The Wolf-Rayet mass-luminosity relation

We consider the mass-luminosity relation proposed for the Wolf-Rayet stars on the basis of detailed numerical models. It is found that the linear form of this relation can be explained in a straight-forward manner and is due to essentially three factors, (i) the WR stars are approximately chemically homogenous, (ii) the stars evolve under constant radiation pressure, and (iii) the stars evolve with high mass loss.     

The empirical mass-luminosity relation

On the basis of the most recent data for visual and spectrophotometric binaries, the empirical mass-luminosity relation has been investigated. It is shown that, for the sample collected, the relation may be divided into three parts, for which numerical relations are given. A table summarizing the observational results on the fractional mass of the secondary component in visual systems is given.     

The empirical mass-luminosity relation for low mass stars

This work is devoted to improving empirical mass-luminosity relations (MLR) and mass-metallicity-luminosity relation (MMLR) for low mass stars. For these stars, observational data in the mass-luminosity plane or the mass-metallicity-luminosity space subject to non-negligible errors in all coordinates with different dimensions. Thus a reasonable weight assigning scheme is needed for obtaining more reliable results. Such a scheme is developed, with which each data point can have its own due contribution. Previous studies have shown that there exists a plateau feature in the MLR. Taking into account the constraints from the observational luminosity function, we find by fitting the observational data using our weight assigning scheme that the plateau spans from 0.28M_⊙ to 0.50M_⊙. Three-piecewise continuous improved MLRs in K, J, H and V bands, respectively, are obtained. The visual MMLR is also improved based on our K band MLR and the available observational metallicity data.     

Long-period eclipsing binaries: towards the true mass-luminosity relation.I. the test sample,observations and data analysis

The mass-luminosity relation is a fundamental law of astrophysics. We have suggested that the currently used mass-luminosity relation is not correct for the M/M⊙ 2.7 range of mass since it was created utilizing double-lined eclipsing binaries, where the components are synchronized and consequently change each other's evolutionary path. To exclude this effect, we have started a project to study longperiod massive eclipsing binaries in order to construct radial velocity curves and determine masses for the components. We outline our project and present the selected test sample together with the first HRS/SALT spectral observations and the software package, FITTING BINARY STARS(FBS), that we developed for the analysis of our spectral data. As the first result, we present the radial velocity curves and best-fit orbital elements for the two components of the FP Car binary system from our test sample.     

Physical conditions of ionized gas and mass-luminosity distribution in NGC 7793

The physical state of ionized gas in NGC 7793 was studied by spectroscopical means: the electronic temperature isT _e10⁴K while the electronic density ranges fromN _e1400 cm^–3 in the nucleus toN _e1000 cm^–3 in the emission regions. There are also indications of an excess of nitrogen in the nucleus. TheM/L ratio suggests for NGC 7793, a high proportion of young objects quite uniformly distributed over its body, with a slight concentration towards the nuclear region.     

On the period-luminosity-colour relation for galactic Cepheids

A period-luminosity-colour relation is derived from the data of 29 galactic Cepheids with known distances collected from the literature, and is then compared with the simpler period-luminosity relation. The insignificant reduction in the dispersion seems to argue against the introduction of the colour term. It is, however, demonstrated that this evidence may be fictitious and due to the use of Cepheids, whose membership in a star aggregate is still doubtful. The exclusion of these stars leads to a PLC relation which shows a significantly smaller dispersion than that given by the corresponding PL relation.     

On the Galactic disc age–metallicity relation

A comparison is made between the age–metallicity relations obtained from four different types of studies: F and G stars in the solar neighbourhood, analysis of open clusters, galactic structure studies with the stellar population synthesis technique and chemical evolution models. Metallicities of open clusters are corrected for the effects of the radial gradient, which we find to be −0.09 dex kpc⁻¹ and most likely constant in time. We do not correct for the vertical gradient, because its existence and value are not firmly established.
Stars and clusters trace a similar age–metallicity relation, showing an excess of rather metal-rich objects in the age range 5–9 Gyr. Galactic structure studies tend to give a more metal-poor relation than chemical evolution models. Neither relation explains the presence of old, relatively metal-rich stars and clusters. This might be caused by uncertainties in the ages of the local stars, or pre-enrichment of the disc with material from the bulge, possibly as a result of a merger event in the early phases of the formation of our Galaxy.     

On the mass-radius relation in close binary systems

In a close binary system with circular orbits in which mass transfer occurs when material from one star fills up and possibly spills over its Roche lobe, the usual mass-radius relation cannot be used as it would lead to unreasonable results in some situations.     

