Implications of a strongly peaked polar magnetic field

Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed _m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin ^p cos ^q which peaks near the equator (q p) will correspond to a cos ⁿ magnetic field at high latitudes only if p = 1 and _m = n /R. Recent measurements of n 8 and 600 km² s^–1 would then give _m 7 m s^–1.     

Approximate expressions for Gyrosynchrotron radiation in Transverse Propagation

Two sets of accurate approximate expressions for the gyrosynchrotron radiation in the transverse propagation case are presented for the first time. They contain emissivity _–/BNand absorptivity _– B/Nfor e-mode, effective temperature T _effand frequency of peak brightness _p. The expressions are designed for the range 2 to 7 of electron energy spectral index and for the ranges from 2 to 10 and 10 to 100 of harmonic numbers s(=/_B). Their statistical error is, respectively, ±18% and ±29% for _–/BNand _– B/Nfor 10/_B100, ±128% and and ±170% for 2/_B10.     

The Bilderberg model of the photosphere and low chromosphere

From 17 through 21 April 1967, an international study week was held in the Bilderberg near Arnhem, Netherlands, with the aim of obtaining an internationally acceptable model of the solar photosphere and low chromosphere. It was found that such a model, based on observed intensities and center-to-limb observations of the solar continuous spectrum, could indeed be established. This model, henceforth called the Bilderberg Continuum Atmosphere (BCA), is shown in Table I, which gives the temperature, gas and electron pressures, and other data as functions of the continuous optical depth at 5000 Å between 5000 = 10^–7 and 25. The model is characterized by a flat temperature minimum of 4600 °K between 5000 10^–2 to 10^–4. The model is homogeneous, and in hydrostatic equilibrium. A hydrogen-helium ratio of 10 has been assumed.Much divergence remains in the interpretation of line-profile observations with regard to the establishment of a photospheric model (Section 4). It proved to be as yet impossible to obtain reliable information on the variation with depth of the following functions: temperature fluctuations, turbulence velocities, convective velocities, and vibrational velocity amplitudes (Section 5). Provisionally, it is assumed that _macro = 2 km/sec and _micro = 1 km/sec, isotropic and independent of depth.     

A hypothetical estimated mass of the muon neutrino and the mass of the tau neutrino

Using the see-saw mechanism and estimation of the hypothetical mass of the electron neutrinom _e we find the hypothetical mass of muon neutrinom _µ and hypothetical mass of the tau neutrinom .     

The kink instability in infinite cylindrical flux tubes: Eigenvalues for power-law twist profiles

We develop simple accurate methods of calculating ideal MHD instability eigenvalues for infinitely-long cylindrical tubes, with twist functionT(r)=B /rB _z . A complete theoretical treatment is presented for force-free magnetic equilibria with arbitraryT(r), and detailed semi-analytic results for the kink instability are given for the particular case of a power-law twistT(r)=r , where the index is non-negative. Our results show that the most rapidly growing and energetic instabilities occur in the Gold-Hoyle =0 field, with the instability progressively weakening with increasing . However, the maximum force eigenvalue is always small, so that even in the Gold-Hoyle case (where =O(10^–2) in dimensionless units) only a small proportion of the available magnetic energy can be released in the linear phase. Our results also confirm that the linear pinch (=) is remarkably weak (=O(10^–3)) yet relatively resistant to line-tying! It is shown that the weakness of the force eigenvalue implies that the influence of uniform gas pressure on stability is negligible. Implications for the energy-release mechanism in solar flares are discussed.     

A maximal background spectrum of gravitational radiation

A maximal spectrum of gravitational radiation from sources outside our galaxy is calculated. The sources are galaxies, quasars and events that occur in the early history of the universe. The major contribution is from galaxies whose effect extends over the frequency region 10^–810⁺⁴Hz, peaking at 10^–110 Hz, with a spectral flux of 10 erg cm^–2, s^–1. The main processes of gravitational radiation in the galaxies are stellar collapse into a black hole and dying binary systems. In the region 10^–410⁴ Hz the background spectrum is well above the detection levels of currently proposed detectors. FromMinimal considerations of this spectrum it is determined that the density of gravitational radiation is 10^–39g cm^–3. This background spectrum is sensitive to galactic evolution and especially sensitive to the upper mass limits and mass distribution of stars in galactic models. Therefore, the spectrum could provide information about galactic evolution complementary to that obtained by electromagnetic investigations.     

