Study of the nonradial directional property of the rays of the streamer belt and chains in the solar corona

Based on analyzing corona images taken by the LASCO C1, C2, and C3 instruments, a study is made of the behavior of the streamer belt spanning one half of the 1996–2001 cycle of solar activity, from minimum to maximum activity, in the absence of coronal mass ejections. It is shown that: (1) The position of the streamer belt relative to the solar equator is generally characterized by two angles: _o and _E, where _o is the latitudinal position (near the solar surface) of the middle of the base of the helmet, the top of which gradually transforms to a ray of the streamer belt with a further distance from the Sun, and _E is the latitude of this ray for R>5–6 R from the Sun's center where the ray becomes radial. (2) Only rays lying at some of the selected latitudes _o retain their radial orientation (_oE) throughout their extent. Namely: _o0° (equator), _o±90° (north and south poles), and the angle _o lying in the range ±(65°–75°) in the N- and S-hemispheres. (3) A deviation of rays from their radial orientation in the direction normal to the surface of the streamer belt occurs: for latitudes _o<|65°–75°| toward the equator (>0°) reaching a maximum in the N and S hemispheres, respectively, when _OM40°, and _OM–42° for latitudes _o>|65°–75°| toward the pole (<0°). The regularities obtained here are a numerical test which can be used to assess of the validity of the theory for describing the behavior of the Sun's quasi-stationary corona over a cycle of solar activity.     

A simplified model solar atmosphere

A simplified representation of the temperature distribution in the solar photosphere is proposed: ( ₀) = ₀ - ₁ log ₀. An expression is derived for the emergent continuous spectrum from the simple model. The limitations and applications of the simple model are discussed.     

Depolarization of solar bursts due to scattering by low-frequency waves

The possibility is explored that fundamental plasma emission in solar radio bursts of types I, II, and III is depolarized due to scattering off low-frequency waves. Three ways in which depolarization might occur are identified: (1) one or several large-angle scatters, (2) several small-angle scatters close to the plasma level, and (3) many small-angle scatters well above the plasma level. It is pointed out that the degree p of polarization (p = 1 initially) may be approximated by p() = cos after one large-angle scatter through an angle , and that for backscatter ( > /2) the sense of polarization changes (from o-mode to x-mode senses). Possibility (2) involves coupling between the o- and x-mode components through their longitudinal parts, and is explored in some detail. The wave vectors k required for the scatterings are identified, and it is suggested that ion-sound waves are suitable for possibility (1) and whistlers for possibility (2). The whistlers may be generated by the streaming electrons themselves.Large-angle scattering is favourable for depolarizing type I emission, as proposed by Wentzel, Zlobec, and Messerotti (1986). Scattering by whistlers near the plasma level is favourable for depolarizing type III bursts. Several predictions are made based on these possibilities.     

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.     

Polarization of fundamental type III radio bursts

The fundamental of type III bursts is only partially polarized, yet all theory for emission near the plasma frequency predicts pure o-mode emission. I argue depolarization is inherent in the burst itself. The o-mode radiation is intensely scattered and mode-converted when it temporarily falls behind its own source and finds itself in the medium that is already disturbed by the electron beam. In particular, mode conversion is very efficient and yet causes only modest angular scattering at the height were _p + 0.5.The predicted minimum polarization nearly equals the polarization of the harmonic, as observed. Spike polarization is naturally explained by the earlier arrival of the scattered o-mode. Additional residual polarization depends on the refraction at the site of emission; larger beam velocities imply higher polarization, as observed, because a larger fraction of the radiation escapes without mode-conversion. The polarization at the frequencies where U-bursts reverse is of particular interest.Support is acknowledged from the NSF Solar-Terrestrial Research Program.     

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.     

The effect of metallicity on the empirical relations for RR Lyrae stars

It has empirically been shown that, for a given value of the effective temperature, the correction in (B-V) due to line blanketing varies linearly with the metallicity parameter S. Next, on the basis of considerations different from those used to obtain a similar result by Sturch (1966), a relation between reciprocal effective temperature _e (=5040/T _e ) and intrinsic line-free colour index(B-V) _o,c has been obtained based on the _e and (B-V) values for five RR Lyr variables. Relations between _e and intrinsic colour(B-V) _o for different groups of stars having a S parameter in the range 0S11 have also been obtained.     

cD galaxies of apparent supergiant sizes due to the curvature of space

By combining two two-dimensional subspaces, closed into themselves due to curvature, it is possible to create a model of three-dimensional space of the same properties. If the Universe is a space of this type, its effect is that of a monstrous lens. Close objects are observed to diminish according to the normal law of perspective; however, the remote galaxies are seen to be very highly magnified.The apparent angular size² of a galaxy is more than the size¹ in flat space according to relation:² =¹ cosec , where is the angular distance from the observer to the galaxy. The diameter² d of a galaxy in curved space must be in the same relation to a diameter¹ d with no curvature of space:² d=¹ d cosec . The apparent angular size² and diameter² d are distorted shapes in consequence of an optical illusion caused by the spatial curvature.It is necessary to distribute the multitude of galaxies into two parts in accordance with their location on the close or reverse hemihypersphere of the Universe. The minimum of apparent angular size² of a galaxy of diameter¹ d is at the equatorial zone.The most likely candidates for location in the reverse hemi-hypersphere are cD's of apparent supergiant sizes due, probably, to the curvature of space. The existence of supergiant sizes of galaxies is the second indirect proof, besides superluminal velocities, that the Universe is closed into itself through curvature. The third indirect evidence, i.e., inductive confirmation of the same fact, is the superposition of galaxies which need not inevitably be a new alternative to the present theories of collisions, cannibalism, merger, etc.The fourth indirect proof of the positive curvature of the Universe is the occurrence of background radiation, because that must vanish in hyperbolic space irrespective of its origin. The gravitational lens effect acquires another theoretical form, as usual, in the case of remote galaxies, because it is impossible to distinguish between gravitator and lensing image.     

