Nonlinear theory of the two-point correlation function

We consider the influence of the nonlinear stage of gravitational instability on the two-point correlation functions of gravitationally bound objects. Based on the theory of nonlinear gravitational contraction of a single density peak of dissipationless matter (Gurevich and Zybin, 1988a,b; 1990) we develop a method for calculating the two-point correlation functions of different objects of any mass. The method works good in the region of strong correlations and can be easily extended to calculate higher correlation functions. We show that the main contribution to the correlation function _i in the region of strong correlations _i 1 is made by pair systems located outside large clusters of objects. In this region the shape of _i is determined only by the nonlinear dynamics of gravitational contraction of dissipationless matter and has the form _i C ^–, where 1.8 is a universal parameter.     

Some results of ionospheric investigations by means of coherent radiowaves emitted by satellites

In this paper we discuss theoretical expressions, determining the difference of Doppler shifts of various coherent radiowave frequencies emitted by a radiator moving in the ionosphere or interplanetary medium. The rotating Doppler effect (Faraday effect) caused by the Doppler shifts ±H of the ordinary and extraordinary waves is also considered. In a three-dimensional inhomogeneous ionosphere, stationary in time (N/t = 0), is determined in the general case, by an equation with three variables. The equation for proper depends only on the local value of the electron concentration N _c around the radiator and on integral values, determining, by means of additional calculations, the angle of refraction or its components, the horizontal gradients of electron concentration N/x and N/y, and in some cases, the integral electron concentration ₀ ^zcN dz. We describe the analysis of the measurements, made with the satellites Cosmos I, II and partially XI, assuming that N/t = N/y = 0, with a two variables equation. The expected errors are considered. The results coincide well for different points (Moscow, The Crimea, Sverdlovsk) and thus agree with the measurements of _H and with height-frequency ionospheric characteristics. The curve giving electron concentration versus height N (z) in the outer ionosphere (above the maximum of F2), shows a new maximum higher than the main maximum of the ionosphere N _MF2 at 120–140 km. At this maximum the value of N (z) is (0.9–0.95) N _MF2. The new data on the large-scale horizontal inhomogeneities of the ionosphere, exceed the previous ones by about a factor 10. By means of the irregular variations of the spectrum W() of the inhomogenous formation is determined. Three unknown constant maxima with values 16 to 18 km, 28 to 32 km and 100 to 120 km are found. The spectrum W () mainly characterizes the local properties of the ionosphere along the orbit of the satellite.     

Temperature Fluctuations,H II Region Abundances,and Primordial Helium

There is evidence for temperature fluctuations in Planetary Nebulae and in some Galactic H II regions. If such fluctuations occur in the low metallicity, extragalactic H II regions used to probe the primordial helium abundance, the derived 4He mass fraction, YP, could be systematically different from the true primordial value. Although this effect could be large, there are no data which allow us to estimate the size of the temperature fluctuations for the extragalactic H II regions. Therefore, we have explored this effect via Monte Carlo simulations of the data in which the abundances derived from a fiducial data set are modified by T chosen from a distribution with 0 T Tmax where Tmax is varied from 500 K to 4000 K.     

Hubble Space Telescope Observations of Nebular Morphologies and Their Implications

The morphologies of nebulae, as revealed by HST observations are presented. Mechanisms for the formation of axisymmetric and point-symmetric nebulae are reviewed. Critical observations that can test the models presented in this paper are suggested.     

A New Mechanism of Coronal Heating

The interaction between network magnetic fields and emerging intranetwork fields may lead to magnetic reconnection and microflares, which generate fast shocks with an Alfvén Mach number M _A<2. Protons and less abundant ions in the solar corona are then heated and accelerated by fast shocks. Our study of shock heating shows that (a) the nearly nondeflection of ion motion across the shock ramp leads to a large perpendicular thermal velocity (v _th), which is an increasing function of the mass/charge ratio; (b) the heating by subcritical shocks with 1.1 M_A 1.5 leads to a large temperature anisotropy with T/T 50 for O⁵⁺ ions and a mild anisotropy with T_/T 1.2 for protons; (c) the large perpendicular thermal velocity of He⁺⁺ and O⁵⁺ ions can be converted to the radial outflow velocity (u) in the divergent coronal field lines; and (d) the heating and acceleration by shocks with 1.1 M_A 1.5 can lead to u(O⁵⁺) v _th(O⁵⁺) 460 km s^–1 for O⁵⁺ ions, u(He⁺⁺) v _th(He⁺⁺) 360 km s^–1 for He⁺⁺ ions, and u(H⁺) v _th(H⁺) 240 km s^–1 for protons at r=3–4 R . Our results can explain recent SOHO observations of the heating and acceleration of protons and heavier ions in the solar corona.     

