Showing papers in "Astrophysics and Space Science in 1975"

Fourier analysis with unequally-spaced data*

Abstract: The general problems of Fourier and spectral analysis are discussed. A discrete Fourier transformF N (v) of a functionf(t) is presented which (i) is defined for arbitrary data spacing; (ii) is equal to the convolution of the true Fourier transform off(t) with a spectral window. It is shown that the ‘pathology’ of the data spacing, including aliasing and related effects, is all contained in the spectral window, and the properties of the spectral windows are examined for various kinds of data spacing. The results are applicable to power spectrum analysis of stochastic functions as well as to ordinary Fourier analysis of periodic or quasiperiodic functions.

Cosmic neutrinos of ultra-high energies and detection possibility

Abstract: The fluxes and spectra of galactic and extragalactic neutrinos at energy 1011–1019 eV are calculated In particular, the neutrino flux from the normal galaxies is calculated taking into account the spectral index distribution The only assumption that seriously affects the calculated neutrino flux atE v ≳1017 eV is the power-like generation spectrum of protons in the entire considered energy region The normal galaxies with the accepted parameters generate the metagalactic equivalent electron component (electrons+their radiation) with energy densityω e≈85×10−7 eV cm−3, while the density of the observed diffuse X-ray radiation alone is 100 times higher This requires the existence of other neutrino sources and we found the minimized neutrino flux under two limitations: (1) the power-law generation spectrum of protons and (2) production of the observed energy density of the diffuse X-an γ-radiation These requirements are met in the evolutionary model of origin of the metagalactic cosmic rays with modern energy densityω M8≈36×10−7 eV cm−3 The possibility of experiments with cosmic neutrinos of energyE v ≳3×1017 eV is discussed The upper bound on neutrino-nucleon cross-section σ<22×10−29 cm2 is obtained in evolutionary model from the observed zenith angular distribution of extensive air showers In Appendix 2 the diffuse X-and γ-ray flux arising together with neutrino flux is calculated It agrees with observed flux in the entire energy range from 1 keV up to 100 MeV

Open and closed magnetospheric tail configurations and their stability

Abstract: The asymptotic theory valid for magnetospheric tail configurations that vary only weakly in the antisolar direction is used to derive a number of explicit properties. The conditions under which the magnetopause converges to form a closed magnetosphere or diverges (open magnetosphere) are identified and discussed. It is shown that the presence of the high latitude low pressure tail lobes guarantees the open solution. The large value of the Mach-number of the unperturbed solar wind is the reason for the slow variation of the plasma and field quantities along the tail. Criteria for (two-dimensional) stability are discussed and it is shown that they can be expressed in terms of simple topological properties of the equilibria. Closed magnetopheres turn out to be stable, open magnetospheres with sufficiently stretched field lines are subject to an instability which — as shown earlier —may be the cause of magnetospheric substorms.

Cosmic-ray streaming and anisotropies

Abstract: The paper is concerned with the differential current densities and anisotropies that exist in the interplanetary cosmic-ray gas, and in particular with a correct formulation and simple interpretation of the momentum equation that describes these on a local basis. Two examples of the use of this equation in the interpretation of previous data are given. It is demonstrated that in interplanetary space, the electric-field drifts and convective flow parallel to the magnetic field of cosmic-ray particles combine as a simple convective flow with the solar wind, and that there exist diffusive currents and transverse gradient drift currents. Thus direct reference to the interplanetary electric-field drifts is eliminated, and the study of steady-state and transient cosmic-ray anisotropies is both more systematic and simpler.

Numerical simulation of the plasma double layer

Abstract: A one-dimensional particle-in-cell computer simulation is used to model the formation of an electrostatic double layer. The conditions for the onset of the layer formation are explored and a relation between the length of the layer and the electrostatic potential difference across is found.

Fourier analysis of the light curves of eclipsing variables. I

Abstract: The aim of the present paper will be to pioneer a new approach to the analysis of the light changes of eclipsing binary systems in the frequency domain, and to point out its merits in comparison with a conventional treatment of the same problem in the time-domain which has been developed so far.

