The evolutionary history of PSR 0655+64 and PSR 1913+16

We intend to point out that existing evolutionary scenario for the genesis of the binary radio pulsars like PSR 0655+64 (P1 d) and 1913+16 (P8 hr) having short orbital periods and relatively massive companion (>0.5M _*) is inconsistent in that it does not allow for a prolonged phase of angular momentum transfer. We propose here a modified evolutionary scenario where there is such a prolonged phase of angular momentum transfer from a low mass helium star to the neutron star mediated by an accretion disk along the so-called caseB evolutionary track.     

A two-parameter scheme for the evolution of symmetrical galaxies

In the present paper, a general evolutionary scheme for axisymmetrical rotationally supported equilibrium models for galaxies is considered. Its main phases are: an expansion phase of the initial protogalaxy, assumed to consist into an homogeneous gas sphere structured into clouds, from recombination to maximum expansion, during which it is surmized that angular momentum is acquired by tidal interactions by the expanding configuration; then a violent relaxation collapse phase, following maximum expansion and ending into a virialized deformed polytropic configuration; the reaching of virialization is considered as an adequate initial state for the new phase of virialized contraction of the gaseous component, due to the collisions of the constituent gas clouds, while the stellar component, due to the stars already formed according to a generalized Schmidt-type law during the early expansion and violent relaxation phases, is assumed to have reached a stabilized situation.The initial mean density and radius for both galaxy and component clouds expressed as functions of the density fluctuation spectrum at recombination, act as physical parameters determining the characteristics of the system at maximum expansion, together with the total amount of angular momentum acquired during the expansion phase. The main physical parameters at virialization are then completely specified when the initial distribution of the clouds inside the galaxy is assigned and the constants appearing in it are derived by normalization with the observed data.We find for systems of given mass that the larger the angular momentum per unit mass is: (1) the larger are the equatorial semiaxis at maximum expansion and at virialization and the lower the mean density; (2) the larger is the time elapsed up the maximum expansion and to virialization; while for systems of different mass, we obtain that to the larger mass correspond the larger time elapsed up to maximum expansion and to virialization, and the lower mean density.For the contraction phase following virialization, two limiting cases are considered: (A) either the star component already present at virialization is entirely neglected; (B) or it is thought to contract as the gas component. In such cases, it is found for systems of equal mass that lower angular momenta lead to final configurations characterized by no or small flat gaseous components (which may correspond to lenticulars and early type spirals) while the contrary is true for large angular momenta (corresponding to late type spirals and irregulars). As mass and angular momentum per unit mass decrease, according to an assumed lawj M, the allowed configurations on the late type side of the morphological sequence tend towards earlier and earlier types, until for masses low enough (10¹⁰ m ), only halo type configurations seem to exist. According to this view, the observed lack of spirals with masses below 10¹⁰ m and the wide mass range exibited by the stellar halo type galaxies might be interpreted. In general, it appears that in the limit of the approximations made, a morphological sequence of galaxies can be described by two parameters, mass and angular momentum.     

The angular momentum-vs-mass relation for spectroscopic binaries

The spectroscopic binaries, considered as a single data point, fall roughly on the universal power-law of index 1.8 for angular momentum vs total mass, as defined by planets, spiral galaxies, and numerous other objects. But the individual systems in theSeventh Catalogue of the Orbital Elements of Spectroscopic Binary Systems define a curve of rather shallower slope, 1.63±0.07, over more than two orders of magnitude in mass and four in angular momentum. Various subsets (long and short periods; single and double line systems; known and unknown orbital orientations) all yield slopes from 1.48 to 1.77. These values, as well as the slightly larger one found for eclipsing systems by Sisteró and Marton, are very much what one would expect, given the form of Kepler's Third Law and the Stellar mass-radius relation.If only these well-known pieces of physics are at work, then the still-wider visual binaries should yield a slope near 5/3. Catalogues currently in press will permit easy testing of this prediction. It seems unlikely that deep clues to the origin of either binary systems or angular momentum are to be found from considerations of this nature.     

Transfer of solar angular momentum by inertial induction

Transfer of angular momentum from the Sun to the planetary system has been found to be inevitable in all evolutionary models for the origin of the solar system. In cold theories it has been proposed to be achieved through friction whereas electromagnetic forces are considered to be the agent for this transfer in hot theories. In the present paper it has been shown that the required order of magnitude of angular momentum can be transferred by another mechanism based on the principle of inertial induction. In the previous theories most of the transfer had been assumed to have taken place during the pre-Main-Sequence period whereas in this proposed theory most of the transfer takes place during the Main-Sequence period of the Sun. The paper does not intend to go into the details of planet formation and the evolutionary process but confines itself only to the problem of angular momentum transfer.     

The angular momentum-vs-mass relation and the distribution of mass ratios for visual binary systems

The investigation of the angular momentum vs mass relation for binary stars is completed with a study of the 847 systems contained in theFourth Catalog of Orbits of Visual Binary Stars. Because bothJ andM of a visual binary depend steeply on the distance to the system (5th and 3rd powers, respectively), and many of the distances are not well known, the study makes use of an auxiliary parameterR which is independent of distance and proportional toJM ^–5/3.R appears to be uncorrelated withM for the 789 systems for which both can be determined. The non-correlation implies thatJ M ^5/3, expected from Kepler's third law, provides a better fit to the visual binaries than doesJ M ², predicted by some more complex considerations.The distribution functionf(q=M ₂/M₁) of mass ratios for the visual binaries results as a byproduct of the investigation. It peaks extremely sharply towardq=1.0 (much more so than for spectroscopic binaries). Because most visual binaries are wide enough to consist of stars that condensed independently (and so that can be thought of as chosen at random from an initial mass function), one expects the realf(q) to rise toward low ratios. Observational selection against the discovery and study of systems with large magnitude differences between the components must be very large indeed to account for the discrepancy between expectation and observation. The alternative is a mechanism for formation of wide binaries that favours equal components. The distribution of mass ratios for eclipsing binaries is given in an appendix. It peaks strongly atq=0.6–0.75 and largely reflects processes of angular momentum, mass, and energy exchange between the stars in contact systems.     

A thermodynamic origin of a universal mass-angular momentum relationship

The distribution functions for the total linear and angular momentum ofN particles selected from an equilibrium gas are derived. The most probable momentum increases withN. If the particles of an astronomical system are assumed to come from an original cosmic gas, universal mass-versus-momentum relations can be derived. The derived mass-versus-angular momentum relation is similar but not identical to that which has been reported. The derived relationship applies to the initial conditions and evolutionary effects may account for the difference between this prediction and the observed relationship.     

Close binary systems before and after mass transfer: A comparison of observations and theory

From a search through the literature 174 close binaries with known absolute dimensions have been sampled. Distinction is made between systems before and after mass exchange. Mass, period and mass ratio distributions and relations of the group of unevolved binaries (i.e., prior to mass exchange) are transformed into corresponding distributions and relations of evolved binaries. The transformations are based upon theM _1f=g(M _1f) relation derived from an extended set of published theoretical computations of the evolution of close binaries. From this relation the following characteristics of the system after mass exchange are computed:M _1f,M _2f (andq _f),P _f. Five different modes of mass transfer were applied for the computation of the values ofP _f andM _2f. The variation of the period was calculated using the formalism given by Vanbeverenet al. (1979). The results are compared to the observations of binary systems after mass exchange, and are discussed together with an analysis of the effect of several selection effects present in the distributions. The main conclusion is that, during mass exchange in close binaries, more than 50% of the mass is lost to the system in the process of transfer, removing a large amount of angular momentum.This research is supported by the National Foundation of Collective Fundamental Research of Belgium (F.K.F.O.) under No. 2.9009.79.     

