Comptel analysis of GRB 940217

COMPTEL on board CGRO has observed a very strong (S[> 0.3 MeV] = 2.03 × 10^–4 erg cm^–2), complex, and long lasting (162 s) gamma-ray burst on February 17, 1994 (GRB 940217). Temporal fluctuations occur on timescales as short as 100 ms. Hard-to-soft spectral evolution has been observed during the burst emission and also within individual peaks. The photon spectra obtained within the 6 peaks can be modelled by single power law spectra and by broken power laws with break energies at around 1 MeV. The best-fit power law slopes vary between 1.1 and 3.5 throughout the event. The burst is located at [ ₂₀₀₀, ₂₀₀₀] = [29.5°, 3.8°] with a 3 error radius of 0.9°. COMPTEL does not detect any significant post-burst emission (as reported by EGRET) at low energies (< 30 MeV), and our upper limits are marginally consistent with the EGRET detections. Using high energy spectral and temporal information, distance limits to GRB 940217 have been derived.     

The libration of a satellite caused by the tidal field of its planet

The tidal field caused by the second order zonal harmonic of the gravitational field of a planet is discussed according to the fernwirkungsgesetz (principle of local action) of Weyl (1921) introducing an accurate and simple form of the gravitational potential of the planet in elliptic coordinates. It is seen that the tidal field can be described at each point as a small rotation of the local canonical frame which causes a libration and a precession of the axis of rotation of the satellites of the planet. It is also shown that at each point P, is one third of the angle between the line of force through P and the line from P to the center of mass of the planet. All the formulae obtained, to compute and , are in closed form.     

Representation of the Earth's gravitational potential

The paper represents the Earth's gravitational potentialV, outside a sphere bounding the Earth, by means of its difference V from the author's spheroidal potential. The difference V is in turn represented as arising from a surface density on the sphere bounding the Earth. Because of the slow decrease with ordern of the normalized coefficients in the spherical harmonic expansion ofV, the density anomalies from which the higher coefficients arise must occur in regions close to the Earth's surface. The surface density is thus an idealization of the product of the density anomaly and the crustal thicknessb. Values of are computed from potential coefficients obtained from two sources, Rapp and the Smithsonian Astrophysical Observatory. The two sources give qualitative agreement for the values of and for its contour map. The numerical values obtained for are compatible with the idea that the responsible density anomalies are reasonably small, i.e., less than 0.05 g/cm³, and occur in the crust alone.This paper was prepared under the sponsorship of the Electronics Research Center of the National Aeronautics and Space Administration through NASA Grant NGR 22-009-311.     

Strong transverse fields in δ-spots

Spectroscopic measurements of the strength and direction of transverse magnetic fields in six -spots are presented. The field direction is determined by the relative strength of the - and -components at different polarizer orientations, and is, with one exception, parallel to the neutral line and as strong as the umbral field. Field strengths determined by line splitting are as high as 3980 G.     

Unified Hamiltonian stability theory

We show that the spectral stability of Hamiltonian equilibria and periodic orbits may be analyzed by the same method. This is accomplished via the Cayley transform, =(+1)/(–1), which maps the unit circle onto the imaginary -axis. The advantages and disadvantages of the new method over previous techniques are elucidated.     

A note on σ-stability in hydromagnetics

The concept of -stability is reviewed and applied to the case of aligned magnetoatmospheric flow. A sufficient condition for -stability is derived, and the upper bound arising from this condition is investigated as a function of .     

A search for soft X-ray emission from stellar sources

With the soft X-ray detector (0.2–0.284 keV) aboard the Astronomical Netherlands Satellite (ANS) we have searched for X-ray emission from hot star coronae and peculiar stars. On Sirius ( CMa) and Capella ( Aur) X-ray emission has been measured at 6 and 5 level, respectively, above background. In all other cases the search revealed no evidence for soft X-ray emission. Upper limits to the luminosities of about 25 star coronae (main-sequence stars, (sub)giants, and supergiants) and of 4 peculiar stars ( Sco, Lyr, P Cyg, and Car) have been obtained.Paper presented at the COSPAR/IAU Symposium on Fast Transients in X-and Gamma-Rays, held at Varna, Bulgaria, 29–31 May, 1975.     

Геометрическая интерпретация необходимых условий устойчивости треугольных точек либрации общей задачи трех тел

. . . , , m ₁, m₂, m₃, n ( .

