General-relativistic hierarchical cosmology: An exact model

An exact solution of Einstein's equation is stated in which the density (), pressure (p), scale factorS and metric coefficients are functions of only one dimensionless self-similar variable,ct/R, wheret is cosmic time andR is a co-moving radial coordinate. The solution represents a cosmology that begins as a static sphere having R ^–2 and evolves into an expanding model which is pressure-free and has a hierarchical type of density law ( R ^–, approximately, with =a number, 02). It is suggested that this model should supersede the previous models of Wesson and other workers, since it appears to be the simplest cosmology for a hierarchy.     

A static theory of the stability of the equilibrium

A static relativistic theory of the stability of the equilibrium of an isentropic spherically-symmetric star is deduced from the properties of a functionu which is solution of a second-order differential equation, and which is related to the model by means of the formulau = m(v, c)/c, wherem is the mass-energy inside the coordinate volumev and c is the central mass-energy density.Work done in the Laboratorio Astrofisico di Frascati, Roma.     

Detection of background gravitational radiation by Doppler tracking of spacecraft

Low-frequency gravitational radiation, with wavelengths reaching or exceeding interplanetary distances, and with a mean energy density of the order of the critical cosmological density _c , generates a frequency-shift of order/10^–15 h ₀(1/10⁸km)(/ _c )^1/2 in electromagnetic signals transponded by interplanetary spacecraft at a distancel from the Earth.     

Central holes in disks of spiral galaxies

On the basis of the solutions obtained in the previous paper, the changes in the scenario of the standard model of the Big Bang are found. The chaos degree (constrainst on fluctuation spectra) is obtained, which could be still preserved by the initially completely chaotic Universe at the time of light elements nucleosynthesist _es. The time boundaries of hadron and lepton eras and the time the electron neutrinos and neutrons become frozen in reactions of weak interaction may be shifted up to 1.4 times. The corresponding temperatures may shift off from the standard ones 0.88 times if the mean-square level of fluctuations is close to unity. If the density of the energy of fluctuations concentrated in the short-wave region of the spectrum is less than 1.5 ^– , the nucleosynthesis leads to a helium abundance coinciding with the observe one. If at the timet _es the maximum of the spectral density of the energy is in the long-wave region, that is _max ct _es the level of the chaos during the period of nucleosynthesis is restricted to 1.76 (where |C _K |² d³ K,C _K is Fourier component of the amplitude of metric fluctuations). In particular, the protogalactic vortical disturbances with a wide spectrum 4 × 10^{3 -1}( = K/K, = /_crit) are compatible with the observed helium abundance.     

On the interplanetary cosmic-ray scintillations

The equation for the two-particles cosmic-ray distribution function is derived by means of the Boltzmann kinetic equation averaging. This equation is valid for arbitrary ratio of regular and random parts of the magnetic field. For small energy particles the guiding-center approximation is used. On the basis of the derived equation the dependence between power spectra of cosmic-ray intensity and random magnetic field is obtained. If power spectra are degree functions for high energy particles ( 10 GeV nucleon^–1), then the spectral exponent of magnetic field lies between and –2, where is the spectral exponent of cosmic-ray power spectra. The experimental data concerning moderate energy particles are in accordance with =, which demonstrates that the magnetic fluctuations are isotropic or cosmic-ray space gradient is small near the Earth orbit.     

Why are spicules absent over plages and long under coronal holes?

One-dimensional hydrodynamic simulations are performed in order to examine the influence of initial atmospheric structures on the dynamics of spicules. This is an extended version of our previous spicule theory: spicules are produced by the shock wave (MHD slow mode shock) which originates from a bright point appearance (sudden pressure increase) at the network in the photosphere or in the low chromosphere. Simulation results well reproduce the observational facts that spicules are absent over plages and long under coronal holes. The physical reason is that the growth of a shock wave during its propagation through the chromosphere is small in plage regions and large in coronal hole regions, since the growth of a shock is determined by the density ratio ( _{h 0}/ _c ) between the bright point and the corona. An empirical formula H _max ( _{h 0}/ _c )^0.46 is obtained, where H _max is the maximum height of spicules above the transition region. The cross-section of the vertical magnetic flux tube is assumed to be constant in the numerical simulations.     

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.     

Linearly expanding universes in JBD-theory

The assumption of a linearly expanding universe for the JBD-cosmological equations generates a set of solutions for the barotropic equations of statep= (=const.). These solutions turn out to be valid for closed space-except in the casep= which is for open space. The gravitational constant which is inversely proportional to the scalar field increases with time if >–1/3 and decreases for <–1/3. No solution exists for =1/3. The Brans-Dicke parameter is negative if <–1/3.     

Density fluctuations in the universe after the recombination period

It is shown that the cosmic matter gas after the recombination period can be regarded in a very good approximation as a general relativistic Boltzmann gas in the very vicinity of equilibrium. As a consequence, spatial temperature fluctuations (T/T)10^–5 imply immense density fluctuations up to (p/p)10⁵.     