The stability parameters of three-body periodic orbits

Formulae containing the elements of the variational matrix are obtained which determine the linear iso-energetic stability parameters of periodic orbits of the general three-body problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The procedure is applied for the determination of horizontally critical orbits among the members of sets of vertical-critical periodic orbits of the threebody problem. These critical-critical orbits have special importance as they delimit the regions in the space of initial conditions which correspond to possibly stable three-dimensional periodic motion of low inclination.     

Visual binary systems in the solar neighbourhood: The mass-ratio distribution

Nearby visual binaries, with both components on the Main Sequence, have been considered in order to obtain information about the distribution of their mass ratios. These systems have their primary components ranging from A0 to G9. The data have been corrected for selection effects and the differences V of the visual magnitudes have been transformed into mass-ratio values.The frequency distribution of the mass ratios appears to be bimodal, with a peak around unity and a maximum at about 0.25. It is suggested that this feature may be indicative of different mechanisms of formation for wide binaries.     

Disc system delta Capricorni

FirstUBV photoelectric photometry of the eclipsing binary system Cap has been presented. An improved period of 1^d.022766 has been given. The duration of primary eclipse comes out to be more than double the duration given earlier. The depth has also been found to have increased. The light changes during eclipses show slight asymmetry. Eccentricity appears to be present in the system. Light and colour curves show variations. Primary component appears to be surrounded by a disc, the size of which is comparable to the size of the primary component. Two dips are seen around phases 0.20 and 0.67, the first appears more definitive, and is attributed to the wave-like distortion, like the one found in RS CVn binaries. The discussion reveals that Cap is a very complicated system.     

Tidal evolution in close binary systems

The aim of the present paper will be to give a mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum — an evolution activated by viscous friction of dynamical tides raised by the two components on each other. The first section contains a general outline of the problem; and in Section 2 we shall establish the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure. In Section 3 we shall investigate the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for given amount of total momentum; while in Section 4 we shall compare these results with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known to us from evidence furnished by the observed rates of apsidal advance.The results show that all such systems — be these of detached or semi-detached type — disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than a percent of the total — a situation characteristic of a state close to the minimum energy for given total momentum. This appears, moreover, to be true not only of the systems with both components on the Main Sequence, but also of those possessing evolved components in contact with their Roche limits.Under such conditions, a synchronism between rotation and revolution (characteristic of both extreme states of maximum and minimum energy) is not only possible, but appears to have been actually approached — if not attained — in the majority of cases. In other words, it would appear that — in at least a large majority of known cases — the existing close binaries have already attained orbits of maximum distension consistent with their momenta; and tidal evolution alone can no longer increase the present separations of the components to any appreciable extent.The virtual absence, in the sky, of binary systems intermediate between the stages of maximum and minimum energy for given momentum leads us to conjecture that the process of dynamical evolution activated by viscous tides may enroll on a time-scale which is relatively short in comparison with their total age — even for systems like Y Cygni or AG Persei, whose total age can scarcely exceed 10⁷ yr. A secular increase of the semi-major axes of relative orbits is dynamically coupled with a corresponding variation in the velocity of axial rotation of both components through the tidal lag arising from the viscosity of stellar material. The differential equations of so coupled a system are given in Section 5; but their solution still constitutes a task for the future.The Lunar Science Institute Contribution No. 90. The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

Observed mid-to-high latitude interchange of atmospheric angular momentum and some implications

The global distribution of atmospheric angular momentum (M) during 1977–1978 and 1982–1983 is examined to identify evidence of prominent short term interchanges of relative atmospheric momentum between mid and high latitude zones, in both hemispheres. Thirty day detrended angular momentum time series, prepared from the NMC gridded zonal wind data are examined in latitude bands. These data exhibit obvious quasi-coherent oscillations with periods near 30 days plus variations with shorter periods. An examination of latitude/altitude cross sections of zonal winds reveals that the oscillations are present almost simultaneously at all altitude levels between 1000 and 50 mb. Cross latitude teleconnections, evident as strong anticorrelated signatures between adjacent latitude bands are observed in the midlatitudes of both hemispheres. Comparison of these signatures with the time integrated flux of angular momentum across the nodal interface confirms that direct eddy transport of momentum is occurring. Transport of momentum from the mid latitude bands results in an increase in the momentum of the higher latitude bands and vice versa. Transport of planetary angular momentum by a Hadley/Ferrel type meridional circulation is specifically ruled out although that process may contribute to seasonal and longer term modulations. The short term oscillations in M can reach magnitudes which dominate the global variation in momentum, as noted in the recent 1982–83 El Niño episode in which the January 1983 momentum peaked at a decadal high. Similar El-Niño like changes in the trans-latitude momentum redistribution are observed in the Southern Hemisphere winters, following the Northern Hemisphere episode. Overall, our results confirm and describe in more detail the long recognized fact that momentum can be selectively redistributed between tropical, temperate, and high latitudes, in patterns indicative of the development and dissipation of interacting regions, described variously in studies of the index cycle, seesaws and teleconnections. In emphasizing the large scale coordination of these interchanges, and moreover their occasional very short time scales, these results will hopefully stimulate studies relating atmospheric behavior in distant regions thereby contributing to improvements in forecasting the circulation process.     

Algorithm for IAU north poles and rotation parameters

In 1970 the IAU defined any object'snorth pole to be that axis of rotation which lies north of the solar system's invariable plane. A competing definition in widespread use at some institutions followed the right hand rule whereby the north axis of rotation was generally said to be that that of the rotational angular momentum. In the case of the latter definition, the planet Neptune and its satellite Triton would have their north poles in opposite hemispheres because Triton's angular momentum vector is in the hemisphere opposite from that of Neptune's rotation angular momentum.The IAU resolutions have been somewhat controversial in some quarters ever since their adoption. A Working Group has periodically updated the recommended values of planet and satellite poles and rotation rates in accordance with the IAU definition of north and the IAU definition of prime meridian. Neither system is completely satisfactory in the perception of all scientists, and some confusion has been generated by publishing data in the two different systems.In this paper we review the IAU definitions ofnorth and of the location ofprime meridian and we present the algorithm which has been employed in determining the rotational parameters of the natural satellites. The IAU definition of the prime meridian contains some ambiguities which in practice have been specified by the numerical values published by the IAU working group but which have not yet been explicitly documented. The purpose of this paper is to explicitly document the algorithm employed by the IAU working group in specifying satellite poles and rotation rates.     

The role of loop footpoints rotation in single loop flares

We consider that single loop flares can be caused by the rotation of loop footpoints. Choosing a typical geometry for this case we find from MHD equations self-consistent expressions and a set equations governing behaviour of all physical quantities. Numerical simulations have revealed that under the determined conditions for the initial azimuthal velocity and current the pinch instability takes place. The most important parameters of the problem are the plasma and the ratio of the initial values of longitudinal and poloidal components of the magnetic field-B ₁. Thus, calculations show that the critical pinch time increases with the increase ofB ₁ and decreases with the increase of plasma . So the most effective flares are probable for the most high loops with strong currents. ForB ₁=10 and =0.01 the critical pinch time is 2.5 s. The critical twist angle for magnetic field depends on the initial one. For low intial twist which corresponds to bigB ₁ the critical one is more less. For exampleB ₁=30 gives 1.8 (when ratio of loop length and radius is 10). Geometrical analysis shows that the present model can explain (for high photospheric rotation) single loop flares taking place on different parts of the loop as on the top of it as closer to one of the footpoints. It depends on the relative rotation momentum of loop footpoints. Subject headings: MHD-Sun:flares.     