Non-BBN Constraints on the Key Cosmological Parameters

Since the baryon-to-photon ratio 10 is in some doubt at present, we ignore the constraints on 10 from big bang nucleosynthesis (BBN) and fit the three key cosmological parameters (h, M, 10) to four other observational constraints: Hubble parameter (ho), age of the universe (to), cluster gas (baryon) fraction (fo fGh3/2), and effective shape parameter (o). We consider open and flat CDM models and flat CDM models, testing goodness of fit and drawing confidence regions by the 2 method. CDM models with M = 1 (SCDM models) are accepted only because we allow a large error on ho, permitting h < 0.5. Open CDM models are accepted only for _M 0.4. CDM models give similar results. In all of these models, large 10 ( 6) is favored strongly over small 10 ( 2), supporting reports of low deuterium abundances on some QSO lines of sight, and suggesting that observational determinations of primordial 4He may be contaminated by systematic errors. Only if we drop the crucial o constraint are much lower values of M and 10 permitted.     

Energetic particles at high latitudes

We review work on diffusion coefficients of energetic particles with an attempt to extract implications on their behaviour at high latitudes. In the ecliptic plane results from solar energetic particle propagation between the Sun and about 5 AU can be described by an effective radial mean free path _r which is approximately constant as a function of distancer. When particle propagation in three dimensions in the heliosphere is considered it is not sufficient to consider _r only. Jovian electrons can be used as probes to determine the parameters of three-dimensional diffusion. In the polar regions diffusion is dominated by its parallel component. Some predictions how should vary with latitude are discussed. For different choices of this variation we present expectations for intensity-time profiles of solar particle events during the Ulysses polar passages.     

Observed Densities in the Universe

Baryons observed in Ly absorbers contribute to the density parameter 0 by bar 0.06 in close agreement with the value of 0.06 from primordial nucleosynthesis (H0=55 km s-1 Mpc-1, = 0 assumed throughout). A number of methods are known to measure 0 from density fluctuations; bound structures tend to yield lower values (m 0.2-0.4), field galaxies over large scales higher, but still undercritical values (m 0.6 ± 0.2). The best compromise value is 0 0.5, but the present methods are blind to diffusely distributed, exotic matter which still could make 0 = 1. A satisfactory solution of 0 (and ) will only come from a fundamental cosmological test (e.g. the Hubble diagram of [evolution-corrected] supernovae type Ia) in combination with the CMB fluctuation spectrum.     

Co2 and Climate: a Geologist's View

Climate is discussed as an integral part of System Earth, determined by a complex interplay of numerous geological, biological and solar processes. The historical and geological record of changing climate and atmospheric CO₂ pressure does not support the current popular vision that this greenhouse gas is the dominant climate controlling agent. When empirically ante post tested against past global climate changes, the forecasts of the climate models mainly based on forcing by atmospheric CO₂ are not borne out. On the other hand, recent studies show that solar variability rather than changing CO₂ pressure is an important, probably the dominant climate forcing factor.     

The magnetogram inversion technique: Applications to the problem of magnetospheric substorms

The magnetogram inversion technique (MIT) is based upon recordings of geomagnetic variations at the worldwide network of ground-based magnetometers. MIT ensures a calculation of a global spatial distribution of the electric field, currents and Joule heating in the ionosphere. Variant MIT-2 provides, additionally, continuous monitoring of the following parameters: Poynting vector flux from the solar wind into the magnetosphere (); power, both dissipated and accumulated in the magnetosphere; magnetic flux in the open tail; and the magnetotail length (l _T) (distance between the dayside and nightside neutral points in the Dungey model). Using MIT-2 and data of direct measurements in the solar wind, an analysis is made of a number of substorms, and a new scenario of substorms is suggested. The scenario includes the convection model, the model with a neutral line and the model of magnetosphere-ionosphere coupling (outside the current sheet), i.e., the three known models. A brief review is given of these and some other substorms models. A new element in the scenario is the strong positive feedback in the primary generator circuit, which ensures growth of the ratio = / _Aby an order of magnitude or more during the substorms. Here _Ais the Pointing vector flux in the Akasofu-Perrault approximation, i.e., without the feedback taken into account. The growth of during the substorm is caused only by the feedback effect. It is assumed that the feedback arises due to an elongation of the magnetotail, i.e., a growth of l _Tby a factor of (23) during the substorm.In the active phase of substorm, a part (the first active phase) has been identified, where the principal role in the energetics is played by the feedback mechanism and the external energy source (although the internal source plus reconnection inside the plasma sheet make a marked contribution). In the second active phase (expansion) the external generator (solar wind) is switched off, and the main role is now played by the internal energy source (the tail magnetic field and ionospheric wind energy).Models of DP-2 DP-1 transitions are also considered, as well as the magnetospheric substorm-solar flare analogy.     

Presupernova models and supernovae

Present status of the theories for presupernova evolution and triggering mechanisms of supernova explosions are summarized and discussed from the standpoint of the theory of stellar structure and evolution. It is not intended to collect every detail of numerical results thus far obtained, but to extract physically clear-cut understanding from complexities of the numerical stellar models. For this purpose the evolution of stellar cores is discussed in a generalized fashion. The following types of the supernova explosions are discussed. The carbon deflagration supernova of intermediate mass star which results in the total disruption of the star. Massive star evolves into a supernova triggered by photo-dissociation of iron nuclei which results in a formation of a neutron star or a black hole depending on its mass. These two are typical types of the sueprnovae. Between them there remains a range of mass for which collapse of the stellar core is triggered by electron captures, which has been recently shown to leave a neutron star despite oxygen deflagration competing with the electron captures. Also discussed are combustion and detonation of helium or carbon which take place in accreting white dwarfs, and the collapse which is triggered by electron-pair creation in very massive stars.Appendix: Notations A mass number of atomic nucleus - B _v(a, b) incomplete beta function - c _p specific heat at constant pressure - c _p sound velocity - c(sub) center of the star - E _e mean energy of an electron captured by nucleus - E _n nuclear energy release from unit mass of the nuclear fuel specified by n - E _thr threshold energy (9.3) - E _thr,0 energy difference between the ground states of daughter nucleus and parent nucleus (9.1) - E energy of gamma ray emitted from daughter nucleus (9.1) - E _v mean energy of a neutrino emitted by electron capture (9.1) - f flatness parameter (2.17) - g local gravitational acceleration (2.16) - H atomic mass unit - H _p scale height of pressure (2.22) - H (sub) hydrogen-burning shell - k Boltzmann constant - l mixing length of convection - L _cr(M _r ) local Eddington's critical luminosity (4.3) - L _n integrated nuclear energy generation rate by nuclear fuel specified by n - L _v neutrino luminosity - L _{v, cr}(M _r ) local Eddington's critical neutrino luminosity (11.2) - M (current) mass of a star - m _M core mass contained interior to the carbon-burning shell - M _Ch Chandrasekhar's limiting mass (9.6) - M _H core mass contained interior to the hydrogen-burning shell - M _He core mass contained interior to the helium-burning shell - M _ms mass of a star at its zero-age min-sequence - M _O core mass contained interior to the oxygen-burning shell - M _r mass contained interior to a shell at r - M _Si core mass contained interior to the silicon-burning shell - M _WD mass of white dwarf (7.1) - M ₀ normalization factor to the non-dimensional mass (3.3) - M ₁ core mass (3.6) - N polytropic index between pressure and density (2.3) - n polytropic index between pressure and temperature (10.1) - N _A Avogadro number - N _ad adiabatic polytropic index - N _e number of electrons in unit mass of matter - NSE nuclear statistical equilibrium - P pressure - ph (sub) photosphere - Q _e mass fraction of the envelope exterior of the shell e (2.14) - R stellar radius - r radial distance of a shell - r ₀ normalization factor to the non-dimensional radius (3.2) - s specific entropy - S _i specific entropy of ions - T temperature - U homology invariant defined by (2.1) - u _gas specific internal energy of gas - u _rad energy of the radiation field per volume in which unit mass of gas is contained (6.4) - V homology invariant defined by (2.2) - _def velocity of deflagration front (6.10) - X concentration by weight of hydrogen - Y concentration by weight of helium - Y _e mole number of electrons in one gram of matter (9.7) - Y _v mole number of neutrinos in one gram of matter - Z concentration by weight of the elements other than hydrogen and helium - z shock strength (6.6) - 1 (sub) usually denotes the core edge (2.13) - ratio of the mixing length to the scale height of pressure (l/H _p ) - ratio of gas pressure to the total pressure - ratio of the specific heats - gD locus of singularity in U-V plane (2.5) - M(H _p ) mass contained within unit scale height of pressure (4.4) - _ec energy rate by electron captures (9.5) - _n nuclear energy generation rate by the nuclear fuel specified by n - _v neutrino loss rate - L _v ^(D) neutrino loss rate excluding the neutrinos from the electron captures (9.4) - non-dimensional density (3.1) - P/, not the non-dimensional temperature (2.7) - _W Weinberg's angle (5.8) - opacity - _v neutrino opacity (11.2) - describes the effect of electron degeneracy in equation of state (2.19) - _ec rate of electron capture - mean molecular weight - _e mean molecular weight of electrons - _e chemical potential of an electron excluding the rest mass (8.1) - _i mean molecular weight of ions - non-dimensional radius (3.1) - non-dimensional pressure (3.1) - matter density - _cr ^GR critical density above which the general relativistic instability sets in - _cr critical density for reimplosion of the core by beta processes (Section 5) - _ign density at the ignition - _nse density above which the deflagrated matter results in NSE composition - _e non-dimensional entropy of electron-per one electron in units of k(9.2) - _ff timescale of free fall (6.2) - _h (H _p ) timescale of heat transport over unit scale height of pressure (4.4) - _n nuclear timescale for a change in temperature (6.1) - non-dimensional mass (3.1) - _e chemical potential of an electron in units of kT (8.1)     

Pulsars as gamma ray sources: Nebular shocks and magnetospheric gaps

I summarize the results of recent research on the structure and particle acceleration properties of relativistic shock waves in which the magnetic field is transverse to the flow direction in the upstream medium, and whose composition is primarily electrons and positrons with an admixture of heavy ions. Shocks which contain heavy ions that are a minority constituent by number but which carry most of the energy density in the upstream medium put 20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) E ^-2, where N(E)dE is the number of particles with energy between E and E+dE. Synchrotron maser activity in the shock front, stimulated by the quasi-coherent gyration of the whole particle population as the plasma flowing into the shock reflects from the magnetic field in the shock front, provides the mechanism of thermalization and non-thermal particle acceleration. The maximum energy achievable by the pairs is _± m _± c ² = m _i c ² ₁/Z _i, where ₁ is the Lorentz factor of the upstream flow and Z _i is the atomic number of the ions. The shock's spatial structure contains a series of overshoots in the magnetic field, regions where the gyrating heavy ions compress the magnetic field to levels in excess of the eventual downstream value. These overshoots provide a new interpretation of the structure of the inner regions of the Crab Nebula, in particular of the wisps, surface brightness enhancements near the pulsar. The wisps appear brighter because the small Larmor radius pairs are compressed and radiate more efficiently in the regions of more intense magnetic field. This interpretation suggests that the structure of the shock terminating the pulsar's wind in the Crab Nebula is spatially resolved, and allows one to measure ₁ 4 × 10⁶, the upstream magnetic field B ₁ to be 3 × 10^-5 Gauss, as well as to show that the total ion flow is 3 × 10³⁴ elementary charges/sec, in good agreement with the total current flow predicted by the early Goldreich and Julian (1969) model. The total pair outflow is shown to be about 5 × 10³⁷ pairs per second, in good agreement with the particle flux required to explain the nebular X—ray source.The energetics of particle acceleration within the magnetospheres of rotation powered pulsars and the consequences for pulsed gamma ray emission are also briefly discussed. The gamma ray luminosity above 100 MeV is shown to scale in proportion to _R ^1/2 , as is in accord with some of the simplest ideas about polar cap models. Models based on acceleration in the outer magnetosphere are also briefly discussed.     

Energy coupling between the solar wind and the magnetosphere

This paper describes in detail how we are led to the first approximation expression for the solar wind-magnetosphere energy coupling function , which correlates well with the total energy consumption rate U _T of the magnetosphere. It is shown that is the primary factor which controls the time development of magnetospheric substorms and storms. The finding of this particular expression indicates how the solar wind couples its energy to the magnetosphere; the solar wind and the magnetosphere constitute a dynamo. In fact, the power P generated by the dynamo can be identified as by using a dimensional analysis. Furthermore, the finding of indicates that the magnetosphere is closer to a directly driven system than to an unloading system which stores the generated energy before converting it to substorm and storm energies. Therefore, the finding of and its implications have considerably advanced and improved our understanding of magnetospheric processes. The finding of has also led us to a few specific future problems in understanding relationships between solar activity and magnetospheric disturbances, such as a study of distortion of the solar current disk and the accompanying changes of . It is also pointed out that one of the first tasks in the energy coupling study is an improvement of the total energy consumption rate U _T of the magnetosphere. Specific steps to be taken in this study are suggested.     

Optical identification of X-ray sources in the Einstein observatory medium and deep surveys

Methods are discussed for establishing the optical identification of X ray sources in the medium and deep X-ray surveys of the Einstein Observatory. Of the 63 X-ray sources with a statistical significance of 5 in the medium survey (Maccacaro et al. 1981), optical identification work is summarized for 51, of which identifications have been made with 30 active galactic nuclei. The optical properties of some of these X-ray selected objects are briefly discussed.The Einstein deep survey of Pavo (Griffiths et al. 1981) is used to illustrate the problems and methods used for securing optical identifications for X-ray sources in the deep survey fields. Identifications have been made with 4 QSOs at the bright end of the optical candidate distribution (together with 3 G stars) and it is shown that a further 7 fainter objects are also likely to be QSOs.     

Characteristics and interpretation of the photometric variability of eta carinae and its nebula

A short review is given on the history of the peculiar variable object Car and on a number of relevant references describing and discussing its physical characteristics and behaviour, based on different types of observational techniques. The star is known to be variable since the 17th century. The excessive mass loss to which it was subject during the 19th century is now visible as an ellipsoidal reflection nebula of 15 diameter: the so-called homunculus. The remainder of the paper is spent on different kinds of problems partly based on the results of a decade of photometric monitoring in the VBLUW photometric system of Walraven. Foreground reddening and reddening by dust in the homunculus are determined and amount to E(B - V) _J = 0 50 and < 6, respectively. Scanning of the homunculus revealed an estimate for the photometric characteristics of the central object, which presumably consists of a massive hot star surrounded by a cooler gas envelope. The total luminosity is derived using fluxes of various sources in the wavelength region 0.15 < < 175 n resulting in M _bol = - 12 3 ± 0 2. The total observed flux corrected for foreground extinction corresponds to a star with R 96 R if T _eff 30 000 K. The mass may be near 150 M . The excess luminosity in 1843, when the star was presumably bolometrically at least 2 5 brighter than at present, may have been caused by envelope-energized pulsations when the star's luminosity was close to its Eddington limit. The temperature should then have been 50 000 K. The mass loss rate, during the excess luminosity phase lasting 30 yr, is estimated to amount to M 4 × 10^-3 M yr^-1. At present the mass loss may be M 10^-4M yr^-1. Since the homunculus is mainly built up from material expelled in the 30 yr interval (from 1830 to 1860), its total mass amounts to M _hom 0.15 M . The historical observations of the colours of Car and a comparison with the characteristics of S Dor type stars, suggest that Car was subject to a number of S Dor type phases similar to those of P Cyg (in the 17th century), S Dor and others. A satisfactory explanation is found for the complete historical light curve. The decrease in light after the 1843 maximum by 9 ^m , presumably consists of a fading of the luminosity excess and the S Dor effect by 2 5 and 3^m, respectively, and a 3 5 extinction by circumstellar dust. The small amplitude light variations which Car showed during the last decade, were studied with the aid of the variations of the Balmer jump. They are presumably caused by temperature variations of the central star.Percy and Welch (1983) (Publ. Astron. Soc. Pacific 95, 491) have observed P Cyg on a number of nights in 1982 and found for the photometric variations a time scale of 30 to 50 days and an amplitude of 0 _. ^m 15.Based partly on observations collected at the ESO, La Silla, Chile.     

