Nature of the symbiotic binary V 1329 Cyg

The published photometric and spectroscopic data of the symbiotic binary V 1329 Cyg are interpreted. It is shown, that V 1329 Cyg is an eclipsing binary with an elliptical orbit orbit (e=0.28). The cooler component fills up the Roche-lobe at periastron. A model of moving gaseous structures in the system is proposed and their influence on the radial velocity curve is shown. The following characteristics of the system are derived: the cooler component is an M6 giant with mass 7.9M , radius 339R and luminosityM _bol=–5.42, the hot component is a white dwarf surrounded by an accretion disk. The mean distance between the components is 842R and in periastron it decreases to 605R .     

Cylindrical oscillations of force-free electromagnetic fields

This paper is devoted to Force-Free Electromagnetic Oscillations in a constant magnetic field. A correction is made in the derivation of the basic equation. The paper confirms the predicted spectrum of frequencies, namely _n = _o (n + 1)^1/2;n = 0, 1, 2, .... In addition it is suggested that hybrid frequency _n = ( _n ² + _H ² )^1/2 should be found in observational data.     

Evolution of galaxies: One-zone model with a birth-rate stellar function depending on gas density and temperature

In this paper closed one-zone models with a birth-rate stellar function depending on gas density and temperature are built up, in order to make a zeroth order approximation of thermo-chemical evolution of galaxies. To get a more realistic picture, the models are allowed first to expand with the universe and then to contract according to three successive time-scales, in order to simulate violent relaxation, rapid contraction, and slow contraction processes.Star formation occurs according to a birth-rate (m, t) _g ⁿ T ^r m ^p ( _g , gas density;T, gas temperature; andm, star mass), which reproduces the usual Schmidt-type law in the limitr0. Further we suppose that synthesized metals and helium are instantaneously mixed when returned to gas component at star death, and that relative metal abundances are time-independent: ( any element heavier than He, ). An energy fraction of each typical supernova event is assumed to heat interstellar medium, which is also though always to maintain a steady state.Under these hypotheses it becomes possible to use the interstellar cooling function of Dalgarno and McCray (1972), which is related to a special cosmic abundance of elements, to express analytically an interstellar cooling function related to any abundance. At this stage, numerical computations are performed up to about 12 Gy and the results analyzed in order to reproduce some morphological features observed in the galaxy, namely: (i) the extreme scarcity of stars with nearly zero metal content; (ii) the metal content and mass fraction of halo stars; (iii) the metal content and mass fraction of disk stars; and (iv) the ratio of the present-day birth-rate to the past birth-rate averaged over the age of the disk. It is found that a whole class of theoretical models exist, with slope of the mass spectrum between –2.5 and –2.6, which range from a Schmidt's law limitn=1.3 andr=0 to the opposite limitn=0 andr=–1.2, and are able to fit more or less at the same extent the observations mentioned above. On the analysis of further computations, it is also shown that an universal birth-rate stellar function is in contradiction with neither a dynamical hystory starting from the initial expansion of proto-galaxies, nor a morphological sequence where the amount of angular momentum is the only free parameter for any given mass, at least for what concerns spiral types. Finally, possible refinements for future work are briefly outlined.     

A high-resolution bragg spectrometer for the observation of the hot interstellar medium X-ray emission

We present a high-resolution Bragg spectrometer designed for the observation of the soft X-ray cosmic diffuse background. The instrument concept is derived from the de Broglie geometry for the study of extended sources. It consists in a mosaïc of spherical TlAP crystals associated with position sensitive detectors located on the focussing surface. The spectral resolution and its variation with the field of view is estimated by Monte-Carlo simulations for different X-ray energies chosen among the most intense lines emitted by an astrophysical plasma in the temperature range 1–4×10⁶K. The estimated sensitivity and the simulations of actual space observations show that the instrument is capable to separate the strongest lines emitted by the most abundant ions (OVII,OVIII, FeXVII, NeIX, etc.) and to map the whole sky during a six month mission.     

Variations in the HCN/HNC abundance ratio in the Orion molecular cloud

We have used observations of the rare isotopes of HCN and HNC to determine the relative abundance of these two chemical isomers along the central ridge of the Orion molecular cloud. The abundance ratio [HCN]/[HNC] decreases by more than an order of magnitude from the relatively warm plateau and hot core sources toward the KL nebula to the colder, more quiescent clouds to the north and south. Even in the cooler regions, however, the ratio is an order of magnitude larger than that found in previous investigations of cold dark clouds. We determine the kinetic temperature in the regions we have studied from new observations of methylacetylene (CH3CCH), together with other recent estimates of the gas temperature near KL. The results suggest that the warmer portions of the cloud are dominated by different chemical pathways than those in the general interstellar cloud material.     

