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 .     

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.     

Extreme-ultraviolet observations of a surge

A flare surge at the limb was observed in CIII 977 Å by the Harvard OSO 6 spectroheliometer. The kinematic behavior of the surge is the same in CIII and in H. The amount of CIII emission is consistent with a model in which the CIII ions occupy sheaths with thickness 100 km surrounding the cooler H-emitting threads. The mass of the material containing CIII ions is about 10^–2 times that emitting H.Now at California Institute of Technology, Pasadena, California.     

Profiles of Hi (La), Mgii (h and k), Caii (H and K) Lines of an active filament at the limb,with the LPSP instrument aboard the OSO-8 Satellite

We scanned the H i L, Mg ii h and k, Ca ii K and H lines simultaneously with the LPSP instrument on OSO-8, to investigate the low and moderate temperature regions of an active region filament. The L line is not reversed except for the innermost position in the prominence. Intensity (k/h), (K/H) ratios are respectively 2 and 1.1, indicating that the Mg ii lines are optically thin, and that Ca ii K is saturated, although not clearly reversed. The results obtained during the second sequence of observations (K saturated before L for example) indicate that within the size of the slit (1 × 10) we are not observing the same emitting features in the different lines.We also observe an important line-of-sight velocity at the outer edge of the feature, increasing outwards from a few km s^–1 to 20 km s^–1 within 2. Less than half an hour later, this velocity is reduced to 15 km s^–1 while the intensities increase. Full width at half maximum intensities for this component indicate turbulence variations from 22 to 30 km s^–1. The observed high velocities at the top of the prominence can be compared with radial velocities that Mein (1977) observed in H at the edges of an active filament and interpreted as velocity loops slightly inclined on the axis of the filament.     

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.     

Late-time emission of the type II Supernovae powered by the radioactive decay56Ni−56Co−56Fe

A one-zone model for the late time SN II energized by the radioactive decay⁵⁶Ni–⁵⁶Co–⁵⁶Fe is presented. The model succeeds in reproducing for the late time evolution of H and [Oi] 6300 emission lines in SN1970g for the reasonable set of parameters: mass of ejecta 4M , boundary velocityv ₀=4000 km s^–1 and amount of⁵⁶NiM _Ni=0.02M . However, a one-zone model does not account for the late time continuum. In the case of SN1980k the radioactive model fits H and [Oi] 6300 emissions att250 day satisfactory but fails at very late time, e.g.,t=670 day when the predicted value of the ratioL(H)/L(6300) is two orders of magnitude smaller than the observed one. We suggest that the strong H emission in SN1980k on the 670th day is due to the interaction of the supernova envelope with the pre-SN wind. The radioactive model for the late time SN II predicts strong Mgii 2800 line and detectable Hei 10830 line in emission and absorption.     

Study of alpha component dynamics in the solar wind using the Prognoz satellite

The analysis of solar wind He⁺⁺ and H⁺ ion distribution functions, collected over five months by the satellite Prognoz 1, shows that these are in general maxwellian but that often tails appear at higher speeds. The existing relation V-T, the observation of ratios of T/Tp 3.83 and V/Vp 1.035 give evidence of preferential He⁺⁺ ion heating and acceleration. The criteria for heating by dissipation of hydromagnetic waves proposed by Barnes and Hung (1973) are tested experimentally. Finally, multifluid models are likely to predict certain observations such as dependence of the velocity ratio V/Vp on the solar wind flux.     

Effects of magnetic shear,spot, and plage rotation on prominence evolution

We have studied the evolution of two dark H filaments as prominences during their disk passage from 12 to 19 February, 1992 and 6 to 17 March, 1992, using Kodaikanal Observatory H and Caii K spectroheliograms. Both the filaments were well outside the spot regions. However, they were connected to sunspots by small threads. Outside the spot regions, the filaments were also anchored between opposite polarity plage regions. Both the filaments were almost straight in the beginning. However, they acquired a curved shape (inverted U-shape) as the spot and plages underwent rotation. It is shown that rotation of the plage and spot plays an important role in the evolution of prominences, one serving as the anchor and the other imparting necessary shear. Once the shear reaches a critical value it starts unwinding the filaments, resulting in the fine structure of the two prominences studied.     