The importance of anisotropic interstellar turbulence and molecular-cloud magnetic mirrors for galactic cosmic-ray propagation

Recent studies suggest that when magnetohydrodynamic (MHD) turbulence is excited by stirring a plasma at large scales, the cascade of energy from large to small scales is anisotropic, in the sense that small-scale fluctuations satisfy the inequality k k , where k and k are, respectively, the components of a fluctuations wave vector and to the background magnetic field. Such anisotropic fluctuations are very inefficient at scattering cosmic rays. Results based on the quasilinear approximation for scattering of cosmic rays by anisotropic MHD turbulence are presented and explained. The important role played by molecular-cloud magnetic mirrors in confining and isotropizing cosmic rays when scattering is weak is also discussed.     

Cosmological variability of fundamental physical constants

Gamow was one of the pioneers who studied the possible variability of fundamental physical constants. Some versions of modern Grand Unification theories do predict such variability. The paper is concerned with three of the constants: the fine-structure constant , the ratio of the proton massm _p to the electron massm _e, and the ratio of the neutron massm _n tom _e. It is shown on the basis of the quasar spectra analysis, that all the three constants revealed no statistically significant variation over the last 90% of the life time of the Universe. At the 2 significance level, the following upper bounds are obtained for the epoch corresponding to the cosmological redshiftsz2–3: /<1.5×10^–3, m _p/m _p<2×10^–3, and m/m<3×10^–4, where x is a possible deviation of a quantityx from its present value,m=m _p+m _n, and the nucleon masses are in units ofm _e. (According to new observational data which became known most recently, m _p/m _p<2×10^–4) In addition a possible anisotropy of the high-redshift fine splitting over the celestial sphere is checked. Within the relative statistical error 3 < 1% the values of turned out to be the same in various quadrants of the celestial sphere, which corresponds to their equality in causally disconnected areas. However, at the 2 level a tentative anisotropy of estimated / values is found in directions that approximately coincide with the direction of the relic microwave background anisotropy.The revealed constraints serve as criteria for selection of those theoretical models which predict variation of ,m _p orm _n with the cosmological time.     

The relevant atomic data

The current status of the theoretical methods for producing the relevant atomic data is surveyed.Proceedings of the Conference Solar Physics from Space, held at at the Swiss Federal Institute of Technology Zurich (ETHZ), 11–14 November 1980.     

A dissection of 30 Doradus and a discussion of other Magellanic Cloud OB associations

I Present the results of ground-based and Hubble Space Telescope photometry and spectroscopy of the stars in the central region (roughly 7×7 arcmin) of 30 Doradus in the Large Magellanic Cloud (LMC). Using photometric data for over 2400 stars (complete toV18 mag), and spectroscopic observations of over 150 stars in the region, the best estimate of the initial mass function (IMF) yields a slope of =–1.5±0.2 for masses > 12M, where the Salpeter slope is =–1.35. I compare these results to other measurements of the IMF for OB associations in the Magellanic Clouds.     

Optical design and testing of a fast,large aperture,infrared space telescope

An optical design study for a next generation infrared space telescope has been performed. The concept is that of a passively cooled telescope of minium aperture 2.5 metre with an F/1.2 primary and wavelength coverage from = 2 to at least 40 m, and possibly to 100 m. Compactness, low thermal emission from the optics and structure, diffraction limited imaging at = 2 m, and sensitivity to misalignment aberrations and manufacturing errors were the main considerations for this study. Ray tracing results are presented showing the characteristics of the various designs considered. A preliminary investigation of stray light properties is also given. Special emphasis has been placed on the testing of such a fast primary, and optical systems using a lateral shearing interferometer are described for testing both the primary and the primary/secondary combination.