A note on the total mass of comets in the solar system

The assumption that the very low albedo determined for Halley's comet is typical of all short period comets, taken together with the assumption that the average sizes of long and short period comets are approximately equal, leads to an increase in the total mass of comets in the solar system by almost two orders of magnitude. If gravitational ejection from the Uranus - Neptune zone during the later phases of planet formation is indeed responsible for the classical Oort cloud between 10⁴–10¹⁵ AU, then the mass of comets in this transplanetary region during cosmogonie times has to exceed the combined masses of Uranus and Neptune by over an order of magnitude. Furthermore, if the recent arguments for as many as 10¹⁴ comets in an inner Oort cloud between ~40– 10⁴AU are valid, then the total mass of comets in the solar system approaches 2% of a solar mass.     

Some peculiarities in the Asteroidal Belt

The analysis of the fine structure of the Asteroidal Belt evidenciates a group of asteroids next to the resonance 4/9 with Jupiter. In this group and in other groups associated to the Hirayama families there are indications that their orbital parameters can be represented by quantum numbers as defined here and in two of our previous works. Together with this the distribution of the eccentricities and inclinations of the orbital planes of short period comets and diverse type of asteroids indicates that they can be classified as objects with e > sin i and objects with e > sin i with a limit e = sin i which determinates geometrical properties of the orbits related with discrete states in the solar system. This study lets open the possibility of following studies in order to confirm the quantum characteristics of the Asteroidal Belt being these characteristics common to all the solar system and depending of the same fundamental constant of action per mass unit H ₀ = 1/2 ₀ × T ₀ (potential × time) because only a small part of all the available data in the Asteroid Belt is used here.     

Experiences numeriques sur des billards C1 formes de quatre arcs de cercles

The paper deals with some properties of the dynamical system with two degrees of freedom defined by the motion of a particle in a certain type of billiard. These properties are studied by means of numerical experiments. Most results are represented in the now classical surface of section. One parameter families of billiards with a C¹ boundary constructed with four arcs of circles are defined; we use the property that the four meeting points of such billiards lie on the same circle. These billiards may be convex or non convex. They generalize the ‘oval’ billiard with two axes of symmetry studied by Benettin and Strelcyn. We call them generalized billiards. We find the following results:

1. The periodic orbit along the small diameter of a billiard is stable or unstable in the linear approximation according to the position of the center of each relevant are with respect to the opposite one. This orbit is always stable if the billiard is symmetric with respect to its large diameter.
2. When the center of an arc lies on the opposite arc two different transition patterns from order to chaos are observed for the same billiard. If the billiard is of the Benettin and Strelcyn type three distinct nested chaotic seas are seen two of which are separated by a pseudo-invariant curve generated by a so called cancellation orbit.
3. The total area of non chaotic regions is greater for symmetric billiards.
4. Peanut shaped billiards always look ergodic. It can happen also that strictly convex asymmetric billiards look ergodic. This is important since no strictly convex billiard is known for which ergodicity has been proven. The conjecture is proposed that a generalized billiard with neither 2-periodic nor 4-periodic stable orbit in the linear approximation is ergodic.
5. Transverse invariant curves such as the one found by Hénon and Wisdom seem common for billiards with two axes of symmetry but probably do not exist for asymmetric billiards.

There are therefore several properties which differentiate symmetric billiards from asymmetric ones. We conclude by emphasizing that C¹ generalized billiards are indeed inadequate models for smooth mappings in general.     

Quadratic analytical solution of general systems through formal hamiltonization

A technique for the quadratic analytical solution of general nonlinearly perturbed periodic systems is presented. It relies on a device recognized as early as Birkhoff (1927), through which any system of ordinary differential equations can be cast in Hamiltonian form through the introduction of a set of auxiliary conjugate variables. The particular implementation applies the author's quadratic Hamiltonian approach, utilizing Lie transforms (so admitting of easy inversion), and featuring the ability to determine the frequencies of the system to twice the order of the solution at the last step. The method is exemplified through an analysis of the van der Pol equation to find the solution to second order, and frequencies to fourth, of the limit cycle of the system. Finally, the relationship of the approach to other perturbation techniques, particularly the vector/matrix Lie transform method, is discussed.     

Precursor heating and acceleration by Langmuir waves: The type II Supernova case

The effect of shock wave propagation is investigated with respect to precursor heating and acceleration, upstream, with the aim of explaining Supernova (SN) observations.A model is presented, where two different sources of Langmuir waves produce upstream heating and acceleration: (1) Langmuir waves excited by resonance beam particles, that are accelerated through the shock front by Bell's mechanism; and (2) Langmuir waves, created in the post-shock turbulent zone.The most important processes considered in the calculations are: (1) the heating efficiency of beam particles of different velocity; (2) Bell's acceleration efficiency; (3) the spectrum of Langmuir waves created in a turbulent regime; (4) the effects of density, and of the density gradient in the medium, where the shock propagates.The calculations are applied to type II SN. The results show that temperatures of 10⁵–10⁶ K, obtained in the preshock region, can explain P-Cygni observed line profiles. Moreover, accelerations of the plasma in front of the shock up tov10⁸ cm s^–1 by momentum exchange, are in good agreement with observations.Partially supported by Conselho Nacional de Desenvolvimento Cientifico e Technológico (CNPq) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP).