Light-time orbit and apsidal motion of the eclipsing binary U Ophiuchi

A comprehensive period study of the times of minima observed from 1881 to 1985 has been performed. Previous interpretations of the O–C diagram based on light-time effect are confirmed. The light-time orbit of U Oph has been revised using a differential corrections procedure. We get an eccentric orbit withe=0.22±0.06,P=38.7±0.2 yr, and a mass function . In addition, our analysis has revealed short-period apsidal motion (U/P=4515±75) in a slightly eccentric close orbit (e=0.0031±0.0003), allowing a reliable determination of the density concentration coefficient,k ₂=0.0059±4. A comparison with stellar evolutionary models calculated by Jeffery (1984) yields the helium contentY=0.28±0.05 and an age of 3×10⁷ yr for the components of U Oph.     

Der offene sternhaufen NGC 2362

The very young open star cluster NGC 2362 was investigated by the strip method on charts of two photographs taken with the 1-m Schmidt telescope of the European Southern Observatory. Up to the limiting magnitudeM _v ^* =5 _. ^m 8 the cluster contains 100 stars and can be described by the Gaussian density law (6). Further results are: Mass = 246 , central mass density ₀ = 43.1 = 246 pc^-3 , radiusR2.6 pc, mean velocity of the stars = 0.64 km s^–1.

---

---

Mitteilungen Serie A.     

Die Mittleren Geschwindigkeiten Der Sterne In 58 Kugelförmigen Sternhaufen

The mean velocities of the stars in 58 globular clusters are derived from the photometric measurements of Kron and Mayall (1960). The mass-visual brightness ratio is used. The velocities are falling in the interval 2.9v11.6 km s^–1, their mean value is 6.75 km s^–1.

---

---

Mitteilungen Serie A.     

Fourier analysis of the light curves of eclipsing variable stars

The aim of the present paper is to find the eclipse perturbations, in the frequency-domain, of close eclipsing systems exhibiting partial eclipses.After a brief introduction, in Section 2 we shall deal with the evaluation of thea _n ^(l) integrals for partial eclipses and give them in terms ofa ₀ ⁰ ,a ₀ ⁰ (of the associated -functions) and integrals; while Section 3 gives the eclipse perturbations arising from the tidal and rotational distortion of the two components. The are given for uniformly bright discs (h=1) as well as for linear and quadratic limb-darkening (h=2 and 3, respectively).Finally, Section 4 gives a brief discussion of the results and the way in which they can be applied to practical cases.     

Die offenen sternhaufen M36, M38 und NGC 2477

The open star clusters M36, M38 and NGC 2477 were investigated by the strip method on charts of photographs taken with the Schmidt-Spiegel of the German Observatory Hoher List (M36/38) and the Curtis-Schmidt Telescope of the Cerro Tololo Interamerican Observatory (NGC 2477). The results are — Masses: 830, 2350, 4400 ; radii: 6.4, 10.0, 10.0 pc; central densities: 9.9, 15.3, 32.5 pc^–3; density laws: Gaussian (M36), generalized law of Schuster withn=3.00, 2.79; mean velocities of the stars 0.74, 1.01, 1.38 km s^–1.

---

---

Mitteilungen Serie A.     

Apsidal motion in the close binary IT cassiopeiae

In 1982 and 1993, we carried out highly accurate photoelectric WBVR measurements for the close binary IT Cas. Based on these measurements and on the observations of other authors, we determined the apsidal motion $\left[ {\dot \omega _{obs} = {{(11\mathop .\limits^ \circ 0 \pm 2\mathop .\limits^ \circ 5)} \mathord{\left/ {\vphantom {{(11\mathop .\limits^ \circ 0 \pm 2\mathop .\limits^ \circ 5)} {100 years}}} \right. \kern-0em} {100 years}}} \right]$ . This value is in agreement with the theoretically calculated apsidal motion for these stars $\left[ {\dot \omega _{th} = {{(14^\circ \pm 3^\circ )} \mathord{\left/ {\vphantom {{(14^\circ \pm 3^\circ )} {100 years}}} \right. \kern-0em} {100 years}}} \right]$ .     

