Evolution of low-mass close binaries and the problem of orbital period gap in cataclysmic variables

Evolution of close binary composed of a white dwarf primary and a Main-Sequence secondary has been calculated. Angular-momentum loss via gravitational radiation and magnetic stellar wind have been taken into account. We have found that magnetic stellar wind with a rate greater than (10^–10–10^–9)M yr^–1 is able to drive the evolution with mass exchange. If the time-scale of switch-off of wind when the primary becomes fully convective is not longer than 10⁶ yr, mass exchange interrupts due to a contraction of the secondary and the system becomes unobservable. Mass exchange resumes when components approach one another due to loss of momentum via gravitational radiation. The location and width of the thus-arising gap in the orbital periods are comparable to those observed.     

Galactic spiral arms formed by central explosions

We have made calculations of spiral arm formation due to central explosions in a nucleus surrounded by a disc containing most of the galactic mass with the purpose of obtaining estimates on lifetimes of arms and the requirements on the energy involved in the process. The ejected gas is taken to be a few percent, or less, of the central nucleus and is ejected with velocities of the order of 1000 km s^–1. The gas, considered to be in forms of blods, moves under the gravitational force from the disc and the nucleus and the drag force by the gas in the disc. The orbits of the blobs evolve towards the circular orbits of the disc due to this drag force and the velocities in the arms will therefore, after some time, approach those of a normal rotation curve.A relatively open structure will last 5×10⁸ years. Stable ring structures with longer lifetimes may be formed by some explosions. With an energy of 5×10⁵⁷ erg in the initial gas-blod motion and a duration of the explosion of 10⁷ years, the energy output in such explosions has to be >10⁴³ erg s^–1.     

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 accretion matter at the disk rim in Her X-1/HZ Her

The Crosa and Boynton (1980) empirical model for discrete mass transfer in Her X-1 is further developed. The photometric features of the light curve (peaks of an hour duration and 0.3–0.7 ^m amplitude, steps near orbital phase =0); and the linear polarization bursts are assumed to be due to the formation and eclipses of the plasma blobs produced by discrete transfer of matter from optical star surface and its interaction with the accretion disc rim. The long lifetime (20^h) of the cold (3×10⁴ K) blob extending up to 10¹¹ cm above the disc plane, as well as the deep X-ray flickerings (300 s) during the X-ray absorption dips are assumed to arise from a dispersal of accreting matter by the Rayleigh-Taylor instability in a blob moving through a hot corona of the disk atT _c =3×10⁶ K andn _c =3×10¹¹ cm^–3. Thermal equilibrium in the corona and in the blobs are supported by X-ray flux. Within the first few hours after its formation a blob disintegrates into drops withr=5×10⁹ cm,T=3×10⁴ K, andn=3×10¹³ cm^–3 which move then along Keplerian orbits. Frictional interactions of the drops with the corona destroy them on a 20^h time-scale. The proposed model makes it possible to interpret the diverse observational facts and to predict numerous observational displays in the optical, UV, and X-ray bands. The first results of our optical-spectrum observations of blobs are briefly described.     

Some effects of elasticity on lunar rotation

A general Hamiltonian for a rotating Moon in the field of the Earth is expanded in terms of parameters orienting the spin angular momentum relative to the pricipal axes of the Moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love numberk ₂. The principal periodic terms in the longitude of a point on the Moon due to variations of the tide caused by the Earth are shown to have amplitudes between 3.9 × 10^–3 and 1.6 × 10^–2 with a period of an anomalistic month, 3.0 × 10^–4 and 1.2 × 10^–3 with a period of one-half an anomalistic month and 2.4 × 10^–4 and 9.6 × 10^–4 with a period of one-half of a nodical month. The extremes in the amplitudes correspond to rigidities of 8 × 10¹¹ cgs and 2 × 10¹¹ cgs, respectively, the former rigidity being comparable to that of the Earth. Only the largest amplitude given above is comparable to that detectable by the projected precision of the laser ranging to the lunar retrorereflectors, and this amplitude corresponds to an improbably low rigidity for the Moon. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given, where it is shown that elasticity can alter the period of the free wobble of 75.3 yr by only 3 × 10^–4 to 10^–3 of this period. Also, the effect of elasticity on the period of free libration is completely negligible by many orders of magnitude. If the Moon's rigidity is close to that of the Earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the Moon can be determined from variations in the rotation.Currently on leave from the Dept. of Physics, University of California, Santa, Barbara, California.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

X-ray observations of gamma-ray burst sources

We report on preliminary results of EXOSAT observations of three gamma-ray burst error boxes. No source was detected down to a limit of 10^–10 erg cm^–2s^–1, assuming a black-body spectrum for the burst counterpart. Results are interpreted in the framework of current theoretical models.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Spectroscopic observations of delta orionis