Stellar Winds and Globules in H II Regions

Abstract: The interaction of a plane-parallel hypersonic stellar wind with a globule in an Hii region is considered in two approximations. In both approximations, the ionization front on the globule remains strong-D type, and a flow pattern containing two oppositely facing shock waves results. In the first approximation, the structure of the shocked region is calculated assuming that globule gas and stellar wind gas mix well and move at the same velocity. However, this assumption results in a very thick shocked layer and the assumption of good mixing is consequently not well justified. This approximation provides an upper limit on the gas velocities expected in the shocked gas which originated at the globule. In the second approximation, the stellar wind merely applies pressure to balance the momentum flux in the globule gas. The structure of the shocked region is calculated on the assumption that a tangential discontinuity exists between shocked stellar wind and shocked glubule gas. Structures may be produced having velocities ∼10 km s−1 and emission measures ∼103 cm−6 pc with reasonable stellar luminosities and mass loss rates.

Fourier analysis of the light curves of eclipsing variables, II

Abstract: The aim of the present paper will be to extend the Fourier methods of analysis of the light curves of eclipsing binaries, outlined in our previous communication (Kopal, 1975) in connection with systems whose components would appear as uniformly bright discs, to systems whose components exhibit discs characterized by an arbitrary radially-symmetrical distribution of brightness —i.e., an arbitrary ‘law of darkening’ towards the limb — be it linear or nonlinear. In Section 2 which follows a few brief introductory remarks, fundamental equations will be set up which govern the light changes arising from the mutual eclipses of limb-darkened stars — be such eclipses total, partial or annular; and Section 3 will contain a closed algebraic solution for the elements of the occulation eclipses terminating in total phase. Such a solution proves to be no more complicated than it turned out to be for uniformly bright discs in our previous paper; and calls for no special functions for the purpose — as will be put in proper perspective in the concluding Section 4. The cases of transit eclipses terminating in an annular phase, of partial eclipses of occulation or transit type, will be similarly dealt with by Fourier methods in the next paper of the present series.

Chemical potential effects on neutrino diffusion in supernovae

Abstract: The validity of imposing a zero chemical potential for neutrinos in hydrodynamic calculations of collapsing supernovae is investigated in the diffusion approximation of neutrino transport. A coupled system of equations is solved for neutrino and energy diffusion fluxes as well as lepton diffusion in a collapsing supernovae ambient medium, and the results indicate a substantial growth in the neutrino chemical potential for densities greater than 10 to the 12th power gm/cu cm. The rate of energy transport is shown to be significantly affected by increases in Fermi integrals and chemical-potential gradients accompanied by decreases in temperature, and the extent of neutrino particle/antiparticle reactions is found also to affect energy diffusion rates. It is concluded that the photon-like behavior usually assumed for neutrinos may be incorrect and that an extension of the Sn transport approximation to include lepton characteristics is necessary for a definitive answer to the question of neutrino transport in supernovae.

Fourier analysis of the light curves of eclipsing variables, V

Abstract: The methods of analysis of the light changes of eclipsing variables in the frequency-domain, developed in our previous papers (Kopal 1975a, b, c, d) for an interpretation of mutual eclipses in systems consisting of spherical stars, have now been extended to analyse the light variations — between minima as well as within eclipses — ofclose binaries whose components are distorted by axial rotation and mutual tidal action. Following a brief introduction (Section 1) in which the need of this new approach will be expounded, in Sections 2 and 3 we shall deduce the theoretical changes of close eclipsing systems between minima (Section 2) as well as within eclipses (Section 3), which in Sections 4 and 5 will be analysed in the frequency-domain; and explicit formulae obtained which should enable us to separate the photometric proximity and eclipse effects directly from the observed data as they stand-without the need of any preliminary ‘rectification’. Section 6 will contain the explicit forms of the expressions for photometric perturbations in the frequency-domain, due to rotational and tidal distortion of both stars; and the concluding Section 7 will then be concerned with practical aspects of the application of these new methods to an analysis of the observed light changes of close eclipsing systems — in which the proximity and eclipse effects cannot be distinguished from each other by mere inspection.