Investigations into the thermal non-equilibrium of W UMa-type contact binaries

Traditionally, some physical details(e.g., magnetic braking, energy transfer, angular momentum loss, etc.) have to be taken into consideration during investigations into the evolution of contact binaries. However, the real evolutionary processes which usually contain several of these physical mechanisms are very complicated as a result of strong interaction between components. To avoid dealing with these factors, a linear relationship is applied to the temperatures of components. It is found that the higher the mass ratio(M_2/M_1) of a contact system, the weaker the deviation from thermal equilibrium.On this basis, a variation trend of fill-out factor(f) changing with mass ratio can be inferred, which is consistent with observations. Moreover, if we stick to this point of view, it should be natural that the number of semi-detached binaries in the predicted broken-contact phase of relaxation oscillations is less than the number in the contact phase.     

Hydrogen depletion and the evolution of cataclysmic variables to low mass X-ray binaries

Certain cataclysmic variables may evolve into low mass X-ray binaries if the white dwarfs can steadily accrete sufficient mass to exceed the Chandrasekhar limit. We present spectra of a recurrent nova and a low mass X-ray binary which are very similar to each other, and are also unusual for the strengths of the observed He II emission. We suggest that this similarity is not coincidental, but is evidence for an evolutionary link between the two classes of objects. A hydrogen depletion in the accreting gas is implied from the emission line fluxes, and may be an important parameter in determining whether accreted gas remains bound to the white dwarf, enabling eventual core collapse to occur.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F. R. G., 16–19 June, 1986.     

White dwarf models of supernovae and cataclysmic variables

If the accreting white dwarf increases its mass to the Chandrasekhar mass, it will either explode as a Type I supernova or collapse to form a neutron star. In fact, there is a good agreement between the exploding white dwarf model for Type I supernovae and observations. We describe various types of evolution of accreting white dwarfs as a function of binary parameters (i.e, composition, mass, and age of the white dwarf, its companion star, and mass accretion rate), and discuss the conditions for the precursors of exploding or collapsing white dwarfs, and their relevance to cataclysmic variables. Particular attention is given tohelium star cataclysmics which might be the precursors of some Type I supernovae or ultrashort period X-ray binaries. Finally we present new evolutionary calculations using the updated nuclear reaction rates for the formation of O+Ne+Mg white dwarfs, and discuss the composition structure and their relevance to the model forneon novae.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

The formation and evolution of low-mass close binaries with compact components

We discuss the formation and evolution of interacting low-mass close binaries with a He-1CO- or ONe-dwarf neutron star or a black hole as a compact component. Mass exchange leads to cataclysmic events in such systems. The rate of semidetached low-mass close binary formation is 5×10^–3 yr^–1 if the accreting component is a He degenerate dwarf, 5×10^–3 yr^–1 if it is a CO-dwarf and 3×10^–8 yr^–1 if it is a neutron star. Systems with compact accretors arise as the result of the common envelope phase of close binary evolution or due to collisions of single neutron stars or dwarfs with low-mass single stars in dense stellar clusters. Evolution of LMCB to the contact phase in semi-detached stages is determined mainly by the angular momentum losses by a magnetic stellar wind and radiation of gravitational waves. Numerical computations of evolution with momentum loss explain observed mass exchange rates in such systems, the absence of cataclysmic variables with orbital periods 2^h–3^h, the low number and the evolutionary status of systems with orbital periods shorter than 80^m. In conclusion we list unsolved problems related to magnetic stellar wind, the distribution of young close binaries over main initial parameters, stability of mass exchange.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

The inclination changes in the problem of two triaxial rigid spheroids

The first-order perturbations of a system of two triaxial rigid spheroids under Hori-Lie transformation are investigated. The time dependence of the configuration of the three angular momentum vectors, two rotational and one orbital, is studied. The problem is simplified by the introduction of a new time parameter , such thatt is the hyperelliptic function of . The projectionsH ₁ andH ₂ of the rotational momentum vectors into the direction of the total angular momentum vector of the system are then harmonic or exponential functions of . The trajectory in theH ₁,H ₂ plane is a part of an ellipse or hyperbola respectively. If this conical section intersects a certain critical contourC, the system is bounced back along the original trajectory. The motion of the relative configuration of the angular momentum vectors is periodical except in a special aperiodic case. The expressions for the periods are given.