Strained co-ordinate methods in rotating stars

It was shown in a previous paper, Smith (1975), that the determination of the structure of rotating polytropes by expansion in the small rotational parameter constitutes asingular perturbation problem as arises also, for example, in large Reynolds' number approximations in fluid dynamics. The technique used by him — the method of matched asymptotic expansions — is, in fact, just an extension of the Prandtl boundary layer theory familiar in this latter context. In this paper — the first of two — we introduce an alternative procedure: the method of strained co-ordinates; and for comparison purposes again consider rotating polytropes. In Paper II we extend this approach to differentially rotating stars and present an illustrative example.     

Physics of large-scale star formation: The GAS-Dynamic aspect

The subject of the review is the nature of regions of large-scale starbursts in galaxies. Theoretical investigations are presented and discussed, for the most part. Principal attention is devoted to the gas-dynamic approach to the problem. The review has the following plan. First we give a brief summary of empirical data on superassociations as regions of collective star formation on the largest scale in disk and irregular galaxies (Sec. 2); we then describe one possible gas-dynamic scenario for the origin of these objects (Sec. 3); the key physical mechanism on which the scenario is based — a collision of shock waves — is studied on the basis of general considerations (Sec. 4), as well as using computer simulation (Sec. 5) and laboratory experiments with shock waves (Sec. 6); the possibilities for the occurrence of this process under the specific conditions of the interstellar medium in disk and irregular galaxies are discussed in Sec. 7; in Sec. 8 we then consider features of large-scale collective star formation in barred galaxies; the evolution of spiral shocks that can initiate this process is the subject of Sec. 9; possible means of generation of large-scale regions of star formation like superassociations at the center of a bar (Sec. 10) and near its ends (Sec. 11) are then described; a brief conclusion is given in Sec. 12.In memory of Victor Amazaspovich AmbartsumianTranslated from Astrofizika, Vol. 39, No. 4, pp. 627–663, October–December, 1996.     

The host galaxies of nearby Seyfert 1 nuclei

We use optical and infrared imaging data of a complete hard X-ray selected sample of AGN to investigate the host galaxies of nearby Seyfert 1 nuclei. We disentangle the emission due to the unresolved point source and the resolved host galaxy by means of luminosity profile fitting. The stellar colours in the nucleus are redder inB — V andV — K than in normal spiral bulges or current stellar evolutionary models, probably due to dust obscuration.J — H colour is quite normal butH — K usually very red, probably indicating a large contribution from reradiating hot dust to the IR colours. No significant difference in IR colours oi the stellar component is found with respect to a comparison sample of Liners and starbursts, except that the reradiating dust in Seyferts tends to be hotter and lie closer to the nucleus.B — V colour gets slightly bluer towards the nucleus, whereasV — K andJ — K have red gradients.B — V andJ — K gradients are not correlated and are likely to be caused by different mechanisms. There is a clear correlation between the AGN and host luminosity. Finally, we present optical colour ratio maps of two Seyfert nuclei, NGC 3227 and NGC 7469. The blue, ringlike or elongated structure in the maps and its correspondence with molecular CO geometry is interpreted as evidence for circumnuclear star formation in these AGN.     

Equatorial orbits in superposed dipole and uniform magnetic fields

In the present work we study the equatorial motions of charged par ticles that are performed within a field consisting of the superposition of a dipole field—that could represent the magnetic field of a planet — and of a uniform magnetic field normal to the dipole's equator. We use a non-dimensional coordinate system in which the velocity of the charged particle is unit. The model depends on two parameters: the constant of the generalized momentum and the parameter of the interplanetary magnetic field. It is proved that the motion is always bounded. The regions of the motion and the corresponding orbits are studied with respect to the constant of the generalized momentum. We also, investigate numerically conditional periodic and asymptotic orbits.     

Two-component temperature analysis of OSO-5 X-ray flare data

Using data covering the 2.6–10 Å wavelength range from the OSO-5 satellite a four-parameter model of the emitting region in a flare process is derived. The thermal emission spectrum of Landini and Fossi is used to calculate the plasma parameters, electron temperature and emission measure. The X-ray flare data is explained by a model which treats the source volume as two time-varying temperature regions.     

The onset of condensation: Association reactions

Association reactions are important in a variety of astronomical regions for increasing molecular complexity and as a prelude to condensation. Theories are presented for the two mechanisms — three-body and radiative — by which association reactions occur in the gas phase. The theory for three-body association is in satisfactory agreement with a variety of laboratory studies. This agreement lends confidence to the idea that both theories can be utilized for association reactions of astrophysical importance.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium held at the Lunar and Planetary Institute, Houston, 6–8 September, 1978.     

“Stickiness” in mappings and dynamical systems

We present results of a study of the so-called “stickiness” regions where orbits in mappings and dynamical systems stay for very long times near an island and then escape to the surrounding chaotic region. First we investigated the standard map in the form x_i+1 = x_i+y_i+1 and y_i+1 = y_i+K/2π · sin(2πx_i) with a stochasticity parameter K = 5, where only two islands of regular motion survive. We checked now many consecutive points—for special initial conditions of the mapping—stay within a certain region around the island. For an orbit on an invariant curve all the points remain forever inside this region, but outside the “last invariant curve” this number changes significantly even for very small changes in the initial conditions. In our study we found out that there exist two regions of “sticky” orbits around the invariant curves: A small region I confined by Cantori with small holes and an extended region II is outside these cantori which has an interesting fractal character. Investigating also the Sitnikov-Problem where two equally massive primary bodies move on elliptical Keplerian orbits, and a third massless body oscillates through the barycentre of the two primaries perpendicularly to the plane of the primaries—a similar behaviour of the stickiness region was found. Although no clearly defined border between the two stickiness regions was found in the latter problem the fractal character of the outer region was confirmed.     

On the state of ionization of the local interstellar medium

The abundance ratio of neutral hydrogen to helium, as deduced from interplanetary observations of Lyman-alpha and He 584 Å radiation by Mariner 10, is significantly lower than the cosmic abundance ratio of these elements, thus showing that the local interstellar medium (LISM) is partly ionized. The effect of various sources of ionization — especially electron impact and EUV photon flux — on hydrogen and helium is discussed. It is shown that the observational data on the temperature of the LISM, on the diffuse EUV flux and on the neutral and electron densities in the nearby interstellar medium (NISM) are not all compatible. However, if the diffuse EUV flux below 912 Å as deduced from the preliminary analysis of Voyager observations is not representative, then it is easy to reconcile all observations. In this case an important source of ionization of the LISM would be electron impact, yielding an ionization degree of about 50% for the hydrogen component.     

The far UV spectrum of the O4V ((f)) star 9 Sagittarii

A detailed list of line identifications of the far UV spectrum of the O4V((f)) star 9 Sagittarii (HD 164794) in the wavelength range 1174-2000 Å is presented. The identification is based on two spectra recorded in 1981 (on 16 April—SWP 13729 and on 24 August—SWP 14805) by the International Ultraviolet Explorer (IUE). In the list many unclassified lines are included. The radial velocities of all lines, classified and unclassified, are measured for both spectra and the mean velocities for different ions are discussed.     

The deduction of energy spectra of non-thermal electrons in flares from the observed dynamic spectra of hard X-ray bursts

The derivation of dynamic spectra of high energy electrons in flares from high resolution hard X-ray observations is considered. It is shown that the Bethe-Heitler formula for the electronproton bremsstrahlung cross-section over the 20–100 keV range of energies admits of a general analytic solution for the electron spectrum in terms of the X-ray spectrum, in a form convenient for computation. The bearing of this analysis on different models of flare conditions is considered. In examining the hypothesis that the X-rays are produced in regions of high ambient density, the duration of the burst being governed by modulation of the electron source rather than by the decay of trapped electrons injected impulsively, it is emphasised that the energy spectrum of the electrons at their source is different from their effective spectrum in the X-ray emitting region. This spectrum, at the source, is found to be much steeper than that in the X-ray region which means that the entire energy of the flare could reside in the injected electrons.     

Short-term variability of Cyg X-1

The short-term X-ray variability distinguishes Cyg X-1, which is the most likely candidate for a black hole, from other X-ray sources. The present status of our knowledge on this short-term variation, mainly from the UHURU, the MIT and the GSFC observations, is reviewed. The nature of impulsive variations which compose the time variation exceeding the statistical fluctuation is discussed. There are indications that the energy spectrum of large pulses is harder than the average spectrum, or that the large pulses are the characteristics of the hard component of the spectrum if it is composed of two, soft and hard, components. Features of the variations may be partly simulated by the superposition of random shot-noise pulses with a fraction of a second duration. However, the autocorrelation analysis and the dynamic spectrum analysis indicate that the correlation lasts for several seconds and in the variation are buried some regularities which exhibit power concentrations in several frequency bands; 0.2–0.3, 0.4–0.5, 0.8, 1.2–1.5 Hz. There are several possible interpretations of these results in terms of; e.g. (a) a mixture of shot-noise pulses with two or more constant durations, (b) the shape of the basic shot-noise pulse, (c) bunching of the pulses, (d) superposition of wave-packets or temporal oscillations. But we have not yet reached any definite understandings in the nature of the variabilities. The substructure of the fluctuations on a time scale of milliseconds suggested by two investigations is also discussed.Paper presented at the COSPAR Symposium on Fast Transients in X- and Gamma-Rays, held at Varna, Bulgaria, 29–31 May, 1975.     

Weak solar fields and their connection to the solar cycle

We discuss the weak solar magnetic fields as studied with the BBSO videomagnetograph (VMG). By weak fields we mean those outside active and unipolar regions. These are found everywhere on the Sun, even where there never have been sunspots. These fields consist of the network and intranetwork (IN) elements. The former move slowly and live a day or more; the latter move rapidly (typically 300 m s^–1) and live only hours. To all levels of sensitivity the flux is concentrated in discrete elements, and the background field has not been detected. The smallest detectable elements at present are 10¹⁶ Mx. The IN elements emerge in bipolar form but appear to flow in a random pattern rather than to the network edges; however, any expanding network element is constrained by geometry to move toward the edges.Because of the great number and short lifetime of the IN elements the total flux emerging in that form exceeds that emerging in the ER by two orders of magnitude and the flux in sunspots, by a factor 10⁴. However, the flux separation is small and there is no contribution to the overall field. In contrast with our earlier results, merging of IN fields is more important than the ephemeral regions as a source of new network elements.The conjecture that all solar magnetic fields are intrinsically strong is discussed and evidence pro and con presented. For the IN fields the evidence suggests they cannot exceed 100 G. For the network fields there is evidence on either side.Reconnection and merging of magnetic fields takes place continually in the conditions studied.Because there is a steady state distribution, the amout of new elements created by merging or emergence must balance that destroyed by reconnection or fission and diffusion of the stronger elements.Solar Cycle Workshop Paper.     

On the possibility of nuclear processes in atmospheres of flare stars

A resume of the main results obtained in the framework of fast electron hypothesis is presented. The fast electrons are possessed by strong constant properties, that is, nearly monoenergetic in spectrum and with the energy of 3. Fast electrons appear spontaneously in all kinds of cool dwarfs, young and old, and stimulate the generation of all types of flares, faint and powerful, in all ranges of electromagnetic waves — optical, ultraviolet, radio, X-ray. The general flare mechanisms are inverse Compton effect at the faint and moderate flares and nonthermal bremsstrahlung at powerfulness. This hypothesis explains an enormous number of observational facts and relationships — all these are illustrated by two tree-like diagrams in Figures 1 and 2.In the second part, the problem of the spontaneous appearance of fast electrons above the stellar atmosphere is discussed. The nature of the fast electrons in universal and is independent of the physical conditions of the star or its atmosphere. Their origin have nothing in common also with the well known acceleration processes, including the magnetic and hydrodynamic nature, in stellar atmospheres. At present nuclear decay processes seem to be most probable for the appearance of fast electrons in outer regions of stellar atmospheres. Some decay processes are examined with various probability of their realization. Creation of the radioactive nucleus¹³N as a result of capture of H by¹²C and its consequent decay with the escape of a positron seems most probable; as this fast positron will act just like a fast electron. It is outlined the high effectivity of this process in binary systems.     