Evolution of Massive Close Binaries. II: The Post X-Ray Binary Stage: Origin of Run-away and Binary Pulsars

Abstract: The further evolution of a massive X-ray binary consisting of a compact object and an OB supergiant is outlined. The supergiant exceeds its critical Roche lobe and a second stage of mass transfer starts. The remnant of the mass losing star — a pure helium star — develops a collapsing iron core and finally undergoes a supernova explosion. If the compact companion is a black hole the system remains bound; if the compact companion is a neutron star the system is disrupted unless an extra kick allowing an asymmetric explosion is given. Computations were performed for the massive binary 22.5M⊙+2M⊙. The possible final evolutionary products are: (1) a black hole and a compact object, in a binary system, (2) two run-away pulsars, (3) a binary pulsar.As final parameters for the described system the eccentricity and period for the recently discovered binary pulsar 1913+16 may be found. An orbital inclination ofi=40° may be derived. The probability for the generation of binary pulsars is very low; in most cases the system is disrupted during the supernova explosion.

Solar magnetic fields and convection. I. Active regions and sunspots

Abstract: A phenomenological model of solar magnetic fields is developed, which differs drastically from all currently popular (diffuse-field) models. Its acceptance would require a review of a major part of theoretical solar physics including convection. Active Regions (ARs), and the nature and effects of surface magnetic fields in general.(i)Magnetic flux concentrations seen in sunspots, in ARs and even in quiet regions are not caused by convective motions but by long-lived (⪞1yr) flux ropes. These widely separated, helically twisted ropes originate beneath the convection zone and throughout their lives are impervious to supergranule or granule motions.(ii)Upon reaching maturity a flux rope develops an upward loop whose horizontal section emerges through the solar surface during a period of ≈ 3 days, during which period numerous individual flux tubes erupt from the rope to form an Arch Filament System. The main features of the system are explained, including the puzzling swing of its axis.(iii)On emerging, the leading (I) rope end is vertical while the following (f) end is inclined as suggested by Babcock, and the two dominate convection in their vicinity. This model explains the main features of a spot group including the notable east-west asymmetry.(iv)A spot decays because the flux rope unwinds and then may either split into large sections or ‘fray’ by the loss of numerous flux tubes from its outer surface. The tubes are themselves twisted and so develop kinks.(v)Fraying slowly extends to depths of ⪞105 km, but all flux tubes remain attached to the rope ends; they are rigid enough to resist being upended, and so form a unipolar magnetic region. The fields of ⪞1000 G observed at supergranule boundaries are not due to the concentrating effect of gas motions as often stated; nearly vertical, quasi-permanent flux tubes are merely moved back and forth by the gas motions.(vi)The model provides a test for any convection zone model; in particular it is incompatible with the dynamo theory. It is also incompatible with models of convection which attribute the formation of sunspot fields to the supergranulation.

Pulsed gamma-ray emission from neutron and collapsing stars and supernovae

Abstract: Three mechanisms generating pulsed γ-ray emission at late stages of stellar evolution are investigated: (1) γ-ray burst produced by the absorption of neutrino emission of a collapsing star in its envelope; (2) γ-ray burst of thermal emission when the outer layers of a compact star (R=0.01–0.1R ⊙) are heated up by a powerful shock wave; and (3) γ-ray emission due to ejection of matter from neutron stars at an active stage of their existence. In case (1) the expected flux of γ-quanta with the energy 0.1 MeV amounts to about 10−4 cm−2 which is considerably less than the observed flux. However, observation of such γ-ray pulses would be an important supplement to the direct observations of neutrino emission of collapsing stars. In case (2) the outer layers of the star are heated up to the temperature of about 108 K. This results in a short burst with the emission energy ∼ 1042–43 erg whose main part is concentrated in the X-ray range (∼ 25 keV). In this case approximately 10% of the energy is emitted in the γ-ray range (≳ 0.1 MeV). Generally speaking, this mechanism is sufficient as to the energy for accounting for the observed bursts; however, probably under the condition that supernovae are exploding in our Galaxy. This involves difficulties concerning the frequency of bursts and the spectrum of emission. In case (3) ejection of chemically non-equilibrium matter from the neutron star leads to an intensive emission which is produced due to fission of superheavy nuclei, β-decay of radioactive elements and radiative capture of free neutrons. Ejection of matter from the neutron stars may be related to the observed jumps of periods of pulsars. From the observed gain of kinetic energy of the filaments of the Crab Nebula (∼ 2×1041 erg) the mass of the ejected material may be estimated (∼ 1021 g). This leads to energies of the γ-ray bursts of the order of 1038–1039 erg, which agrees fully with observations at the mean distance up to the sources 0.25 kpc. As distinct from the outbursts of supernovae it would seem that no difficulties concerning the burst frequency and the spectrum of emission are encountered. From the mechanisms of γ-ray emission examined here the mechanism connected with the ejection of matter from neutron stars seems to be the most promising as far as the interpretation of observations is concerned.

The alignment of the Crab pulsar magnetic axis

Abstract: The magnetic distortion is estimated for neutron stars in which the matter in the interior consists of superfluid neutrons and superconducting protons. For type II proton superconductivity, the arrangement of magnetic flux in a two-dimensional lattice of quantized fluxoids and the kinetic energy of the supercurrent carriers cause some components of the spatially averaged stress tensor for field and superconductor to be several orders of magnitude greater than the components of the Max-well stress tensor for a uniform distribution of the same magnetic flux. It is shown that for the Crab pulsar PSR 0531+21, which is considered to have the greater part of its mass in the form of superfluid neutrons and superconducting protons, the magnetic distortion is almost certainly more important than the clastic energy of the outer shell in determining the departure of the inertia tensor from its spherically symmetric form. With the assumption that internal and external magnetic fields have the same symmetry axis, the external field dipole moment of the Crab pulsar is predicted to be approximately perpendicular to the spin direction, in agreement with a number of published interpretations of observational data.

Diffraction of light and lens effect of the stellar gravitation field

Abstract: The purpose of the present communication is to consider the focussing of light by gravitational ‘lenses’ (stars). Finite estimates of the gainq on the optical axis (r»0) can be obtained with an account of diffraction of light.

Solar magnetic fields and convection. II. Magnetic diffusivity and flux concentration

Abstract: The traditional model of solar magnetic fields is based on convection which dominates generally weak, diffuse fields and so tends to create increasingly tangled fields. Surplus fields must be eliminated by merging of opposite polarities; for example a solar dynamo of period≈10 yr requires fields to be reduced to a scale of<100 km or diffusivity to be increased by a factor of≈107 over molecular diffusivity. It is now shown that the true requirements of any diffuse-field theory are far more stringent, and that surplus fields must be eliminated within a single eddy period of 1 day (10 min) for the supergranules (granules). The reason is that during that period fresh fields are created with flux and energy comparable with those of the old fields. The numerical models of Weiss and Moss are used to confirm this result which is fatal to all diffuse-field theories. The basic error in these theories is found in the assumption that because heat and other passive properties of a fluid diffuse much faster in the presence of turbulence, passive magnetic fields should do likewise. The error is that the heat content of an eddy is not increased by the motion while the magnetic flux and energy are increased rapidly.It is shown that the observed concentrations of surface fields into strengths of≳100 G cannot be accounted for by observed surface motions. Nor are they accounted for by the numerical models of turbulence of Weiss or Moss whatever values of the magnetic Reynolds number are assumed.A detailed comparison is made between both small-scale and large-scale surface magnetic features and the predictions of the diffuse-field theory. The differences appear irreconcilable and the features only explicable in terms of the twisted flux-rope model.

Optically thick accretion onto black holes

Abstract: Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of\(\mathfrak{M} = \mathfrak{M}_ \odot \) is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn0=108 cm−3 andT0=104 K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×1033 erg s−1, which primarily arises from the optical surface (τ∼1) ofT∼104 K. The accretion flow is characterized by τ∼1 and (v/c)τ∼10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at τ∼1. The radiative equilibrium is strictly realized at (v/c)τ∼10.