The H profile in the spectrum of Orionis shows phase-dependent changes, with a period of variation equal to the orbital period fo the binary system. The profile shape changes from a normal absorption profile at zero phase to a P Cygni-type at a later phase, to an absorption profile having emission at the centre of the profile, to a normal absorption profile at the end of the period. The spectra have been obtained at the Cassegrain focus of Kavalur Observatory telescopes (50 and 100 cm) at 17.2 Å mm^–1 reciprocal dispersion and resolution 0.3 Å at 6562.817 Å. Assuming that the P Cygni profile is formed by a spherically-symmetrical region, the analysis gives a shell radius of 2.18 stellar radius and an electron density in the shell equal to 6.54×10^–9 cm^–3, with the observed expansion velocity of 50 km/s^–1, a mass loss of 1.3×10^–7 M per year.An analysis has been carried on the radial velocity data of earlier observers and the present radial velocity data. It is found that the orbital elements change. The presence of apsidal motion is confirmed by the increasing value of . The radial velocity of the centre of mass, , shows periodic variation. These observations confirm the presence of a third body. The values ofK (mean amplitude),P (period),a sini, and mass functionf(m), indicate a regular decrease, thereby confirming the mass transfer/mass loss from the system.     

Effects of suprathermal grains

Grains ejected from stars at velocities of 10⁷ cm s^–1 and/or grains accelerated by the pressure of starlight in the intercloud medium to velocities in the range 2×10⁶–10⁷ cm s^–1 are slowed to velocities of about 2×10⁵ cm s^–1 in a typical interstellar cloud. The interaction of fast grains with gas atoms as they are slowed in clouds could provide (a) the dominant heat source for interstellar clouds; (b) sites for molecule formation; and (c) a mechanism of providing a pressure balance between clouds and the intercloud medium.Paper presented at the Symposium on Solid State Astrophysics, held at the University College, Cardiff, Wales, between 9–12 July, 1974.     

Collapse of the presolar nebula

The hydrodynamical axially symmetric collapse of a 3M -cloud with an initial density of 10^–20 g cm^–3 has been investigated. In order to first arrive at an equilibrium configuration a temperature of 15 K has been assumed. During about 9 free-fall times the cloud has artificially been cooled down to the (Jeans-) critical temperature of 8 K. Thus, the dynamical collapse studied in this paper starts from an equilibrium configuration following a slow quasi-hydrostatic contraction. Two sequences corresponding to a different choice of the initial angular velocity _i = 10^–14 s^–1 (Case A) and _i = 10^–15 s^–1 (Case B) have been computed. In both cases a fast spinning, optically thick disk-like core of low mass and temperature forms for which fission into two or even more pieces is very likely to occur.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

The interrelationship between cosmic dust and the microwave background

Attention is given to the radiation of microwaves by charged dust in space. Presently-used particle distributions do not restrict the presence in space of large numbers of small (r<10^–6 cm) silicate grains, but it is shown that such densities (10^–25–10^–26 g cm^–3) of small grains would produce a microwave background with an energy density of the same order of magnitude as the energy density of the (presumed) cosmological 3 K background. Limits set by the isotropy of the latter are: (HI clouds)10^–26, (Galactic plane)10^–30, (Halo)10^–32, (Local Group)10^–34 g cm^–3. These limits imply that either there is a cutoff in particle distributions atr10^–6 cm, or that the density of silicate grains in space has been generally overestimated, or that cosmic rays have broken up a lot of grains so that they now form a population of grains of very small size (10^–7 cm) which are difficult to detect by conventional methods. One way to look for the latter population is by studying expected distortions of the 3 K spectrum to the short wavelength side of the portion hitherto observed (grains may have a size distribution able to give an approximate black-body curve for radiation from larger grains of 10^–6 cm size), and by testing the effective energy density of the 3 K field in other galaxies.     

Implications of the Galilean satellites ice envelope explosions III. The origin of the Trojans and of some comets