Thermal bifurcation in the upper photosphere inferred from heterodyne spectroscopy of OH rotational lines

We have obtained low noise (S/N > 10³), high spectral resolution (/ 10 ⁶) observations of two pure rotation transitions of OH from the solar photosphere. The observations were obtained using the technique of optically null-balanced infrared heterodyne spectroscopy, and consist of center-to-limb line profiles of a = 1 and a = 0 transition near 12 m. These lines should be formed in local thermodynamic equilibrium (LTE), and are diagnostics of the thermal structure of the upper photosphere. We find that the = 0R22(24.5)e line strengthens at the solar limb, in contradiction to the predictions of current one-dimensional photospheric models. Our data for this line support a two-dimensional model in which horizontal thermal fluctuations of order ±800 K occur in the region ₅₀₀₀ 10^–3–10^–2. This thermal bifurcation may be maintained by the presence of magnetic flux tubes, and may be related to the solar limb extensions observed in the 30–200 m region.Observations of the = 1R11(29.5)f line, at 885.643 cm^–1, show that it is anomalously weak in the photospheric spectrum. We argue that the source function in the core of this line has been substantially increased by interaction with the 9j-7i transition of Mgi at 885.524 cm^–1, which is itself too weak to appear in the disk center spectrum.Visiting Astronomer, Kitt Peak National Observatory, which is operated by the Association of Universities for Research in Astronomy, under contract with the National Science Foundation.     

The motion of a satellite in an axi-symmetric gravitational field

The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C _jk ⁿ (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin²t - i inclination of the orbit - J _n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S _jk ⁿ (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M₊+m) (gravitational constant times the sum of the masses of Earth and satellite) - _n,k coefficients ofR component of disturbing acceleration (funtions off) - _n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X ₀ ^n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node     

Cherenkov emissions of Langmuir plasmons and light neutrinosby the flux of neutrinos

We consider the system of neutrino-antineutrino – plasma taking into account theirweak Fermi interaction, when the density of neutrinos andthe plasma particles are rather high and their collective interactionplays a vital role. New fluid instabilities driven by strong neutrino flux in aplasma are observed. It is shown that a bunch of neutrinos, drifting witha constant velocity across a homogeneous plasma, can also induce emission oflower energy neutrinos due to scattering, i.e. the decay of a heavy neutrino_H into a heavy and a light neutrino _L(_HHL) in a plasma. Furthermore we find thatthe neutrino production in stars does not lead in general to energy lossesfrom the neutron stars.     

The three principal secular resonances ν5, ν6, and ν16 in the asteroidal belt

We review theoretical and numerical results obtained for secular resonant motion in the asteroidal belt. William's theory (1969) yields the locations of the principal secular resonances ₅, ₆, and ₁₆ in the asteroidal belt. Theories by Nakai and Kinoshita (1985) and by Yoshikawa (1987) allow us to model the basic features of orbital evolution at the secular resonances ₁₆ and ₆, respectively. No theory is available for the secular resonance v₅. Numerical experiments by Froeschlé and Scholl yield quantitative and new qualitative results for orbital evolutions at the three principal secular resonances ₅, ₆, and ₁₆. These experiments indicate possible chaotic motion due to overlapping resonances. A secular resonance may overlap with another secular resonance or with a mean motion resonance. The role of the secular resonances as possible sources of meteorites is discussed.     

Free-convection effects on MHD flow past a porous plate with step function change in suction velocity

Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) ^1/2–1/2 - M magnetic field parameter - N _u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - ₁ suction velocity att0 - ₂ suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function     

Analysis of Multicolor Observations of 3C 66A in 1993-1998

The results of multicolor observations of the blazar 3C 66A, obtained in the course of the project OJ-94, are analyzed. It is established that the energy distribution of the variable source in the optical and IR ranges can be represented, on the average, by a power law: F ^-0.92. Since the blazar's emission is strongly polarized, there is no doubt of the synchrotron nature of the variable source responsible for the blazar's activity.     

