Reconsidering Schwarzschild's original solution

We analyse the Schwarzschild solution in the context of the historical development of its present use, and explain the invariant definition of the Schwarzschild's radius as a singular surface, that can be applied to the Kerr‐Newman solution too.     

Chemo-dynamical Evolution of the ISM in Galaxies

Chemo-dynamical models have been introduced in the late eighties andare a generally accepted tool for understanding galaxy evolution. Theyhave been successfully applied to one-dimensional problems, e.g. theevolution of non-rotating galaxies, and two-dimensional problems,e.g. the evolution of disk galaxies. Recently, also three-dimensionalchemo-dynamical models have become available. In these models thedynamics of different components, i.e. dark matter, stars and amulti-phase interstellar medium, are treated in a self-consistent wayand several processes allow for an exchange of matter, energy andmomentum between the components or different gas phases. Some resultsof chemo-dynamical models and their comparison with observations ofchemical abundances or star formation histories will be reviewed.     

Libration Points in Schwarzschild's Circular Restricted Three-Body Problem

The restricted three-body problem in Schwarzschild's gravitational field is analyzed. The existen- ce of the equilibrium points in the orbital plane is discussed and the corresponding positions are established. There are three collinear libration points, and, if they exist, two triangular libration points (situated in the orbital plane of the primaries). If triangular points exist, they may not form equilateral triangles; the triangles are isosceles for equal masses of the primaries, and scalene else.     

Diffraction of electromagnetic waves in Schwarzschild's space-time

In order to study the gravitational lens effect in detail this paper investigates the electromagnetic radiation generated by an electric dipole oscillating with high frequency in the Schwarzschild metric outside the horizon. Expressions for the Newman-Penrose tetrad components characterizing the radiation field are derived in a suitable approximation. The Poynting vector is discussed in the region behind the deflecting mass (black hole, neutron star) in the fully coherent case for large distances of source and observer from the centre of the lens. Intensity and gain in the focal region coincide with the corresponding values applying to scalar radiation. An observer sees double images of the source outside the focal region. The results (positions of the images, relative intensities) are compared with those occurring in the case of an incident plane wave (recently treated by Herlt and Stephani) and with the properties of the images in the (geometrical optics) limit of incoherent radiation.     

Schwarzschild's solution and possible restriction of its physical applicability

In this paper we make an attempt to obtain the form of Schwarzschild's formula for centrally-symmetrical space-time assuming that the whole matter of the Universe possesses a dilatational degree of freedom. Then we show that there is one additional requirement which prevents the existence of an impenetrable region as it is permitted by Schwarzschild's solution.Geomagnetic Institute, Grocka, Yugoslavia     

Exact optics – V. Null tests for the mirrors of Schwarzschild's spectrograph camera

Null tests are described for the strongly curved and highly aspheric mirrors of a set of 'exact optics' spectrograph cameras based on the design of Schwarzschild. For f /1.0 and f /1.333 cameras having a focal length of 100 mm the tests of each mirror are well within the Rayleigh limit and would permit construction on a larger scale. The ray-theoretical image diameters at the edge of the field of view of these two cameras are under 10 μm unless they are scaled up to an aperture greater than 450 mm.     

A three-dimensional numerical method for modelling weakly ionized plasmas

Astrophysical fluids under the influence of magnetic fields are often subjected to single- or two-fluid approximations. In the case of weakly ionized plasmas, however, this can be inappropriate due to distinct responses from the multiple constituent species to both collisional and non-collisional forces. As a result, in dense molecular clouds and protostellar accretion discs, for instance, the conductivity of the plasma may be highly anisotropic leading to phenomena such as Hall and ambipolar diffusion strongly influencing the dynamics.
Diffusive processes are known to restrict the stability of conventional numerical schemes which are not implicit in nature. Furthermore, recent work establishes that a large Hall term can impose an additional severe stability limit on standard explicit schemes. Following a previous paper, which presented the one-dimensional case, we describe a fully three-dimensional method which relaxes the normal restrictions on explicit schemes for multifluid processes. This is achieved by applying the little-known Super TimeStepping technique to the symmetric (ambipolar) component of the evolution operator for the magnetic field in the local plasma rest frame, and the new Hall Diffusion Scheme to the skew-symmetric (Hall) component.     