The temperature and internal kinematics of M8

A photoelectric Fabry-Pérot spectrometer is used to record the line profiles of H and [Nii] at 22 points in the nebula. The ratio of intensity H/[Nii] is used to derive an electron temperature distribution with values between 5700° and 9100° showing a peak at the centre of density. These temperatures are compared with the H Doppler temperatures to estimate excess velocities of mass motion. Together with the shifts of the H line centres, these lead to an evaluation of the velocity field in the nebula.It is suggested that the nebula consists of a core expanding at about ±10 km/sec^–1 surrounded by a thick peripheral shell in which large scale mass motions are small. Non-thermal broadening suggesting turbulent velocities at about the speed of sound is observed in this shell and is attributed to small scale dynamic effects in a non-smooth density distribution. The effect of such expanding cores on heliocentric velocities of galacticHii regions is discussed.     

Simultaneous measurements of magnetic fields and brightness fields using a 4-image spectroheliograph

The use of an auxiliary beamsplitter with the Kitt Peak 15-foot spectroheliograph permits spectroheliograms to be taken simultaneously in 4 identical images of the sun. By using two of these images for a Zeeman spectroheliogram, a third image for a Fei 4071 spectroheliogram, and the fourth image for a 6107Å continuum spectroheliogram, simultaneous measurements of magnetic fields and brightness fields have been obtained. Within the limits of intensity variations imposed by doppler shifts and brightness fluctuations of the continuum, a quantitative relation does exist between the measured values of brightness and magnetic field strength of the photospheric network. For intensities measured +0.12 Å from the core of Fei 4071, this relation is ln(1 +I/I) = ¦B ¦, whereB refers to the component of magnetic field normal to the solar surface,I/I is the fractional excess of brightness of the magnetic regions relative to the brightness of non-magnetic regions, and = (6±2)%/100 gauss.Kitt Peak National Observatory Contribution No. 538.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.Visiting Astronomer, Solar Division, Kitt Peak National Observatory.     

Complete determination of the magnetic field vector and of the electron density in 14 prominences from linear polarizaton measurements in the HeI D3 and Hα lines

The present paper is devoted to the interpretation of linear polarization data obtained in 14 quiescent prominences with the Pic-du-Midi coronagraph-polarimeter by J. L. Leroy, in the two lines Hei D₃ andH quasi-simultaneously. The linear polarization of the lines is due to scattering of the anisotropic photospheric radiation, modified by the Hanle effect due to the local magnetic field. The interpretation of the polarization data in the two lines is able to provide the 3 components of the magnetic field vector, and one extra parameter, namely the electron density, because the linear polarization of H is also sensitive to the depolarizing effect of collisions with the electrons and protons of the medium. Moreover, by using two lines with different optical thicknesses, namely Hei D₃, which is optically thin, and H, which is optically thick ( = 1), it is possible to solve the fundamental ambiguity, each line providing two field vector solutions that are symmetrical in direction with respect to the line of sight in the case of the optically thin line, and which have a different symmetry in the case of the optically thick line.It is then possible to determine without ambiguity the polarity of the prominence magnetic field with respect to that of the photospheric field: 12 prominences are found to be Inverse polarity prominences, whereas 2 prominences are found to be Normal polarity prominences. It must be noticed that in 12 of the 14 cases, the line-of-sight component of the magnetic field vector has a Normal polarity (to the extent that the notion of polarity of a vector component is meaningful; no polarity can be derived in the 2 remaining cases); this may explain the controversy between the results obtained with methods based on the Hanle effect with results obtained through the Zeeman effect. A dip of the magnetic field lines across the prominence has been assumed, to which the optically thick H line is sensitive, and the optically thin Hei D₃ line is insensitive.For the Inverse prominences, the average field strength is 7.5±1.2 G, the average angle,, between the field vector and the prominence long axis is 36° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 29° ± 20°, and the average electron density is 2.1 × 10¹⁰ ± 0.7 × 10¹⁰ cm^–3. For the Normal prominences, the average field strength is 13.2±2.0 G, the average angle,, between the field vector and the prominence long axis is 53° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 0° ± 20° (horizontal field), and the average electron density is 8.7 × 10⁹ ± 3.0 × 10⁹ cm^–3.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

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.     