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The conditions of stability of the constant libration solutions of the general three-bodies problem obtained by E. Routh through investigation of the linearized perturbed motion equations are analised. To the values of the masses of the three bodies which satisfy boundary conditions of the region of stability the locus of all corresponding centers of masses is laid down in accordance with. It occurs that this locus is a circle, its centre coinciding with the geometric centre of the trianglem ₁, m₂, m₃ and its radius being a function of exponent in the law of attraction of the bodies. The motion may be stable only if the centre of masses of the bodies lies outside the circle mentioned above. In the case of the Newtonian law of attraction the radius of this circle equals 0,943 |r_max| where |r_max| is a distance of the vertex from the centre of the trianglem ₁, m₂, m₃. Thus stability is possible (if it is generally possible) inside a very small region in this case.

     

Continental drift and rotation of the Earth

It is shown, based on certain simplifying assumptions, that an island the size of Greenland, drifting across the North Atlantic at 10 m/century produces a change in secular rotation T=0.01 s.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

On the Freundlich red shift

The Freundlich red shift of wavelengths in the solar spectrum is discussed. Born's approach on the photon-photon interaction is used in conjunction with Melvin's recalculation of Freundlich's universal constant in order to derive the cross-section for scattering in the solar atmosphere. The new cross-section appears to be = 1.58 × 10^–18 cm², which is about one thousand times Born's estimate for the effective cross-section. However, a modified value of the constant is in a good agreement with the one obtained by Ter Haar by scattering process methods, which leads to 10^–18 cm² for the photon-photon interaction cross-section of the solar atmosphere. A new expression for Freundlich's red shift formula is obtained. Some numerical examples are given and some interesting aspects of Freundlich's parameters are discussed.     

On the Power in the Legendre Modes of the Solar Radial Magnetic Field

The power in the different modes of an expansion of the solar radial magnetic field at the surface in terms of Legendre polynomials,P , is calculated with the help of a solar dynamo model studied earlier. The model is of the Babcock–Leighton type, i.e., the surface eruptions of the toroidal magnetic field – through the tilt angle, , formed by the magnetic axis of a bipolar magnetic region with the east-west line – are the sources for the poloidal field. In this paper it is assumed that the tilt angle is subject to fluctuations of the form, = ()+ <> where <> is the average value and () is a random normal fluctuation with standard deviation which is taken from Howard's observations of the distribution of tilt angles. For numerical considerations, negative values of were not allowed. If this occurred, was recalculated. The numerical integrations were started with a toroidal magnetic field antisymmetric across the equator, large enough to generate eruptions, and a negligible poloidal field. The fluctuations in the tilt angle destroy the antisymmetry as time increases. The power of the antisymmetric modes across the equator (i.e., odd values of ) is concentrated in frequencies, _p, corresponding to the cycle period. The maximum power lies in the =3 mode with considerable power in the =5 mode, in broad agreement with Stenflo's results who finds a maximum power at =5. For the symmetric modes, there is considerable power in frequencies larger than _p, again in broad agreement with Stenflo's power spectrum.     

The configuration of a thin,rotating self-similar disk in general relativity

Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density and an angular velocity . Self-similarity as a statement of the absence of scales implies that and can be written as=c ²/4Gr, =c/r, and demands that and be pure numbers.     

Velocity dispersion profiles ofN-body simulations

The time evolution of the velocity dispersion as a function of radius, called v-profiles, of threeN-body simulations of Wielen are presented in units ofr/R _G (whereR _G is the gravitational or virial radius) and discussed as a function of mass sample. The evolution of the radial and tangential components of the velocity dispersion is discussed, and each v-profile is fitted to a simple power law in the halo (0.15r/R _G2.0). Several structural features appear at late time intervals: (a) an upturn in the radial component of v which occurs in a decreasing shell (closer to the core) in time, (b) the v-profile of the massive particles mimics that of the total sample, since equipartition of kinetic energy does not obtain, and (c) a local minimum atr0.3–0.5R _G appears in one model which coincides with the local minimum in the number density profiles and possibly with feature (a).The line-of-sight v-profile, called LS-profile, of each model as a function of time and mass sample are also presented and discussed. They contain the same structural features as the v-profiles. Projection factors at small radii are also discussed. The LS-profiles of the models can be compared with the observed velocity dispersion profiles of clusters of galaxies in Struble (1979a).     

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.     