The velocity correlation function in cosmic-ray diffusion theory

The concept of velocity correlation functions is introduced and applied to the calculation of cosmic ray spatial diffusion coefficients. It is assumed that the pitch angle scattering coefficient is already known from some other theory, and is reasonably well-behaved. Previous results for the coefficient for diffusion parallel to the mean field are recovered when the velocity-changing mechanism is artificially restricted to pitch angle scattering. The velocity correlation method is then applied to the more general case where there are fluctuations in the local mean field. It is found that the parallel diffusion coefficient is reduced in proportion to the amplitude of the field fluctuations, and that the ratio of the perpendicular to parallel diffusion coefficients cannot be greater than B _x ² /B ₀ ² . It is shown in the appendix that the Liouville form of the scattering equation implies that the Fokker-Planck coefficients ²/t=2D and /t=D /, and that all higher-order coefficients are identically zero.     

A differential equation for the classical collapse problem

The classical gravitational collapse problem is analysed on the basis of an integral equation connecting the evolutionary time (defined as dt/d log ) with the density and the collapse function , or by an equivalent first-order non-linear differential equation. The general behaviour of solutions is discussed, and some particular cases are studied.     

Plane and cylindrical hydromagnetic shock waves

The Chisnell-Chester-Whitham method has been used to investigate the propagation of diverging plane and cylindrical shock waves through an ideal gas in presence of a magnetic field having only constant axial and variable azimuthal components, simultaneously for both weak and strong cases. Assuming an initial density distribution ₀=r ^–w , where is the density at the plane/axis of symmetry andw is a constant, the analytical expressions for shock velocity and shock strength have been obtained. The expressions for the pressure, the density, and the particle velocity immediately behind the shock have also been derived for both cases.     

Absolute and relative amplitudes of variations in radius of classical cepheids

On the basis of observational data for the absolute R and relative R/R amplitudes of variations in radius of galactic classical cepheids (55 stars from Balona and Stobie (1979) and 30 stars from Sollazzoet al. (1981)), four kinds of empirical linear relations are obtained: log(P V)–logR, logP–logR, log(P V)–log(R/R), and logP–log(R/R);P, R, and V are the pulsation periods, the mean stellar radii, and the amplitudes of light variations, respectively. Three groups of stars are considered: short-period cepheids (SPC)-with logP1.1; long-period cepheids (LPC)-with logP>1.1; and s-cepheids (sC). Both the R values and the R/R values increase withP andP V, for a given group of variables. A comparison is performed with our results obtained from data in other sources (Kurochkin, 1966; Gieren, 1982; etc.). The investigated relations can be applied for determining R and R/R of galactic classical cepheids, by using their observedP and V. All studied galactic classical cepheids have R/R<0.35, R<10R for SPC and 10R <R60R for LPC. The sC have smaller R and R/R values than other classical cepheids, at the same periods (the difference is about 2 times for R and 1.4–2.8 times for R/R); the studied sC have R/R in the range 0.025–0.075 and R in the range 1–3R (only Y Oph has R8R ).     

Coronal temperatures and temperature gradients from OSO-7 spectroheliograms

Temperatures and temperature gradients for the outer corona are obtained from brightness gradients of EUV lines that were measured with the spectroheliograph on OSO-7. Brightness gradients show considerable deviations from isothermal model calculations that include collisional excitation and photoexcitation. A negative temperature gradient that gives both positive and negative ion abundance gradients appears to be able to account for the discrepancy. For 284 of Fe xv, perhaps the strongest line from the outer corona, measurements during 1972 appear to be consistent with (i) a temperature near 2.3×10⁶K near the equator at = 1.3±0.1 solar radii from the solar center; (ii) (/T) dT/d values near -0.7 that extend from as low as = 1.2 to about = 1.8. Temperatures from strong lines of Fe xiv and Fe xvi indicate that variations of about ±0.2×10⁶K exist along lines of sight where emission is appreciable. There appears to be some agreement between these results and temperature measurements from ion abundances in the solar wind and Doppler width of 5303.     

Annihilation radiation from thermal electron-positron plasma on the ground Landau level: The case of low magnetic fields

The intensity and polarization of two-photon annihilation in a magnetic fuieldBB _cr =4.4×10¹³ G are studied in detail for a, one-dimensional thermal distribution of annihilating electrons and positrons on the ground Landau level. With the increase of temperatureT the total annihilation rate and energy losses decrease, being higher than for the isotropic thermal distributions at the sameT. The shapes of intensity spectra at sin =0 ( is the angle betweenB and wave-vector) are close to those in the isotropic case. The widths and blue-shifts of the spectra decrease with increasing sin and increase with increasingT. Logarthmic singularities arise in the spectra atE»mc ²/sin . Power-like parts are formed in the wings of the spectra forkTmc ² and not too small sin . The direction-integrated spectra reach their (finite) maxima, atE=mc ² for anyT. The radiation concentrates near the plane, perpendicular to the magnetic field forE close tomc ² and is beamed along the magnetic field forE far frommc ². Energy-integrated angular distributions are stretched alongB, the stronger the higherT. The rediation is linearly polarized in the plane formed by the magnetic field and weve-vector. Typical values of the polarization inside the cores of the annihilation spectra are (kT/mc ²) sin and [ln (kT/mc ²)]^–1 forkTmc ² andkT sin mc ², respectively. Annihilation radiation dominates over Bremsstrahlung in thee plasma atkT7mc ². The results are useful for interpretation of the annihilation radiation in the gamma-ray bursts. They permit to estimate temperature, gravitational potential, and emission measure of radiating regions and the beaming of the radiation.     

