Fourier analysis of the light curves of eclipsing variables. XIII

New expressions for the fractional loss of light _l ⁰ have been derived in the simple forms of rapidly converging expansions to the series of Chebyshev polynomials, Jacobi polynomials, and Kopal'sJ-integrals. In these expansions, which are a supplement to those given by Kopal (1977b), variablesk andh occur in different products that simplify the numerical computation. The treatment follows the new definition of _l ⁰ which has been recently developed by Kopal (1977a).     

Theory of the Trojan asteroids,IV

In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies ₁ and ₂. In terms of thecritical masses m_j(₂), or the associatedcritical energies _j ² (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |₂– _j ² |<_j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 0²1, lying in: and (2) despite the clustering of _j ² (m) atj=, the family () includes, for ²=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL ₃.In a similar manner, the family () can be extended to the horseshoe branch 1<_{2 2} ² .     

Hα and radio observations of LSI+61o303

Quasi simultaneous H and radio observations of LSI+61^o303 during August-September 1993 are presented. The radio data show that during the studied epoch the outburst has peaked at radio phase 0.6, at level100 mJy. No significant variations in the H profile at phases 0.5 to 0.65 have been detected. A remarkable increase of the EW and FWHM of the H blue peak is observed at radio phase 0.23. Possible reasons are considered.     

Numerical stabilization of Keplerian motion

The time transformation dt/ds=r is studied in detail and numerically stablized differential equations are obtained for =1,2, and 3/2. The case =1 corresponds to Baumgarte's results.     

Linearly expanding universes in JBD-theory

The assumption of a linearly expanding universe for the JBD-cosmological equations generates a set of solutions for the barotropic equations of statep= (=const.). These solutions turn out to be valid for closed space-except in the casep= which is for open space. The gravitational constant which is inversely proportional to the scalar field increases with time if >–1/3 and decreases for <–1/3. No solution exists for =1/3. The Brans-Dicke parameter is negative if <–1/3.     

The behaviour of the infrared lines of neutral oxygen and the balmer lines of hydrogen in the spectra of early-type stars with emission lines

The equivalent widths of the oxygen lines at 7774 and 8446 and of H (and some H) have been measured for 22 early-type, emission-line stars. A strong correlation between H and 8446 intensities has been found, although there is no such correlation between H and 7774. This confirms the probability that Bowen's mechanism is operative (the neutral oxygen 3³ D state is overpopulated because the excitation energy of Ly- nearly coincides with that of theOi 1025 line). The possibility of using 8446 and H equivalent widths for a comparison of oxygen to hydrogen abundances in these stars is discussed.     

Does the gravitational “constant” increase?

The possibility that the gravitational coupling constantG is an increasing function of the cosmic timet is discussed.In Section 1 the Maximal Power Hypothesis (MPH) stating that no power in Nature can exceed the upper boundc ⁵/G (Gunn's luminosity) is advocated.In Sections 2, 3, and 4 the MPH is employed on the cosmological scale to support the idea of an increasingG. In Section 2 the increasingG is obtained by two assumptions - the MPH and the energy conservation law - and by nothing else.In Section 3 the increasingG follows naturally from the MPH in the Einstein-Cartan theory of gravity. The arguments proposed in Sections 2 and 3 lead todG(t)/dt > 0 but cannot specify the form ofG(t). In Section 4 the MPH is applied to the energy of the vacuum and leads to a relation betweenG and the cosmological term,G S ³, valid in a matter-dominated universe (S =S(t) is the expansion factor). This relation plus the time-dependence law (suggested by many authors) t ² = constant, plustH > 2/3 (suggested by observations on the age of globular clusters;H is the Hubble parameter) implies an increasingG. One finds also GU, whereU is the mass density of the universe, in agreement with other studies.     

Analysis of the light curves of RT Persei by automatized fourier techniques

A new method has been developed by Kopal (1977c, Paper XII) to make use of expressions for the fractional loss of light ₀ ^l of the arbitrarily limb-darkened stars in the form of Hankel transforms of zero-order, in order to evaluate the explicit forms of the ₀ ^l s for different types of eclipse, as well as of the momentsA _2m of the respective light curves in a closed form. The automated method has been tested successfully on the light curves of RT Persei. Also, a photometric curve fit of RT Persei is investigated by application of numerical quadratures to determine the theoretical light curve appropriate for the Roche model. Finally a comparative discussion is given of various methods of light curve analaysis.On leave from Department of Physics, University of Ferdowsi, Mashad, Iran.     

Fourier analysis of the light curves of eclipsing variables,XX

In the present paper _n ⁰ , for occulation and transit eclipses of partial phases, are evaluated numerically by means of the Runge-Kutta methods. Section 2 contains the required differential equations of _n ⁰ with respect to the modulusX orC, and Section 3 includes the numerical method of the solutions of these differential equations. Theoretical values of ₀ ⁰ and ₁ ⁰ , with corresponding values ofC, are also added in this section.     