Fourier analysis of the light curves of eclipsing variables. III

Abstract: The aim of the present paper will be to extend our new methods of analysis of the light curves, of eclipsing binary systems, consisting of spherical components, by Fourier approach to eclipses oftransit type — which arise when the eclipsing component happens to be smaller of the two. Our present principal concern will be transit eclipses, terminating in annular phase, of stars characterized by arbitrary radially-symmetrical distribution of brightness over their apparent discs — a phenomenon which will cause the light of the system to vary continuously during annular phase. In the first section which follows this abstract, an outline of the problem at issue will be given. Section 2 has been devoted to an analysis of light changes arising in the course of partial phases of transit eclipses; and the concluding Section 3 will contain an analysis of the corresponding light changes, during annular phase. Unlike for occultation eclipses considered in our previous paper (cf. Kopal, 1975b), the momentsA 2m of the light curves due to eclipses of transit type can again be expressed in terms of the geometrical elements of such eclipses in a closed form for limb darkening characterized by any value ofn; but the use of such functions will require auxiliary tables (now in preparation) for applications to practical cases. A parallel treatment of partial eclipses of the occultation or transit type — eclipses which stop short of totality or annular phase — is being postponed for a subsequent communication.

Wave zone structure of NP 0532 and infrared radiation excess of Crab Nebula

Abstract: At the distancer≳1015 cm from NP 0532 the plasma concentration decreases so that the intense low-frequency wave (ν=30 Hz) can propagate. The interaction of this wave with the electrons ejected from the pulsar should result in the IR radiation withFν∼102 fu at λ∼10 μ. This flux is the order of the excess IR radiation from the Crab Nebula.

Fourier analysis of the light curves of eclipsing variables. IV

Abstract: The methods of analysis of the light changes of eclipsing variables in the frequency domain, developed in our previous papers (Kopal, 1975b, c) for total or annular eclipses of arbitrarily limbdarkened stars, have now been extended to the case of partial eclipses of occultation as well as transit type. In Section 2 which follows brief introductory remarks the even Fourier sine coefficients are formulated — in the guise of the momentsA2m of the light curve — in terms of the elements of the eclipse; and their use for a solution for the elements is detailed in Section 3. A brief appendix containing certain auxiliary tables to facilitate this task concludes the paper.

Decaying Nuclei and the Age of Cosmic Rays in the Galaxy

Abstract: The propagation of radioactive nuclei of cosmic rays in a flat diffusion galactic model (sources and the main gaseous mass are concentrated in the galactic disc) is considered. The corresponding results are not reducible to the results of a simple homogeneous model. It is shown that the recent data on the Be10 nuclei abundance in cosmic rays do not contradict the occurrence of a large cosmic ray halo.

Optical Properties of Particulates

Abstract: Optical properties of small particles of olivine (less than 0.1 μ) have been studied in the ultraviolet as an example of an insulating solid. Very little structure survives in the ultraviolet extinction curves for such small particles. By contrast ‘surface modes’, observed for graphite small particles in the ultraviolet and for olivine particles in the infrared, produce dominant and persistent structure in extinction. The general trend of optical properties of graphite is surprisingly similar to the behavior required to explain all features of the interstellar extinction and albedo curves from near visible to 1000 A. Measured extinction of small olivine particles in the infrared agrees with calculations based on newly measured optical constants, but dominant sharp structure in the 10μ region still presents a bit of a problem in explaining ‘silicate’ features in astronomical data.

Evolution of Massive Close Binaries. I: The X-Ray Binary Stage

Abstract: X-ray binaries such as Cen X-3, Cyg X-1, Vela X-1, 2U1700-37, SMC X-1, Cir X-1, with periods ranging from 2d.087 to 12d.28, are probably evolution products of massive binary systems. The massive primary starts losing mass after core hydrogen burning and undergoes a supernova explosion. The evolution of binary systems consisting of a 20M⊙ primary and secondaries of respectively 14, 10, 8 and 6M⊙ was computed from Main Sequence stage through the X-ray phase, until the second mass transfer phase. Estimates were performed for the evolution of a secondary of 4M⊙. It may be seen that some of these systems during their X-ray phase match the observed mass ratios and periods.

Cosmic ray antiproton and positron production in the interstellar medium

Abstract: We have calculated the energy spectra of cosmic ray secondary antiprotons and positrons using the latest available data on inclusive reactions. Using the measured positron spectrum, we have found that the amount of matter traversed by the cosmic rays in the few GeV region to be 4.7 (+ or - 1.5) g/sq cm of interstellar hydrogen. The computed antiproton to proton ratio is about .0004 for energies 5-10 GeV. This is sufficient to make observations of antiprotons feasible from balloon flights. We have also pointed out the type of information that can be obtained if accurate information of the spectra of these two components becomes available.