A method for modelling the surface of irregular celestial bodies

Die Funktion R9 der Oberfläche von unregelmäßigen Himmelskörpern (kleine Monde wie Phobos und Deimos, Kometenkerne oder kleine Asteroiden) wird nach Kugelfunktionen entwickelt. Es wird eine Methode angegeben, nach der die Entwicklungskoeffizienten durch Vergleich der berechneten Konturen mit den Konturen bestimmt werden, die aus einer Folge von Abbildungen des Körpers gewonnen wurden. Bei gegebenen Entwicklungskoeffizienten kann diese Methode für Orientierungssysteme von Raumschiffen beim Anflug auf den Himmelskörper verwendet werden. Weiterhin können physikalische Größen, wie das Volumen, die Schwerpunktskoordinaten, Trägheitsmomente und Gravitationsfeld analytisch berechnet werden. Unter der Voraussetzung, daß das Gravitationspotential experimentell bestimmt werden kann, wird eine Methode zur Berechnung des radialen Dichteprofiles des Körpers beschrieben.     

Spectral energy distribution modelling of southern candidate massive protostars using the Bayesian inference method

Concatenating data from the millimetre regime to the infrared, we have performed spectral energy distribution (SED) modelling for 227 of the 405 millimetre continuum sources of Hill et al. which are thought to contain young massive stars in the earliest stages of their formation. Three main parameters are extracted from the fits: temperature, mass and luminosity. The method employed was the Bayesian inference, which allows a statistically probable range of suitable values for each parameter to be drawn for each individual protostellar candidate. This is the first application of this method to massive star formation.
The cumulative distribution plots of the SED modelled parameters in this work indicate that collectively, the sources without methanol maser and/or radio continuum associations (MM-only cores) display similar characteristics to those of high-mass star formation regions. Attributing significance to the marginal distinctions between the MM-only cores and the high-mass star formation sample, we draw hypotheses regarding the nature of the MM-only cores, including the possibility that the population itself comprises different types of source, and discuss their role in the formation scenarios of massive star formation. In addition, we discuss the usefulness and limitations of SED modelling and its application to the field. From this work, it is clear that within the valid parameter ranges, SEDs utilising current far-infrared data cannot be used to determine the evolution of massive protostars or massive young stellar objects.     

Multiwavelength modelling the SED of supersoft X-ray sources I. The method and examples

Radiation of supersoft X-ray sources (SSS) dominates both the supersof X-ray and the far-UV domain. A fraction of their radiation can be reprocessed into the thermal nebular emission, seen in the spectrum from the near-UV to longer wavelengths. In the case of symbiotic X-ray binaries (SyXBs) a strong contribution from their cool giants is indicated in the optical/near-IR. In this paper I introduce a method of multiwavelength modelling the spectral energy distribution (SED) of SSSs from the supersoft X-rays to the near-IR with the aim to determine the physical parameters of their composite spectra. The method is demonstrated on two extragalactic SSSs, the SyXB RX J0059.1-7505 (LIN 358) in the Small Magellanic Cloud (SMC), RX J0439.8-6809 in the Large Magellanic Cloud (LMC) and two Galactic SSSs, the classical nova RX J2030.5+5237 (V1974 Cyg) during its supersoft phase and the classical symbiotic star RX J1601.6+6648 (AG Dra) during its quiescent phase. The multiwavelength approach overcomes the problem of the mutual dependence between the temperature, luminosity and amount of absorption, which appears when only the X-ray data are fitted. Thus, the method provides an unambiguous solution. It was found that selection of the model (a blackbody or an atmospheric model) is not of crucial importance in fitting the global X-ray/IR SED. The multiwavelength modelling of the SED of SSSs is essential in determining their physical parameters.     