Computer simulation of the particle acceleration in pulsar magnetospheres

In the spherically-symmetric case, a computer simulation of the electron acceleration inside the outflow channel of the pulsar magnetosphere is produced. The stationary motion of electrons is shown to be unstable in the case of > _c, where is a parameter describing inhomogeneity of the background charge, and _c is its critical value. The arising non-stationary motion of electrons leads to a formation of electron bunches, which move chaotically. The mean electron energy appears to be much greater at the non-stationary motion, than at the stationary one. The time-averaged parameters of the non-stationary electron flow and their dependence upon have been investigated. Distributions of the mean values of parameters (charge density, electron velocity, electric field energy density, pressure, and internal energy of the gas composed of the electron bunches) over the magnetosphere altitude have been investigated. The mean spectra of the charge density have been obtained. The results of numerical investigation of the spherically-symmetric model are used for estimation of the electron energy and of the electron flux in the case of the more realistic model. The radioemission loss is estimated, and is shown to be large enough for explaining the radiopulsar phenomenon as a thermal radioemission of the pulsar magnetosphere. In particular, such common properties of the pulsar radioemission as the high bright temperature, the sharp radioemission directivity, and the characteristic turn-over of the radioemission spectrum at the frequency of the order 10⁸ Hz are found a natural explanation in frames of this model.     

Models of clusters of point masses with large central redshifts

Conclusions In the Newtonian case we have obtained an isotropic self-consistent distribution of gravitationally interacting point masses which satisfies the transport equation without collisions, and the gravitational equation for an arbitrary powerfunction density distribution =r^–s, s<3.For =r^–2 the analogous self-consistent solution was obtained for the anisotropic distribution function both in Newtonian and GTR cases.The GTR solutions with =r^–2 have central redshifts which increase without limit in accordance with the law 1+zr^–1/ as we approach the center. In the isotropic case, they appear to be stable when the mean velocities are much less than the velocity of light u<0.2c, >21.The hydrodynamic GTR solution was found for a perfect gas at constant temperature (but variable T=T(g₀₀)^1/2) which also has z for r0.We should like to thank K. Thorne, L. Hazin, and M. Podurets for valuable discussions. K. Thorne was particularly helpful in supplying unpublished results on circular orbits obtained by American authors.Astrofizika, Vol. 5, No. 2, pp. 223–234, 1969     

Quantum theory of the dielectric constant of a magnetized plasma and astrophysical applications

A quantum mechanical treatment of an electron plasma in a constant and homogeneous magnetic field is considered, with the aim of (a) defining the range of validity of the magnetoionic theory (b) studying the deviations from this theory, in applications involving high densities, and intense magnetic field. While treating the magnetic field exactly, a perturbation approach in the photon field is used to derive general expressions for the dielectric tensor . The properties of are explored in the various limits. Numerical estimates on the range of applicability of the magnetoionic theory are given for the case of the one-dimensional electron gas, where only the lowest Landau level is occupied.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

Singposts of shock waves in the metagalactic medium

Explosions of quasars and young galaxies at large redshifts must cause propagation of blast waves in the metagalactic medium. The shock waves formed can, during the radiative cooling stage, produce dense cold spherical shells around the epicentres of explosions. But, even before that, at the stage of adiabatic expansion, each spherical shock-wave front, if it lies on one line-of-sight with a more distant quasar, can imprint into the quasar spectrum a specific absorption doublet with a distance between the components (in the rest frame) ₀ 3 Å. The L doublet components have a small but the same equivalent widthW ₀ 0.3 Å, the ratioW ₀/₀ weakly depending onW ₀ ifW ₀ is small. We demonstrate here that such absorption L doublets are really present among the L forest in the absorption spectra of distant quasars which are, according to Sargentet al. (1980), of mostly intervening (and not intrinsic) origin. Further accumulation of data on absorption doublets, which can serve as direct indicators of metagalactic shock-waves, may provide valuable information about the physical conditions in the metagalactic gas at large redshifts.     

Hα Emission Stars in the Cepheus OB3 Region

H emission objects were searched for, using the objective-prismSchmidt plates in a 36 deg² sky area covering the Cepheus OB3 association.Hundred and eight emission stars have been found, 68 of which are newfindings to our knowledge. The properties of the IRAS point sourcesidentified with H emission stars indicate that most of theH emission stars are T Tauri stars or related objects. Hemission stars associated with IRAS sources and those unassociated havedifferent distributions, suggesting an age sequence among them.Altogether, they show a ring- or shell-like surface distribution, whichalmost coincides with that of heated dusts, and these distributionsappear to be encompassed by an HI shell.     

Spatial development of X-ray emission during the impulsive phase of a solar flare

The flare of 11 November, 1980, 1725 UT occurred in a magnetically complex region. It was preceded by some ten minutes by a gradual flare originating over the magnetic inversion line, close to a small sunspot. This seems to have triggered the main flare (at 70 000 km distance) which originated between a large sunspot and the inversion line. The main flare started at 172320 UT with a slight enhancement of hard X-rays (E > 30 keV) accompanied by the formation of a dark loop between two H bright ribbons. In 3–8 keV X-rays a southward expansion started at the same time, with - 500 km s ^–1. At the same time a surge-like expansion started. It was observable slightly later in H, with southward velocities of 200 km s^–1. The dark H loop dissolved at 1724 UT at which time several impulsive phenomena started such as a complex of hard X-ray bursts localized in a small area. At the end of the impulsive phase at 172540 UT, a coronal explosion occurred directed southward with an initial expansion velocity of 1800 km s^–1, decreasing in 40 s to 500 km s^–1.Now at Fokker Aircraft Industries, Schiphol, The Netherlands.     

Simultaneous radio and white light observations of the 1984 June 27 coronal mass ejection event

We present the two-dimensional imaging observations of radio bursts in the frequency range 25–50 MHz made with the Clark Lake multifrequency radioheliograph during a coronal mass ejection event (CME) observed on 1984, June 27 by the SMM Coronagraph/Polarimeter and Mauna Loa K-coronameter. The event was spatially and temporally associated with precursors in the form of meter-decameter type III bursts, soft X-ray emission and a H flare spray. The observed type IV emission in association with the CME (and the H spray) could be interpreted as gyrosynchrotron emission from a plasmoid containing a magnetic field of 2.5 G and nonthermal electrons with a number density of 10⁵ cm^–3 and energy 350 keV.On leave from Indian Institute of Astrophysics, Kodaikanal, India.     

Les raies du triplet de l'helium de la Nova Delphini 1967

The aim of this paper has been to study the neutral helium triplet emission lines identified in the spectrum of the envelope of Nova Delphini. By comparing the observed flux of the neutral helium lines with that calculated theoretically by Robbins, we find that the optical thickness in the center of the line 3889 is of the order of 21.50 for summer 1969. The optical thickness obtained by this method is here denoted _tran(3889).On the other hand, we obtain the number of neutral helium atoms in the 2³S state [N(2³S)] by considering the equilibrium between the mechanisms that populate and depopulate this state. We then find that the depopulation by photoionization due to the radiation of Ly (Hi), transitions to the 2¹S, 2¹p and 2³p states by electron collision, photoionization due to the continuum radiation of the central star, are 82.70%, 13.20%, 2.40%, 0.90% and 0.80% respectively. We find that the mechanism of the photoionization by Ly is the dominant mechanism of depopulation of 2³S state. We calculated ( 3889) of the order of 82.37, fromN(2³S), obtained in the preceding paragraph. The optical thickness obtained by this method is here denoted _bal(3889).The difference between _tran(3889) and _bal(3889) is very large and it cannot be attributed to calculation errors. We have considered all the mechanisms that can depopulate the 2³S state, so we then conclude that the difference between _tran(3889) and _bal(3889) is due to the heterogeneity of the envelope of the Nova, already found by us in our previous study of the profiles of the permitted and forbidden lines. Finally, we find from this study a filling factor of the order of 0.30.     

A new examination of absorption line density in the Lα forest of QSOs

The distribution of the absorption lines in the L forest of QSOs is re-examined in relation to both absorption and emission redshifts by analyzing a sample consisting of 20 QSO L forests.On the one hand, the -value in the relationN(z _abs)=N ₀(1+z _abs) is re-estimated by applying the maximum likelihood (ML) method to all the L forests in our sample as a whole as well as to the forests for individual QSOs. The global estimated is 2.20±0.28 and both the quasars with highest and lowestz _em do not individually have a significant effect on it. A non-parametric test on the estimate of from individual QSOs shows that there is no significant difference between the numbers of positive and negative -values. This does not, therefore, favour the idea that for individual QSOsN(z _abs) decreases with increasingz _abs.On the other hand, the possible correlation between the absorption line density and the emission redshift of the QSO itself, which was found by Bianet al. (1986, 1988) and re-discovered independently by Tytler (1987), is shown once again not only by the largerz _em QSOs having larger mean density, but more importantly, at a rather high confidence level, by the fact that, at the same values ofz _abs, QSOs with largerz _em possess a greater number of L absorption lines.A discussion of the inverse effect suggests that it is still hard to say whether this effect really exists.     

Spectroscopic study of Hα-emission objects in IC 1396

Spectral observations of 53 H-emission objects of the HII-region IC 1396 were carried out with moderate resolution using the 2.6m telescope of the Byurakan Astrophysical Observatory. Factor analysis of this observational material indicates that there are two dominant factors. Factor 1 (Fig. 1), which is the more significant factor, resembles the spectrum of a star of spectral type F5 with a strong H line in absorption. Factor 2 (Fig. 2), in contrast, appears as a later-type spectrum with H and H in emission. The result obtained can be explained by the transient nature of the H-emission.Translated fromAstrofizika, Vol. 37, No. 3, 1994.