Secondary explosions of the primary ice fragments ejected in the explosion of the electrolyzed massive ice envelopes of the Galilean satellites are capable of imparting velocities of up to ~5km s^–1 to the secondary fragments. As a result, the secondary fragments can enter the orbits of the irregular satellites (Agafonova and Drobyshevski, 1984b) and the Trojan libration orbits. In the latter case a perturbation velocity of V 0.3–2 km s^–1 is sufficient.The primary fragments ejected by the gravitational perturbations due to the Galilean satellites sunward from Jupiter's sphere of action move faster relative to the Sun than Jupiter does and therefore reach their first aphelion ahead of Jupiter in the neighborhood of L ₄. At the same time the fragments propelled from Jupiter's sphere of action beyond the planet's orbit approach it again in their perihelia behind Jupiter in the region of L ₅. The concentration of the fragments and, hence, the frequency of their collisions and explosions at L ₄ turn out to be much greater than those at L ₅. As a result, the number of the secondary fragments of diameter 15 km captured into libration orbits ahead of Jupiter can be as high as many hundreds and should exceed by more than a factor 3.5 that captured behind Jupiter.Since the icy mix of the fragments contains hydrocarbons and particulate material (silicates and the like), after ice sublimation from the surface layers the Trojans should reveal type C and RD spectra typical for Jupiter's irregular satellites, comet nuclei and other distant ice bodies of similar origin. Among the Trojans there cannot be rocky or metallic objects which are known to exist in the main asteroid belt.It is shown that a velocity perturbation of 150–200 m s^–1 resulting from a purely mechanical impact of two bodies may be sufficient to move collision fragments from the orbits of the Trojans to horseshoe-shaped trajectories with a subsequent transfer to the cometary orbits of Jupiter's family.     

Secular perturbations of resonant asteroids

Secular perturbations of asteroids are derived for mean motion resonance cases under the assumptions that the disturbing planets are moving along circular orbits on the same plane and that critical arguments are fixed at stable equilibrium points. Under these assumptions the equations of motion are reduced to those of one degree of freedom with the energy integral. Then equi-energycurves on (2g-X) plane (g and X being, respectively, the argument of perihelion and (1–e²)^1/2) are derived for given values of the two constant parameters, the semi-major axis and =(1–e²)^1/2 cos i, and the variations of the eccentricity and the inclination as functions of the argument of perihelion are graphically estimated. In fact this method is applied to numbered asteroids with commensurable mean motions to estimate the ranges of the variations of orbital elements.The same method is also applied to the Pluto-Neptune system and the results are found to agree with those of numerical integrations and show that the argument of perihelion of Pluto librates around 90°.     

Irregular extrasolar systems and dynamical instability

The astrometric search for extrasolar planetary systems can regard, at least in the first stage, only systems with high mass ratio (10^–2) of the largest planets to the central star. The formation of such systems is probably a common occurrence in the galaxy, as indicated by various theoretical arguments; these systems could have evolved in a regular way (near-circular and coplanar orbits, Titius-Bode law, etc.) until the most massive accumulating protoplanet exceeded the critical value of the mass ratio corresponding to dynamical instability. This phenomenon has been extensively investigated in recent years, showing that a three- orN-body system becomes unstable (for relative separations similar to the planetary ones) for >10^–2. Therefore, it seems likely that observations of systems within this range of mass ratio will show the irregular end-products of processes related to the instability (close encounters or ejections), which affected drastically the orbital configuration in the last phase of the planet formation.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Oscillations and waves in a sunspot

Observations have been made in H of the vertical velocity distribution in a sunspot. Over the umbra the pattern consists of structures of scale-size 2–3. The velocity distribution undergoes oscillations with a period of about 165 s and typical amplitude ±3 km s^–1, but the pattern breaks down after one or two cycles because the period of oscillation varies typically by ±20 s from place to place. Transverse waves develop in the outer 0.1 of the umbral radius and propagate outwards with a velocity of about 20 km s^–1, becoming gradually invisible by or before the outer penumbral boundary; the amplitude is about ±1 km s^–1 at the umbra-penumbra border.The penumbral waves are believed to be basically of the Alfvén type, with 3 × 10^–8 g cm^–3. The umbral oscillations presumably represent gravity waves. In both cases the fluxes are inadequate by two orders of magnitude to account for the sunspot energy deficit.     

High-dispersion spectroscopy of the symbiotic star AX Per: A binary model with rapid mass accretion

Results of high-dispersion spectroscopy (10 Å mm^–1) of the symbiotic star AX Per carried out in the years from 1979 to 1987 are reported. The emission line [FeVII] 6086 consists of a narrow and a broad component; the radial velocity of the narrow one varies according to the photometric period 681.6 days. This variation (K=30.6±1.5 km s^–1) seems to be due to the orbital motion of the hot star. The radial velocity of absorption lines varies with an inverse phase dependence and a much smaller amplitude (K=5.6±2 km s^–1), which may reflect the orbital motion of the red giant. The variation of the radial velocity of the emission lines of FeII, ect. (K=6.7±1.5 km s^–1) might be due to the rotation of the red giant. The profile of H emission line suddenly changed around the phase of the photometric minimum, which could be explained as a result of an eclipse of the emitting region by the red giant. On the other hand, some problems remain open in the behaviour of the radial velocities of H and HeI 5876.The observed results support a binary model of AX Per consisting of a rather massive (3M ) M-type giant and a Main-Sequence star (0.6M ). AX Per seems to be in an early stage of the Case C mass transfer, and the estimated very high mass accretion rate (10^–4 M yr^–1) is consistent with the theoretical models. The narrow component of the emission line of [FeVII] 6086 might be emitted in radiatively driven polar jets on the hot star of which luminosity is close to the Eddington limit.A new identification as ZrII at 6106.47 Å is proposed for the emission line at 6106 Å.     