On the variability timescales and magnetic field in OJ 287

The continuum spectrum of OJ 287, like most other BL Lac objects, is featureless- no emission or absorption lines are observed. However, OJ 287 shows variations at different timescales in flux and polarization at various wavelength bands. Using the available variability data one can estimate the sizes of the emission regions in the source from light travel time arguments. We assume the emission mechanism to be synchrotron radiation by high energy electrons with single power law energy distribution. Theoretical synchrotron spectrum in the frequency range 10¹¹–10¹⁷ H _z is compared with the observed spectral shape, obtained from new multifrequency quasi-simultaneous observations, to estimate the lower and upper cut off frequencies. These frequencies are used to obtain theoretical values of the variability timescales and magnetic field in the emission region. We obtain a value of 0.93 G for the magnetic field and 5.184×10⁴ sec for the cooling time from the quiescent continuum spectrum. The shock-in-jet model explains the spectrum where shocks accelerate the particles and amplify the magnetic field in the jet. This timescale is compared with the one obtained from observed short timescale variability (20 minutes) with proper beaming correction. The short timescale variations (200 minutes in the source frame), possibly caused by an additional, flaring, component of the source, are also used to calculate compressed magnetic field. The observed and theoretically estimated variability timescales and the shape of the spectrum suggest that there are more than one emission components in OJ 287.     

Dynamics,interrelations and evolution of the systems of asteroids and comets

The dynamics of larger interplanetary bodies is reviewed, with emphasis on evolutionary problems, interrelations, and open questions. Observational biases distinguishing the sample of known objects from the whole population are briefly discussed. A schematic division of the solar system into zones with different regimes of motion, and a rough taxonomy of orbit types are attempted. The role of individual major planets in controlling the dynamical evolution of interplanetary objects, in particular by stabilizing resonances and destabilizing close encounters, is compared. There are significant evolution asymmetries due to boundary conditions and preferential evolutionary paths; individual major displacements in the phase space of orbital elements conserve the Tisserand invariant with respect to the planet responsible, thus favouring certain evolutionary sequences against others. Very limited lifetimes of some orbit types imply a long-term balance between source and sink, and require a continuous supply of objects from other types of orbits. In this respect, the ultimate fate of extinct comets is of particular interest. Under very specific conditions, nongravitational effects of mass loss can result in stabilization of a formerly unstable orbit. Since the dividing line between the two basic interplanetary populations distinguished by origin and composition — the asteroids and the comets — is essentially that between stable and unstable motion, orbital data can be used to specify which of the known asteroid-like objects may be devolatilized cometary nuclei.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Comparisons of solar flare X-ray producing and escaping electrons from ∼ 2 TO 100 keV

Using observations from the ISEE-3 spacecraft, we compare the X-ray producing electrons and escaping electrons from a solar flare on 8 November, 1978. The instantaneous 5 to 75 keV electron spectrum in the X-ray producing region is computed from the observed bremsstrahlung X-ray spectrum. Assuming that energy loss by Coulomb collisions (thick target) is the dominant electron loss process, the accelerated electron spectrum is obtained. The energy spectrum of the escaping electrons observed from 2 to 100 keV differs significantly from the spectra of the X-ray producing electrons and of the accelerated electrons, even when the energy loss which the escaping electrons experienced during their travel from the Sun to the Earth is taken into account. The observations are consistent with a model where the escaping electrons come from an extended X-ray producing region which ranges from the chromosphere to high in the corona. In this model the low energy escaping electrons (2–10 keV) come from the higher part of the extended X-ray source where the overlying column density is low, while the high energy electrons (20–100 keV) come from the entire X-ray source.     