Free particle modelling of hypervelocity asteroid collisions with the Earth

This paper presents a time-dependent two-dimensional numerical model of the impact phenomena. The model deals with formation and evolution of a crater, formation of an impact jet, and with global deformation and dynamical parameters of the impacted body. The model is applied to study the problem of deformation of the Earth when impacted by an asteroid. A hydrodynamical code of the free particle numerical method (HEFP) is applied to a silicate asteroid (impactor) and to the multilayered spherical Earth (target) described by the PREM model. The asteroids radii are within a range between 5 and 800 km. The velocity range is 20–30 km s⁻¹. Calculations cover the time intervals up to 2000 s.

Each of the material points of the bodies under consideration (the Earth and an asteroid) is described by its time-dependent position, velocity, specific internal energy, pressure and density. The global results, among others, are as follows: (i) deformation of the Earth's surface; (ii) position of the shock wave within the Earth; (iii) deformation of consecutive layers within the Earth's interior, and (iv) morphology of the crater including behavior of the impact jet and deformation of the impactor.     

Quantitative magnetospheric magnetic field modelling with toroidal and poloidal vector fields

Toroidal and poloidal vector fields allow divergence free magnetic field representations in regions where currents flow. We derive general magnetospheric magnetic fields using combinations of spherical harmonic expansions of the toroidal and poloidal fields. Adding restrictive conditions like the field line topology symmetry or the magnetic field measurements, more specific magnetospheric magnetic field models can be derived. Two examples of this technique are given : an axisymmetric model with a ring current in the equatorial region and a time-dependent model of the Earth's magnetosphere. Our results are compared with the Olson-Pfitzer model.     

Regression modelling in selenodesy

Earth, Moon, and Planets - The existing models of different orders that describe surface and gravitational fields of planets contain a redundant number of members with no useful information, which...     

A thermal modelling of cometary activity with a crystallized water ice nucleus

Arguments are presented to suggest that surface layers of the nuclei of periodic comets consist of crystallized rather than amorphous water ice and thermal modelling of such nuclei is presented. The rate of sublimation of water from a rotating nucleus is found to be greater than that from a uniformly heated nucleus. When the model is applied to P/Halley, the sublimation rate at perihelion is found to be 8.1 × 10²⁹ mol s⁻¹ for a nucleus rotating with a period of 50 hours and 7.6 × 10²⁹ for a uniformly heated nucleus on the premise that the effective radius of the nucleus is 2.5 km. The total sublimation of water per revolution is 5.38 × 10³⁶ molecules for P/Halley and 3.91 × 10³⁶ molecules per P/Crommelin. The result so obtained is discussed in relation to the observational data.     

Shock modelling of Planetary Nebulae

The kinematics of Planetary Nebulae are analyzed in terms of the solutions to the equations of hydrodynamic equilibrium developed by J. Cantó. We apply our analysis to the Planetary Nebulae NGC 6905 and NGC 6537. A detailed spectroscopic study of these objects reveals the existence of high nuclear velocities, together with complex kinematic structures and unusual emission line intensities. Shock ionization clearly plays a key role in these nebulae. Remarkably good agreement is obtained when comparing the synthetic maps and spectra resulting from the shock solutions with the observational data.     

CO modelling of CW leo

Preliminary results are presented of fitting the spectral energy distribution and newly obtained¹²CO and¹³CO J =1-0, 2-1 and 3-2 line profiles of CW Leo. This is done with a model which includes a self-consistent calculation of the gas temperature.     

Atomic modelling of nova shells

Atomic models developed by the author and used to interpret the spectra of cool shells from old classical novae are reviewed. Some of the remaining problems relating to the spectra are discussed briefly. The use of these data in photoionization models is described, and the evolution of nova shells is discussed.