On the influence of gradients in the angular velocity on the solar meridional motions

If fluctuations in the density are neglected, the large-scale, axisymmetric azimuthal momentum equation for the solar convection zone (SCZ) contains only the velocity correlations and where u are the turbulent convective velocities and the brackets denote a large-scale average. The angular velocity, , and meridional motions are expanded in Legendre polynomials and in these expansions only the two leading terms are retained (for example, where is the polar angle). Per hemisphere, the meridional circulation is, in consequence, the superposition of two flows, characterized by one, and two cells in latitude respectively. Two equations can be derived from the azimuthal momentum equation. The first one expresses the conservation of angular momentum and essentially determines the stream function of the one-cell flow in terms of : the convective motions feed angular momentum to the inner regions of the SCZ and in the steady state a meridional flow must be present to remove this angular momentum. The second equation contains also the integral indicative of a transport of angular momentum towards the equator.With the help of a formalism developed earlier we evaluate, for solid body rotation, the velocity correlations and for several values of an arbitrary parameter, D, left unspecified by the theory. The most striking result of these calculations is the increase of with D. Next we calculate the turbulent viscosity coefficients defined by whereC _ro ⁰ and C _o ⁰ are the velocity correlations for solid body rotation. In these calculations it was assumed that ₂ was a linear function of r. The arbitrary parameter D was chosen so that the meridional flow vanishes at the surface for the rotation laws specified below. The coefficients v _ro ⁱ and v _0o ⁱ that allow for the calculation of C _ro and C _0o for any specified rotation law (with the proviso that ₂ be linear) are the turbulent viscosity coefficients. These coefficients comply well with intuitive expectations: v _ro ¹ and –v _0o ³ are the largest in each group, and v _0o ³ is negative.The equations for the meridional flow were first solved with ₀ and ₂ two linear functions of r ( ₀ ¹ = – 2 × 10 ^–12 cm ^–1) and ( ₂ ¹ = – 6 × 10 ¹² cm ^–1). The corresponding angular velocity increases slightly inwards at the poles and decreases at the equator in broad agreement with heliosismic observations. The computed meridional motions are far too large ( 150m s^–1). Reasonable values for the meridional motions can only be obtained if _o (and in consequence ), increase sharply with depth below the surface. The calculated meridional motion at the surface consists of a weak equatorward flow for gq < 29° and of a stronger poleward flow for > 29°.In the Sun, the Taylor-Proudman balance (the Coriolis force is balanced by the pressure gradient), must be altered to include the buoyancy force. The consequences of this modification are far reaching: is not required, now, to be constant along cylinders. Instead, the latitudinal dependence of the superadiabatic gradient is determined by the rotation law. For the above rotation laws, the corresponding latitudinal variations of the convective flux are of the order of 7% in the lower SCZ.     

Apsidal motion in the eclipsing binary system OX cas

Multi-colourWBVR photoelectric observations of the eclipsing binary OX Cas were carried out. The photometric elements, absolute parameters and the angular rate of the apsidal motion ( = 9.1 deg yr^–1 were obtained. The apsidal parameterk ₂ derived for this system is by 15–25% smaller than the theoretical parameterk ₂.     

Simulations of cosmic-ray particle diffusion

The diffusion of charged particles in a stochastic magnetic field (strengthB) which is superimposed on a uniform magnetic fieldB ₀ k is studied. A slab model of the stochastic magnetic field is used. Many particles were released into different realizations of the magnetic field and their subsequent displacements z in the direction of the uniform magnetic field numerically computed. The particle trajectories were calculated over periods of many particle scattering times. The ensemble average was then used to find the parallel diffusion coefficient . The simulations were performed for several types of stochastic magnetic fields and for a wide range of particle gyro-radius and the parameterB/B ₀. The calculations have shown that the theory of charged particle diffusion is a good approximation even when the stochastic magnetic field is of the same strength as the uniform magnetic field.     

K emission-line widths and the solar chromosphere

Closely spaced microphotometer tracings parallel to the dispersion of one excellent frame of a K-line time sequence have been utilized for a study of the nature of the K_2v , K_2R intensities in the case of the solar chromosphere. The frequency of occurrence of the categories of intensity ratio are as follows: per cent; per cent; per cent; per cent; per cent. Two types of absorbing components are postulated to explain the pattern of observed K_2v , k_2R intensity ratios. One component with minor Doppler displacements acting on the normal K₂₃₂ profile, where K_2V >K_2R , produces the cases K_2v K_2R , K_2v = K_2R , K_2v <K_2R . The other component arises from dark condensations which are of size 3500 kms as seen in K_2R . They have principally large down flowing velocities in the range 5–8 km/sec and are seen on K₃ spectroheliograms with sizes of about 5000 kms, within the coarse network of emission. These dark condensations give rise to the situation K_2R = 0.K₂-line widths are measured for all tracings where K_2v , K_2R are measurable simultaneously. The distribution curve of these widths is extremely sharp. The K₂ emission source is identified with the bright fine mottles visible on the surface. Evidence for this interpretation comes from the study of auto-correlation functions of K₂ intensity variations and the spacing between the bright fine mottles from both spectrograms and spectroheliograms. The life time of the fine mottling is 200 sec.The supergranular boundaries which constitute the coarse network come in two intensity classes. A low intensity network has the fine mottles as its principal contributor to the K emission. When the network is bright, the enhancement is caused by increased K emission due to the accumulation of magnetic fields at the supergranule boundary. The K₂ widths of the low intensity supergranular boundary agree with the value found for the bright mottles. Those for the brighter network are lower than this value, similar to the K₂ widths as seen in the active regions.It is concluded that bright fine mottling is responsible for the relation, found by Wilson and Bappu, between K emission line widths and absolute magnitudes of the stars.The paper discusses the solar cycle equivalents that stellar chromospheres can demonstrate and indicates a possible line of approach for successful detection of cyclic activity in stellar chromospheres.     

Linear waves in a radiating and scattering grey medium

The problem on linear waves in a radiating and scattering grey medium is studied using Whitham's method. Analysis of the basic equations distinguishes two limiting cases: the one is theequilibrium case in which the energy exchange between the gas and radiation plays an essential role, and the other is theScattering case in which the effect of energy exchange is negligible. A new type ofradiation acoustic wave with the speed is found in the scattering case. The governing equations for linearized one-dimensional flow are reduced to one equation of radiative acoustics valid to order 1/c, and the criterion for the two limiting cases is derived from studying this equation. The harmonic solution is analytically studied to show that theeffective optical depth corresponding to the wavelength of perturbation gives the measure of the interaction between the gas and radiation. When _eff1, the sound speeda _g ² =P _g / and the propagating speed of radiative disturbancea _f ² =fc ² appear as the modified classical and radiation-induced modes respectively, wheref is the Eddington factor. When _eff1, the isentropic sound speeda _s ² =(P _g +P _r / appears in the equilibrium case, and the radiation acoustic speeda _A ² appears in the scattering case. The dispersion relation of the harmonic solution is numerically calculated. The result shows that the wave pattern depends critically on the ratio=P _g /(P _g +P _r ). When , the speeda _S anda _A arise from the modified classical mode, and when , they originate from the radiation-induced mode.     

A few observations of and remarks on V1500 Cygni

The development of the post-nova light curve of V1500 Cyg inUBV andHβ, for 15 nights in September and October 1975 are presented. We confirm previous reports that superimposed on the steady decline of the light curve are small amplitude cyclic variations. The times of maxima and minima are determined. These together with other published values yield the following ephemerides from JD 2 442 661 to JD 2 442 674: $$\begin{gathered} {\text{From}} 17 {\text{points:}} {\text{JD}}_{ \odot \min } = 2 442 661.4881 + 0_{^. }^{\text{d}} 140 91{\text{n}} \hfill \\ \pm 0.0027 \pm 0.000 05 \hfill \\ {\text{From}} 15 {\text{points:}} {\text{JD}}_{ \odot \max } = 2 442 661.5480 + 0_{^. }^{\text{d}} 140 89{\text{n}} \hfill \\ \pm 0.0046 \pm 0.0001 \hfill \\ \end{gathered} $$ with standard errors of the fits of ±0 _. ^d 0052 for the minima and ±0 _. ^d 0091 for the maxima. Assuming V1500 Cyg is similar to novae in M31, we foundr=750 pc and a pre-nova absolute photographic magnitude greater than 9.68.     

The critical and the saturation content of magnetic monopoles in rotating relativistic objects

Both the critical content _c ( N _m /N _B , whereN _m ,N _B are the total numbers of monopoles and nucleons, respectively, contained in the object), and the saturation content _s of monopoles in a rotating relativistic object are found in this paper. The results are:

The dependence of the frequency spectra of the interplanetary magnetic-field fluctuations on the direction of the mean field

The frequency spectra of the interplanetary magnetic field fluctuations are the projection of their wavenumber spectra onto one dimension. Only the frequency spectra can be measured by spacecrafts. It is studied how their measured size depends on the direction of the mean fieldB ₀, which structures the symmetry of the fluctuations relative to the solar wind system. It is specialized for the slab model, Alfvén waves, magneto-acoustic waves and the isotropic case. For the slab model the frequency spectra are proportional to , whereq is the spectral index and the angle betweenB ₀ and the radial direction. For the diffusion coefficientK _TT the relation holds.     

The light curved in the CM field

In this paper we introduce the CM field in Sections 2 and 3 based on the paper by Wang and Peng (1985), and calculate the light curved in the CM field in Section 4. The result shows thatP makes _CM larger than _C at , and smaller at . Under a special circumstance which source, CM lens, and observer are in the same line, if we get | ₀₌₀ , and | _=/2 , we can determine theP(M) andQ(M) of the CM lens,M is the mass of the CM lens.     

On the structure and mass of the galactic halo

On the basis of a globular cluster study a crude estimate of the total mass of the galactic halo within 20 kpc from the centre is done. It gives a minimal halo mass of the order of , yielding possibilities for a mass as large as . The content of the interstellar matter in the halo is estimated too. It is found that the gas content is a few percents the minimal mass, the gas temperature is very high — about 1×10⁶ K, the magnetic field weak — about 0.25 nT. A weak nonthermal radio emission might be expected from such a halo.     

Synchrotron neutrino-pair radiation in neutron stars

The neutrino-pair radiation by electrons in a non-quantizing magnetic field B is investigated. For a relativistic degenerate electron gas the emissivity of this process is mainly given by \documentclass{article}\pagestyle{empty}\begin{document}$ \varepsilon _r = 5 \times 10^{15} (pF/mc)^{4/3} \,B_{13}^{2/3} T_y^{12/8} \,{\rm erg} \times {\rm cm}^{ - 3} \times {\rm sec}^{- 1} $\end{document} where pF is the electron Fermi momentum. Under typical neutron star conditions at B ∼ 10¹³G neutrino synchrotron radiation appears to be one of the most effective mechanisms of neutrino energy loss in the envelopes of neutron stars; this mechanism may also compete with other known neutrino production mechanisms in the neutron star cores if pion condensate or quark matter is absent.     

The spherically-symmetrical trajectories of spin particles in the Schwarzschild field

The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions , where is the Lie derivative of the Killing vector _j , permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail.     

Evolution of a binary system consisting of a helium star and a white dwarf

Results of evolutionary calculations for a close binary system with a central helium burning He-star filling its Roche lobe and an accreting white dwarf are presented. Values for the mass of the components and the degree of central helium exhaustion before the filling of the Roche lobe are varied. It is shown that in such a system the mass accretion rate will remain for a long time (2–4) Ö 10^–8 yr^–1 ifq<1 (q=M _He,2/M _CO,1). The obtained results are discussed in connection with pre-supernova I phenomenon.