Batse time-resolved observations of GRBs: the burst ‘topographic’ map

It is a well-known observation that many GRBs have spectra with curvature in the less than 1 MeV regime, but flatten out to approximately a -2 power law at higher energies. The large collecting area of BATSE allows spectral studies with unprecedented time resolution. We are conducting a systematic study of time-resolved spectroscopy of GRBs observed by BATSE. Several aspects of this survey are discussed: correlations among fit parameters and between fit parameters and intensity; screening for spectral features using-residual contour maps; and an introduction to the GRB topographic map and its possible qualitative diagnostic abilities.     

Seeing Conditions at Sutherland. Results of the 1992/93 seeing campaign

In order to decide whether the seeing conditions at SAAO/Sutherland justify the erection of a 3.5 m telescope and also to compare Sutherland with the Gamsberg/Namibia site, a seeing campaign covering 15 months has been carried out. For direct comparison with the results of the seeing campaign at Gamsberg twenty years before the same QUESTAR telescope was employed. The seeing is determined by the scattering of the star-trail exposed on a film in the focal plane of the telescope. The campaign commenced in February 1992. Up to May 1993, data for 204 nights, that is 47.3% of the total number of nights, were collected. Due to wind speeds above 30 km h^-1, 25 out of the 204 nights were not considered in the final reduction. The useful 179 nights are evenly distributed over the campaign period. The median seeing value for the whole period is = 0.52. There are differences during the year: the best season gives = 0.42, the worst = 0.67. Each night was divided into three intervals, although data for each of the three intervals were not always available. Generally, there is an improvement in the seeing during the course of a night. The results are compared to the seeing values of Gamsberg/Namibia and ESO/La Silla.     

Rapidly rotating polytropes in the post-Newtonian approximation to general relativity

The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order ⁴, where is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter = ²/2G _c and a relativity parameter, =p _c / _c C ² , wherep _c and _c are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of order ². The critical rotation parameterv _c , which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of . Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5.     

Influence du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité

Résumé On étudie l'effet du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité. Le satellite possède une symétrie dynamique et un moment magnétique propre dirigé suivant l'un des axes principaux d'inertie; le champ magnétique terrestre est assimilé au champ d'un dipôle dont les pôles coïncident avec les pôles terrestres. On néglige les perturbations de la trajectoire du satellite qui est supposée circulaire. La position du satellite par rapport à son centre de gravité est repérée dans un système d'axes lié au plan de l'orbite et le mouvement est décrit à l'aide des angles d'Euler , , . La symétrie sphérique et le choix du moment magnétique sur l'un des axes d'inertie permettent d'éliminer l'angle .La solution pour et peut se développer en séries de puissance d'un petit paramètre . Les séries convergent pour ||<1.Lorsque le moment magnétique est faible on la rotation du satellite rapide, est faible. Les développements sont calculés effectivement jusqu'à ².La comparaison des résultats avec l'intégration numérique du système d'équations différentielles est satisfaisante.

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The effect of the Earth's magnetic field on the motion of a satellite around its centre of mass is investigated. The satellite is assumed to be dynamically symmetric and to be magnetized in the same direction as that of a principal axis. The Earth's magnetic field is assumed to be a dipole field whose poles coincide with the rotation poles of the Earth. The satellite's orbit is circular and perturbations are neglected. The position of the satellite with respect to its centre of mass is given with respect to a coordinate system fixed in the orbital plane and the motion is described by Euler's angles , , . The spherical symmetry and the coincidence of the magnetic moment with a principal axis allow one to eliminate the angle .The solution for and , can be expanded in power series for small parameter .The series converge for <1. is small for a small magnetic moment or a high angular velocity of the rotating satellite. The terms of the expansion of the series are calculated up to ².The comparison of the results with those obtained by numerical integration of the differential equation is satisfactory.

     

Взаимооействие Излучения Рентгеновскооо Истооника с АтмосФерой Нормальной Звезды в Тесных Двойных Системах

, . : , . , . . ( ) . . . HZ Her=Her X1, . . , . , ., hv 15–30 . , . Sco X1 .     

Rosat X-ray light curves of early-type stars

We have investigated ROSAT X-ray data of OB stars to search for evidence of time variability in the X-ray emission from early-type stars. As an example for such studies we present a detailed variability analysis for our two program stars Ori and Ori which have been multiply observed with ROSAT. The long-term analysis of both stars now covers a time range of 2.5 years and includes six pointed PSPC observations, an additional pointed HRI observation of Ori and the ROSAT all-sky survey data of both stars. Over a long time range the X-ray light curves of Ori and Ori show no evidence for variability. In the case of Ori we detected a moderate increase in X-ray count rate during a period of 2 days which can be explained as a strong shock propagating in the wind of an O-type star.