Gamma-ray bursters as sources of cosmic rays

From the little we know of the physical conditions in γ-ray bursters, it seems that they are potentially effective in the acceleration of high-energy cosmic rays (CRs), especially if the bursters are at cosmological distances. We find that, with the observed statistics and fluxes of γ-ray bursts, cosmological bursters may be an important source of cosmic rays in two regions of the observed spectrum: (1) At the very-high-energy end (E > 10¹⁹ eV), where CRs must be of extragalactic origin. (2) Around and above the spectral feature that has been described as a bump and/or a knee, which occurs around 10¹⁵ eV. The occasional bursters that occur inside the Galaxy — about once in a few hundred thousand years if burst emission is isotropic; more often, if it is beamed — could maintain the density of galactic cosmic rays at the observed level in this range. These two energy ranges might correspond to two typical CR energy scales characteristic of bursters: one pertinent to CR acceleration due to interaction of a magnetized-fireball front with an ambient medium; the other to acceleration in the fireball itself (e.g. shock acceleration).     

Fourier analysis of the light curves of eclipsing variables,IX

The aim of the present paper will be to detail the procedure outlined in our previous investigations (Kopal, 1975; Kopalet al., 1976) for a solution of the elements of distorted eclipsing systems by a Fourier analysis of their light changes. This procedure—which constitutes an equivalent, in the frequency-domain, of rectification hitherto practised in the time-domain — should enable us to free the observed momentsA _2m of the light curves from all photometric effects of distortion (between minima as well as within eclipses) — a feat impossible in the time-domain except under very restricted conditions — and thus to make it possible to obtain the geometrical elements of the eclipses which should be free from any obvious source of systematic errors.     

A study of non-thermal radio emission features using fine spectral BAO and high-sensitivity RATAN observations of a solar active region

Based on spectral observations of active region NOAA 8545 on 19 May 1999, we describe the processes responsible for non-thermal long-lasting radio emission and for narrow-band non-drifting bursts observed at the same time. Non-thermal long-lasting radio emission consisted of two components: short-duration (1–2 s) microbursts with fluxes about 0.001 s.f.u. and continuum emission with growing spectrum in the range of 1000–2000 MHz. Energetic electrons continuously existed in the active region for more than 2.2 hours. The nature and parameters of microbursts were discussed by Bogod, Mercier, and Yasnov (2001). Here we consider the continuum source nature. It is shown that the model, taking into account the cyclotron loss-cone instability of hot electrons and the generation of plasma waves at the upper hybrid frequency, may explain the observed continuum source parameters. For the narrow-band non-drifting bursts we consider two models: the first taking into account an excitation of weak shock waves across the magnetic field and the second with an excitation of the upper hybrid waves under the double plasma resonance. Continuum source parameters are close to the last model. Our estimations for the magnetic field strength are as follows: H=120–126 G, which is valid for the region where the electron density of background plasmas n=(1.4–1.9) ×10⁹ cm^–3; H=180–190 G for the region where n=(3.0–4.3) ×10⁹ cm^–3; H=290 G for the region where n _e=2.5×10¹⁰ cm^–3; and H=350 G for the region where n _e=3.5×10¹⁰ cm^–3. The speed of the fast electrons is about 0.10–0.14 c.     

Radio evidence for electron acceleration in a cusp-like structure

In the spectrum of the type IV/II radio burst of 1994 July 18 we found a rare superposition of fast and slowly drifting features in the frequency range 100–300 MHz about 1 min before the onset of the shock induced meter wave type II burst. We take this as signatures of the passage of an MHD-like disturbance and the simultaneous injection of two contradirected electron beams. These beams are manifested as an ordinary type III burst and a reverse drift burst starting at the same frequency. Remarkably, the reverse drift burst is visible only due to its absorbtion trace in an underlying continuum patch. We argue that the superimposed burst features are emitted from a common source which covers the top of a closed magnetic field structure and the immediately superposed part (cusp) of the helmet streamer configuration. The radio source is situated immediately at the electron acceleration site.