The restricted problem of n+ν bodies

The simplest, conventional, and original form of the circular restricted problem of three bodies is briefly described in sidereal and synodic systems using dimensional and non-dimensional variables. This dynamical system is generalized to n2 primary bodies (from n=2) with masses M_i, 1in, interacting with arbitrary force laws (instead of only gravitational forces). The number of bodies of small mass mM_i not perturbing the primaries is increased from =1 to 1 where 1 and the minor bodies are allowed to interact with one another under arbitrary force laws. While the minor bodies (m) do not affect the motions of the primaries (M_i), the primaries influence the motions of the minor bodies with arbitrary force laws.For the case where n=2, 1, and only gravitational forces act on the system, an integral of the system is derived. It is shown that the energy integral of the general problem of N bodies and the Jacobian integral of the classical restricted problem of three bodies are limiting cases of this integral. The role of the integral in bounding the motion of the minor bodies is discussed. Several applications of this system are given.     

Photometry and Spectrophotometry of the Seyfert Galaxy MRK 509 over 23 Years Photometry And Spectrophotometry Of The Seyfert Galaxy Mrk 509

In the time period from 1972-1993, the Seyfert 1 galaxy Mrk 509 showed large variations of its optical continuum and broad emission line fluxes. The broad H and H emission lines have approximately the same profiles, which retain their shape during flux variations. The relationship between the continuum and emission line fluxes varies with time. The spectral energy distribution of the variable continuum based on UBVRI data has the form lgF() lg, with the dereddened = -0.60.     

Secular perturbations in general planetary theory

Based on a general planetary theory, the secular perturbations in the motion of the eight major planets (excluding Pluto) have been derived in polynomial form. The results are presented in the tables. The linear terms of second order with respect to the planetary masses and the nonlinear terms of first order up to the fifth (and partly seventh) degree with respect to eccentricities and inclinations were taken into account in the right-hand members of the secular system. Calculations were carried out by computer with the use of a system that performed analytic operations on power series with complex coefficients.

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qA ( ). . ( ) . .

     

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.     

On the Power in the Legendre Modes of the Solar Radial Magnetic Field

The power in the different modes of an expansion of the solar radial magnetic field at the surface in terms of Legendre polynomials,P , is calculated with the help of a solar dynamo model studied earlier. The model is of the Babcock–Leighton type, i.e., the surface eruptions of the toroidal magnetic field – through the tilt angle, , formed by the magnetic axis of a bipolar magnetic region with the east-west line – are the sources for the poloidal field. In this paper it is assumed that the tilt angle is subject to fluctuations of the form, = ()+ <> where <> is the average value and () is a random normal fluctuation with standard deviation which is taken from Howard's observations of the distribution of tilt angles. For numerical considerations, negative values of were not allowed. If this occurred, was recalculated. The numerical integrations were started with a toroidal magnetic field antisymmetric across the equator, large enough to generate eruptions, and a negligible poloidal field. The fluctuations in the tilt angle destroy the antisymmetry as time increases. The power of the antisymmetric modes across the equator (i.e., odd values of ) is concentrated in frequencies, _p, corresponding to the cycle period. The maximum power lies in the =3 mode with considerable power in the =5 mode, in broad agreement with Stenflo's results who finds a maximum power at =5. For the symmetric modes, there is considerable power in frequencies larger than _p, again in broad agreement with Stenflo's power spectrum.     

The short time-scale light variability of HD 153919 revisited

Using Fourier analysis techniques, we have analysed all the available sets of visual photometric data concerning the X-ray binary HD 153919. This was made in order to clear up the controversy on the possible existence or absence of the small amplitude light variability (T90 min).In this work, great effort has been made to keep a good level of homogeneity and objectivity. The main conclusion is that at the 99.4% confidence level, a periodicity (=15.5 day^–1) is detected in one data set. In this case, we can safely conclude that the short time-scale variability does exist! No other self-conclusive detection can be definitely reported; nevertheless, at the 90% confidence level, the star has a tendency to vary with characteristic frequencies of 15 day^–1, 30 day^–1 and possibly higher multiples.HD 153919 4U1700-37 V884 Sco.     

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.     

New hα survey of chromospherically active binaries

We had observed the high-resolution H profiles of fourteen chromospherically active binaries which are And, 3 Cam, 4 UMi, ² Sgr, Sgr, HR 7333, 33 Psc, UMi, And, UMa, 12 Cam, And, Aur and Dra from August 1990 to August 1991. The H emission and absorption equivalent widths, and the half widths and the radial velocities of these systems were determined. These data have a good supply for the information of the catalog of chromospherically active binary stars. The H profiles of HR 7333, 12 Cam, 4 UMi, UMi and And show marked emission filling in core, but 33 Psc, Sgr, Sgr and And systems show the H as the stronger absorption lines. The observed fourteen binaries presented very different activity levels.