Infrared Spectra of Carbonaceous Chondrites and the Composition of Interstellar Grains

Abstract: Infrared spectra (7–40 μ) of the carbonaceous chondrites, Cold Bokkeveld, Murray, and Orgueil are compared with phyllosilicate minerals and interstellar grain spectra. Similarities in the position and shape of the silicate feature near 9.8 μ suggest that similar silicate minerals are present in primitive meteorites and the interstellar dust.

Wave-trains in the solar wind. III. Alfven waves in the azimuthally- dependent interplanetary medium

Abstract: Applying an Alfvén-Wave-Extended-QRH-approximation and the method of characteristics, we solve the equations of motion for outwardly propagating Alfvén waves analytically for three different cases of an azimuthal dependence of the background solar wind, (a) for a pure fast-slow stream configuration, (b) for the situation where the high-speed stream originates from a diverging magnetic field region, and (c) for the case of (b) and an initially decreasing density configuration (‘coronal hole’). The reaction of these waves on the background state as well as mode-mode coupling effects are neglected. These three solar wind models are discussed shortly. For the superimposed Alfvén waves we find, on an average, that there is a strong azimuthal dependence of all relevant wave parameters which, correlated with the azimuthal distributions of the solar wind variables, leads to good agreements with observations. The signature of high-speed streams and these correlations could clearly indicate solar wind streams originating from ‘coronal holes’. Contrary to the purely radial dependent solar wind, where outwardly propagating Alfvén waves are exclusively refracted towards the radial direction, we now find a refraction nearly perpendicular to the direction of the interplanetary magnetic field in the compression region and closely towards the magnetic field direction down the trailing edge and in the low-speed regime.

Occultation of radio source PKS 2025-15 by comet Kohoutek (1973f)

Abstract: This paper describes the strong fluctuations in the intensity of radio source PKS 2025-15, observed at 327 MHz, during its occultation by comet Kohoutek (1973f) in 1974, January 5. Possible mechanisms which could produce the observed fluctuations are examined. It is difficult to explain the fluctuations in terms of scintillation produced due to the passage of radio waves through the irregular cometary plasma. No detectable radio emission was observed from the comet at 327 MHz.

Viscous universes without initial singularity

Abstract: It is shown that within a certain class of cosmological models (homogeneity and isotropy, two-component non-interacting fluid, density-dependent coefficient of bulk viscosity) the introduction of bulk viscosity effectively removes the initial singularity.

High fluences of low energy (10 25 MeV/amu) C, N, O and heavier ions at 450 km altitude; results from the skylab experiment

Abstract: High fluences (i.e. the integrated fluxes) of C, N, O group of nuclei and some of the heavier ones, in the energy interval 10–25 MeV/amu, have been identified in a Lexan polycarbonate detector assembly exposed on the exterior of the Skylab for 73 days. The existence of large flux of low energy nuclei in the Skylab orbit is surprising since the minimum geomagnetic cut-off energy for fully stripped nuclei (A/Z=2) is ≃50 MeV/amu at the orbit of the satellite, and the period of exposure was a ‘quiet’ one, free from significant solar particle events. We have considered two sources for these particles: (i) partly ionized interplanetary ions accelerated within the magnetosphere and (ii) heavy nuclei trapped in the Earth's radiation belt. The flux and composition of the nuclei observed by us seem to be significantly different from those in the trapped radiation as known at present; hence it seems likely that the major part of the observed flux may be interpreted, in terms of partly ionized interplanetary ions that are further accelerated in the magnetosphere.

On pair production in intense electromagnetic fields occurring in astrophysical situations

Abstract: We show that the pair production rate in a strong magnetic field is substantially altered when an electric field is also included. We illustrate and emphasize this significant alteration by considering a few special cases. In the vicinity of the polar cap of a rotating magnetized neutron star it is currently though thatboth steady electric and magnetic fields must be present. The results presented here then indicate that some considerable degree of caution must be exercised in applying pair production rates calculated under the assumption of zero electric field to the problems of pulsar emission and the generation and maintence of pulsar magnetospheres. In general such rates are very different from the rate computed allowing for the existence of an electric field.