The neutral interface adjoining theHII region DR21

Observations of C100 and C125 atomic carbon recombination lines were made at the Algonquin Radio Observatory, towards the neutral interface separating theHii region DR21 (at RA=20^h37^m14^s, Dec=+42°0900) from its associated molecular cloud. An analysis of the Cn observations in conjunction with a simple model of a neutral interface enabled the derivation of the following parameters: electron density of 300 cm^–3, electron temperature of 30 K, microturbulent velocity of 2.3 km s^–1, and depth of the neutral interface of 0.01 pc. A single,stimulated emission model is sufficient to reproduce the Cn observations in the wavelength range from 4.6 cm (C100) to 21 cm (C166). All the known Cn data do support a pressure equilibrium between the neutral interface and theHii region, after the usual allowance is made for carbon depletion on grains.     

EUV arcades: Signatures of filament instability

We have examined seven active regions of the Skylab period in the EUV (Harvard College Observatory), and in H and K₃ (Observatoire de Meudon, spectroheliograms and patrols) in order to elucidate the magnetic geometry in the coronal environment of filaments. We have also looked for signatures of magnetic reconfigurations associated with instabilities (i.e. velocities or disappearances) of filaments. Out of sixteen H filaments observed, six were stable (lifetime 48^h). All the filaments lay within coronal cavities as seen in lines formed above 1.5 × 10⁶ K (Mgx 625, Sixii 521, Fexvi 417, Fexv 361). None of the stable filaments had arcades or arches spanning the cavities except (sometimes) at the ends of the filaments. On the other hand, most (8/10) of the unstable filaments (having concurrent Doppler shifts or a subsequent DB within 24^h) had arcades or single arches spanning their cavities. The arches were observed in EUV lines with formation temperatures as low as 2–4 × 10⁵ K (Oiv 554, Ovi 1032, Ne vii 465), as well as in hotter lines. A statistical test shows that the arcade/instability vs non-arcade/stability association is significant at the 99% confidence level. We suggest 2 types of scenario relating arcades to instabilities. The more preferable scenario is closely related to the Kuperus/Van Tend model of filament disruptions.     

A spectroscopic study of solar spicules in Hα, Hβ and K

Simultaneous spectra of spicules in H, H and the Ca ii K have been analyzed. These spectra were obtained with the échelle spectrograph of Sacramento Peak Observatory and have a resolution of 1.5 s of arc. Data include absolute intensities, velocities, linewidths and the optical depth at the center of H. Electron densities range between 6 × 10¹⁰cm^–3 and 1.2 × 10¹¹cm^–3, while the range of the electron temperature is between 12000K and 15000K at a height of 5400 km above the limb. The analysis of the variation of the line of sight velocity across spicules shows that their rotation is very small. There is very good correlation in the structure of all three lines.     

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.     

Observations of chromospheric lines from OSO-8

The line profiles of L, Ca ii K and Mg iik were measured with the spectrometer of the Laboratoire de Physique Stellaire et Planétaire on board of OSO-8. The results of these measurements are presented.Mitteilungen aus dem Kiepenheuer-Institut Nr. 181.     

Lα, Lβ (of Hi), k and h (of Mgii), K and H (of Ca ii) observations in a quiescent prominence with the OSO-8 LPSP instrument

A sequence of images taken at different positions in the resonance lines of Ca ii, Mg ii, and H i was obtained over a quiescent prominence with the LPSP instrument on OSO-8. Ca ii K (and H) profiles are reconstructed at different locations in the prominence with a (10 × 5) arc sec² resolution. Significant variations of FWHM and line shifts are found: FWHM range from 0.14 Å to 0.5 Å; blue shifts reach about 14 km s^-1. The ratio of K to H absolute intensities shows a large spread around the average value of 1.2. The same ratio for the Mg ii lines in the whole prominence is higher (1.7), a fact already noticed at the edge of an active prominence (Vial et al., 1979). The ionization degree, as measured by the L/Ca K ratio, shows noticeable variations within the prominence. The L intensity is about 0.3 times the intensity measured in the quiet Sun, and the L/L ratio is less than one half the disk value. These results indicate important variations of the thermal conditions inside the prominence.DASOP, Observatoire de Paris, 92190 Meudon, France.