Synchronization features of the magnetic nova V1500 Cyg

An analysis of an eleven-year photometric study of the first magnetic nova V1500 Cyg from observations made at the Crimean Observatory is presented. The data indicate the existence of a beat period caused by rotational-orbital asynchronization as well as its increase with time. The current rotational period of the primary component — a magnetic white dwarf — was calculated for each year by using the current values of the beat period and a constant value for the orbital period. It is shown that rapid synchronization of the components has not occurred uniformly with time: the rate of increase of the rotational period of the white dwarf was during 1977–1979 and over the next ten years. This would lead to synchronization of the rotational and orbital periods over about 230 year if remains constant at 2.7 · 10^–8.Translated fromAstrofizika, Vol. 39, No. 2, pp. 193–199, April–June, 1996.     

Diffuse component of the cosmic far UV radiation and interstellar dust grains

The diffuse far UV radiation ( 1350–1480 Å) observed in the sky region ofl ^II180°, 0°b ^II40° is analyzed in connection with the distributions of stars and dust grains as well as with optical properties of grains. Its intensity (starlight+scattered light) is about 6×10^–7 erg cm^–2 sec^–1 sr^–1 Å^–1 in the direction ofb ^II0° andl ^II180°. The latitude dependence of the intensity is in approximate agreement with the plane parallel slab model of the galaxy with a reasonable set of parameters. The interstellar scattering gives an albedo close to unity and forward phase function of about 0.6, which are not inconsistent with the model of interstellar grains of Wickramasinghe. The upper limit of the extragalactic UV is 2×10^–8 erg cm^–2 sec^–1 sr^–1 Å^–1 in the same region of wave-length.     

RS CVn-type variables

Photometric observation of HR 1099 inV andB obtained on 18 nights between January and March 1977 is presented. The amplitude of the asymmetric light curve is found to be 0^m.10±0^m.004 both inV andB. On three occasions—namely, JD 2443164. 17, JD 2443176. 14 and JD 2443177.12—the star brightened by 0^m.05. Four H spectrograms at 42 Å mm^–1 dispersion were obtained during October–November 1978. The profile and equivalent width of H of 14 November, 1978 suggest a probable major outburst.Analysis of all available photometry shows that (1) the amplitude and shape of the light curve change in a few orbital periods, (2) the phase of the minimum light migrated towards decreasing orbital phase during the interval JD 2442720 to JD 2443000 and from JD 2443200, there is almost a linear increase of the phase of the minimum light and (3) the phase of the light minimum sometimes shows to and fro behaviour suggesting the migration of the wave is not taking place smoothly.     

Vacuum energy in cosmic dynamics

The analysis of the Th/U ratio in meteorites and the evolutionary ages of globular clusters favour values of the cosmic age of (19±5)×10⁹ yr. This evidence together with a Hubble parameterH ₀>70 km s^–1 Mpc^–1=(14×10⁹ yr)^–1 cannot be reconciled in a Friedmann model with =0. It requires a cosmological constant in the order of 10^–56 cm^–2, equivalent to a vacuum density _v =10^–29 g cm^–3 The Friedmann-Lemaître models (>0) with a hot big-bang have been calculated. They are based on a present value of the baryonic matter density of ₀=0.5×10^–30 g cm^–3 as derived from the primordial⁴He and²H abundances.For a Hubble parameter ofH ₀=75 km s^–1 Mpc^–1, our analysis favours a set of models which can be represented by a model with Euclidean metric (density parameter ₀=1.0, deceleration parameterq ₀=–0.93, aget ₀=19.7×10⁹ yr) and by a closed model with perpetual expansion (₀=1.072,q ₀=–1.0, aget ₀=21.4×10⁹ yr). A present density parameter close to one can indeed be expected if the conjecture of an exponential inflation of the very early universe is correct.The possible behaviour of the vacuum density is demonstrated with the help of Streeruwitz' formula in the context of the closed model with an inflationary phase at very early times.     

Some remarks on the universal X-ray background

It is shown that a universal steady X-ray background with the energy flux 10^–7 erg cm^–2 s^–1 sr^–1 can arise as a superposition of radiation from pulsars (neutron stars) in various galaxies when it is taken into account that supernova outburst occurs in a galaxy at the rate of 10^–2/year.