On the relation of dynamics to statistical mechanics

A new conceptual framework for the foundations of statistical mechanics starting from dynamics is presented. It is based on the classification and the study of invariants in terms of the concepts of our formulation of non-equilibrium statistical mechanics. A central role is played by thecollision operator. The asymptotic behaviour of a class of states is determined by the collisional invariants independently of the ergodicity of the system. For this class of states we have an approach to thermodynamical equilibrium. We discuss the existence of classes of states which approach equilibrium. The complex microstructure of the phase space, as expressed by the weak stability concept which was introduced by Moser and others, plays here an essential role. The formalism that we develop is meaningful whenever the “dissipativity condition” for the collision operator is satisfied. Assuming the possibility of a weak coupling approximation, this is in fact true whenever Poincaré's theorem on the nonexistence of uniform invariants holds. In this respect, our formalism applies to few body problems and no transition to the thermodynamic limit is required. Our approach leads naturally to a ‘classical theory of measurement’. In particular a precise meaning can now be given to ‘thermodynamic variables’ or to ‘macrovariables’ corresponding to a measurement in classical dynamics.     

On the relation between the ERP and the rotation vector

This paper deals with the Earth Rotation Parameters (ERP), and presents a formula to calculate the rotation vector.     

On a relation among lie series

In this paper we discuss the relation between the structures of the series expansion for the Dragt and Finn composition of Lie transforms and for a transformation introduced by Giorgilli and Galgani. A recursive algorithm is presented which is used to generate the series expansion for the composition of Lie transforms. This algorithm strongly resembles the algorithm of Giorgilli and Galgani, and differs from it only in an ordering property. The relation with the algorithms of Kamel and Henrard for Deprit's direct and inverse series is also discussed.     

On the relation between resonance and instability in planetary systems

The factors which affect the linear stability of a periodic planetary orbit in the plane are studied. It is proved that planetary systems with two planets describing nearly circular orbits in the same direction are linearly stable and no perturbation exists which destroys the stability, unless a resonance of the form 1/3, 3/5, 5/7, ... among the orbits of the planets occurs. This latter resonant case is always unstable. Retrograde motion is always linearly stable. Planetary systems with three or more planets in nearly circular orbits in the same direction are proved to be unstable, in the sense that a Hamiltonian perturbation always exists which destroys the stability. The generation of instability in the case of three or more planets is not only due to the existence of resonances, as in the case of two planets, but also to the nonexistence of integrals of motion, apart from the energy and angular momentum integrals. It is also proved that planetary systems with nearly elliptic orbits of the planets are unstable.     

On the relation between activity and rotation in main-sequence stars

Es wird ein modifizierter Index für das chromosphärische Aktivitätsniveau bei Sternen, A'_Call, vorgeschlagen. Dieses wird auf Grund der in den H und K Ca II-Linienkernen gemessenen Strahlungsflußdichte berechnet, ist aber im Unterschied zu anderen bekannten Indizes frei vom Einfluß der Sternfarbe. Die Anwendung des neuen Indexes führt zu einer modifizierten Aktivität-Rotation-Beziehung bei Sternen im unteren Teil der Hauptreihe. Es ist nachgewiesen, daß im Koordinatensystem log A'_Call, log Ro (Ro ist die Rossby Zahl) F-M-Sterne einer allgemeinen Beziehung mit dem Parameter α = 1.6 gehorchen. Die Kurve weist keine Zeichen von Aktivitätssättigung bei Sternen mit niedrigen Rossby-Zahlen auf, aber das Aktivitätsniveau strebt gegen einen konstanten Wert bei langsam rotierenden Sternen mit dünnen Konvektionszonen.     

On the relation between orbital structure and observed bar morphology

We investigate the morphological relation between the orbits of the central family of periodic orbits ( x ₁ family) and the bar itself using models of test particles moving in a barred potential. We show that different bar morphologies may have as a backbone the same set of x ₁ periodic orbits. We point out that by populating initially axisymmetric stellar discs exponentially with test particles in circular, or almost circular motion, we may end up with a response bar which reveals a shape different in crucial details from that of the individual stable x ₁ orbits. For example, a bar model in which the x ₁ orbits are pure ellipses may have a much more complicated response morphology. This depends on the particular invariant curves around x ₁, which are populated in each model.     

On the space-time structure and its relation to quantum mechanics

The Weyl covariant formulation of Dirac's equation by means of a rest mass the Weyl type of which is — 1, implies the introduction of a Riemann structure in addition to the Weyl structure. The Ehlers-Pirani-Schild attempt to specify the space-time structure and the lowest order of the WKB approximation are compatible with each other. Only the requirement that the connection to which the Dirac field couples minimally is identical to the connection the autoparallels of which are the world lines of structure-less test particles, leads to a reduction of the Weyl structure to the Riemannian one.     

On the interpretation of the observed angular-size-flux-density relation for extragalactic radio sources

The interpretation of the observed relation between median angular sizes (θ _m) of extragalactic radio sources and flux density at 408 MHz has been examined. The predictedθ _m-S relations based on well-observed strong sources in parent samples selected at 178 and 1400 MHz, and existing models of the evolving radio luminosity function can be made to fit the observed relation only by invoking cosmological evolution in linear sizes even for theq ₀ = 0 universe. Predictions based on a parent sample at 2.7 GHz are shown to overestimate the contribution of steep-spectrum, compact (SSC) sources in low-frequency samples unless the downward curvature in the spectra of such sources is taken into account. When approximate corrections are made for this effect, predictions based on the 2.7 GHz parent sample cannot obviate the need for linear size evolution as claimed in the literature.