Expanding and superdense astrophysical systems in general relativistic hierarchical cosmology

A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( _i+1/ _i [r _i /r _i+1] is approximately equal to the exponentN in a continuous density law (=aR ^–N) provided (r _i /r _i+1)^3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c ² R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s^–1 Mpc^–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c ² R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R ^N ,N2); (j) for the Galaxy, theory predictsp _G7×10^–12 dyn cm^–2, observation givesp _G5×10^–12 dyn cm^–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 10¹² g s^–1, compared to 10¹¹ g s^–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×10⁹ years for the Sun and 10¹⁰ years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN _B of baryons; (o)N _B10⁵⁷N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L _max10⁵⁹ erg s^–1); (r) larger bodies have longer time-scales of energy radiation atL _max (10^–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR ^–N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.     

Secular resonances in the primitive solar nebula

We present here a very simple model that could explain the relatively high eccentricities and inclinations observed in the minor planet belt. This model is based upon the sweeping of the secular resonances ₆ and ₁₆ through the belt due to the gravitational effect of the dissipation of a primitive solar nebula. The sweeping of the ₁₆ secular resonance (responsible for the high inclinations) is very sensitive to the density profile of the nebula. For the model to work we need a density profile proportional to ^–k with between 1.0 and 1.5.     

The cosmic γ-ray spectrum from secondary particle production in cosmic-ray interactions

The cosmic -ray spectrum below 1 GeV arising from cosmic ray p-p interactions is calculated. Its characteristics are determined by the properties of secondary neutral pion production occurring at accelerator energies. A model is chosen for numerical calculations in which the two dominant modes of neutral pion production at accelerator energies are the production of the (1.238) isobar and one fireball. The effect of -p and p- interactions on the cosmic -ray spectrum is also calculated. The final results are given in terms of both differential and integral -ray energy spectra.     

Charge-coupled device imaging spectroscopy of Mars. 1. Instrumentation and data reduction/analysis procedures

This paper describes the collection, reduction, and analysis of 0.4–1.0 m Mars imaging spectroscopy data obtained during the 1988 and 1990 oppositions from Mauna Kea Observatory and provides a general outline for the acquisition and analysis of similar imaging spectroscopy data sets. The U.H. 2.24-m Wide Field Grism CCD Spectrograph was used to collect 13 three-dimensional image cubes covering 90% of the planet south of 50°N in the 0.4–0.8 m region (/=245 at 0.6 m) and covering 55% of the planet south of 50°N in the 0.5–1.0 m region (/=293 at 0.75 m). Spectra extracted from these image cubes reveal the detailed character of the martian near-UV to visible spectrum. Images at red wavelengths reveal the classical albedo markings at 100–500 km spatial resolution while images at blue wavelengths show little surface feature contrast and are dominated by condensate clouds/hazes and polar ice. Many of the data acquisition, reduction, and analysis steps discussed here are new or unique to imaging spectroscopy data sets. These techniques exploit the information contained within the spatial domain of data such as these, thus allowing more traditional point-spectral analysis techniques to be expanded into an imaging format.     

High accuracy precession measurement with an autometric gyro

A simple reticle with parallel equally spaced lines to transmit light in an autometric gyro is shown to give a signal which can be used for very accurate angular precession measurements. Frequency analysis of the signal is chosen over time domain analysis and/or over a specially designed reticle.Gyro precession will induce a change in the interference structure of the spectrum in addition to dilating the overall frequency distribution. The expected output spectrum has been analytically determined, exhibiting the dependence on spot and reticle line cross sections and line spacing so that they can be precisely determined from the output data.The spectrum structure is extremely sensitive to precession. Computer simulations indicate that accuracy will be limited by reticle line spacing variations to ±4×10^–9 rad. This would allow a Lense-Thirring precession measurement accurate to ±20% in 30 days (accuracy being limited by physical effects common to all such experiments) or a ±1% de Sitter precession measurement in four days.Nomenclature a _n() Fourier coefficients ofI() - a _n ^r () rapidly varying part ofa _n() - a _m ^x ,b _m ^x Fourier coefficients ofI(x) - a (),b () Fourier sine and cosine transforms of _x(x) - angle between star and gyro spin axis - ₀ initial alignment angle - f focal length of optical system - I transmitted light intensity, signal function - l reticle line width - r distance from light spot center - R light-circle radius - = reduced light-circle radius - ₀ reduced reticle center-spin center offset - s reticle line space - T(x) reticle transmission function - angle of gyro rotation - w _g gyro angular velocity This work was supported by the M.I.T. Center for Space Research under NASA Grant NGL-22-009-019.