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 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.     

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 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 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 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     

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 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.     

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.     

Spectrophotometric study of the comet P/Swift-Tuttle (1992t)

Spectrophotometric observations of the periodic comet P/Swift-Tuttle (1992t) were taken through 104 cm telescope of Uttar Pradesh State Observatory Nainital, using EG & G spectrograph coupled with optical multichannel analyser and reticon array detector in the optical region of the spectrum, during four nights of December 1992. The molecular emission bands of CN ( = 0) at 3888 Å, CH + C₃ at 4050 Å and C₂ ( = +1,0, –1) at 4690 A, 5160 Å and 5530 Å respectively, were identified. Column densities and production rates have been determined.     

Cold plus hot dark matter and structure formation of the universe

Cold plus hot (neutrino) dark matter models are studied and compared with the tilted cold dark matter models (which have a non-Zel'dovich initial density perturbation spectrum). For the hybrid dark matter models, a simpler treatment for the relativistic neutrinos is presented. The numerical results of this treatment are shown to be in good agreement with those given by other authors. Comparing the theoretical and the observational results of the quadrupole fluctuations of the cosmic background radiation and the large-scale velocity field of galaxies, the hybrid dark matter models require a fraction of neutrino density 0.3, a fraction of cold dark matter _c 0.7 and a number of massive neutrino speciesN = 1 for the case of Hubble's constantH ₀ = 50 km s^–1 Mpc^–1. The distribution of comoving number density of quasars at high redshifts is studied using the Press-Schechter theory. The calculations show that the hybrid dark matter model ( _c 0.7, 0.3) and the tilted CDM model withn = 0.7 0.8 both account for the observed quasar abundance at high redshift.     

Scanner observations of the Be starsν Gem,κ Ori,β Mon andω CMa

The photoelectric spectrophotometric scans of the Be stars Gem, Ori, Mon and CMa have been analyzed to find out few stellar parameters. The absolute energy distributions of these stars in the wavelength range 350–750 nm have been given. Their effective temperatures and gravities have been estimated from comparisons with non-LTE model atmospheres. The stars Gem and Mon have been found to have Balmer discontinuities in emission. The excess emission in the region 620–750 nm has been observed for Mon and CMa. The evolutionary aspects of these stars are discussed and their masses have been estimated.     

Inverse compton effect and the colorimetric characteristics of flare stars

It is shown that the observed color diagrams(U-B) _f (B-V) _f for pure flare emission of UV Cet type flare stars may be explained within the framework of a fast electron hypothesis. We point out the essential influence on these color indices of the two following factors: (a) the deviations of the normal radiation capability of the star in the infrared region of spectra (on 3.6 m, 4.4 m, and 5.5 m) from the Planckian distribution; (b) the location of the cloud (source) of fast electrons around the star (flare geometry effect). Under the real conditions of the generation of flares around the star the frequency transformation law at the photon-electron interaction has a view =n²₀, wheren may take the different values-from 0.15 up to 4; it depends on the cloud-star-observer geometry. By the observed colors of the flare emission may be understood, in principle, the location of flare source around the star. A possible role of reflection effect at the generation of stellar flares is outlined.     

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     

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.     

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.     

К теории кривых Блеска сверхновых звезд

, . . . (10R ) ( 10 000R ). NGC 5457, NGC 6946 NGC 5236. , , II I . . . , . . 10⁵⁰÷10⁵² , .     

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.     

An Improved Optical Model for the Non-LTE Problem for the CO2 Molecule in the Atmosphere of Mars: Nighttime Populations of Vibrational States and the Rate of Radiative Cooling of the Atmosphere

The estimates of the population of excited vibrational states of the CO₂ molecule and of the rate of radiative cooling of the atmosphere in the 15-m CO₂ band are given for the nighttime mesosphere and thermosphere of Mars. For the first time, these estimates are made (1) with allowance for the overlap of lines in the 15-m band; (2) for a wide set of vibrational states of seven isotopes of the CO₂ molecule, which was used earlier in the solution of a similar terrestrial problem; and (3) using the rate constant for quenching of the CO₂(01¹0) state in collisions with oxygen atoms, which has been recently measured for low temperatures by Khvorostovskaya et al. (2002). The main results are as follows. 1. The approximation of isolated lines provides a satisfactory accuracy of determining the radiative cooling rate and overestimates vibrational temperatures of the states of the ₂ mode by no more than 3 K for the ¹²C¹⁶O₂ molecule and by no more than 2 K for low-abundant isotopes of the CO₂ molecule. 2. A reasonably high accuracy of estimating the cooling rate can be achieved by taking into account only fundamental vibrational transitions in ¹²C¹⁶O₂, ¹³C¹⁶O₂, ¹⁶O¹²C¹⁸O, and ¹⁶O¹²C¹⁷O molecules and the hot transitions 2_{2 2} and 3₂ 2₂ in the ¹²C¹⁶O₂ molecule. 3. The vertical profile of the total rate of radiative cooling displays two peaks. The maximum near a height of 130 km is very sensitive to temperature and to the ratio of the mixture for oxygen in the atmosphere.