with the analysis of the up-to-date data. Among other examples of the application of such equivalence postulates, we haveL(M) (W-type of the WUMa systems)L(M) (main group of the Algol binaries). The quantum units of action seen here are equivalent to those seen in the solar system in one of our previous works. From comparisons with galaxies and single stars, it is evidence that there is not an unique universal functionL=AM ^b, when the fine structure of the relation is analysed: each type of object has its own coefficients,A, b. It sems to be that there are an upper and a lower limit for all the possible functions. The upper limit isL=A _gM^5/3, withA _g1 associated to periodsT Hubble time, and the lower limit isL=GM ^2/c, with 1. The existence of the upper limit can be investigated with studies of pairs of galaxies, and the lower limit can be tested with analysis of single G, K, M stars. The quantical hypothesis introduced here can be checked definitely, when available larger samples of data with low errors, with similar quality as the selected list of almost 80 eclipsing binaries (mainly detached systems) analysed here.