The effect of luminosity-redshift correlation on the analysis of the angular size-redshift relation for radio galaxies

The variation of radio luminosity with redshift and its effect on the analysis of the angular size-redshift ( –z) relation for a bright radio source sample (s ₁₇₈ 10Jy) has been investigated. By assuming a power law dependence of luminosity on redshift of the formP (1 +z), it was found that 4.4 (with correlation coefficientr 0.99) for at leastz 0.3. Correction for such a strongP – (1 +z) correlation when considering the –z data for the sample led to a steeper –z slope. This could be explained by assuming linear size evolution of the formD (1 +z)^–n withn = 2.8 – 3.3 consistent with both theoretical results and those obtained for more homogeneous source samples.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

High velocity neutron stars and γ-ray bursts

The observations of the BATSE instrument on the Compton Gamma-Ray Observatory show that the spatial distribution of -ray burst sources is isotropic but radially non-uniform. As is well known, the spectral features, the time histories and the X-ray tails present in some -ray bursts suggest that they may arise from galactic neutron stars. But, low velocity neutron stars born in the Galactic disk would concentrate toward the galactic plane and center, and could not fit the BATSE results. However, the high velocity neutron stars with velocity 1000 km s^–1 may escape from the Galactic gravitational field and form a nearly isotropic distribution. Here we calculate the three statistical values of V/V _max, sin² b and cos as functions of the intensitiesC _max/C _min and find that they could be fitted by the distribution of high velocity neutron stars under the assumption that the high velocity neutron stars should turn on as -ray burst sources only after some time (perhaps after they have ceased to be radio pulsars). Our calculation shows that the statistical value of cos is more sensitive than sin² b to the angular distribution of high velocity neutron stars, i.e. the deviation of cos from 0 is more readily detected than the deviation of sin² b from 1/3, so we expect that with the increasing sensitivity of instrument and the more exact value of cos , it is possible to determine whether this high velocity neutron star model is correct. Some results are discussed in the text.     

Effect of Krein signatures on the stability of relative equilibria

We consider the linear stability of the equilibrium points of the generic rotating potentials U(r), U(r, ), U(r, and U(r, , . The stability analysis is performed using the concept of Krein's signature. This signature is calculated for all eigenvalues of the above potentials. Thereby, the Lagrangian points of the restricted three-body problem and the synchronous satellites of oblate and prolate planets are also studied. We find also the new positions of the eigenvalues for perturbations of the original L ₄ and L ₅ points of Mars, Jupiter, Saturn, Uranus and Neptune. Finally, we study the problem with the mass ratio µ close to the critical value and the stability of geostationary satellites perturbed by the Moon.     

On symmetrical planetary corotations

Exact corotations are equilibrium points in the phase space of the asteroidal elliptic restricted problem of three bodies averaged over the synodic period, at a mean-motions resonance. If the resonant critical angle is =(p+q) _jup –p–q, exact corotations are double resonant motions defined by the conditionsd/dt=0 andd(– _jup )/dt=0. The first condition is characteristic of the periods resonance(p + q) : p and the second one is a secular resonance equivalent to that usually known as thev ₅-resonance. This paper presents the symmetric solutions =0 (mod ), = _jup (mod ). Corotations have a coherence property which is unique in non-collisional Celestial Mechanics: An elementary calculation shows that, in the neighbourhood of these solutions, the motions cluster aroundp independent longitude values and are, in each cluster, as close together as and are close to the equilibrium values.     

Some elementary geometric aspects in extending the dimension of the space of instants

A local geometric construction is proposed on thepartially ordered set of instantsI. A totally ordered subsetC(I)I is assumed to have 3-dimensional affine coordinate structure,without a specified metric, called the -space ofC(I). Guided by a strong analogy with analytical mechanics theT-configuration space (, ), a real parameter, is constructed where-upon the usual Hamilton-Jacobi theory establishes a simple geometrical construction, viz., the complete figure from the calculus of variations. The duration function, dur:C(I)R is associated withtemporally equidistant hypersurfaces through which pass a congruence of extremal curves to the fundamental integral.     

On mass flow in a complex sunspot

The velocity field in a large complex sunspot is investigated in Fe i 6302.5 Å and in H with a spatial resolution of about 2.5. The Evershed flow is almost parallel to the solar surface. For the inclination angle between the velocity and the horizontal = 4.4°±1.3° is estimated; = 11° is the definite upper limit.     

The Energy Equation in the Lower Solar Convection Zone

As a consequence of the Taylor–Proudman balance, a balance between the pressure, Coriolis and buoyancy forces in the radial and latitudinal momentum equations (that is expected to be amply satisfied in the lower solar convection zone), the superadiabatic gradient is determined by the rotation law and by an unspecified function of r, say, S(r), where r is the radial coordinate. If the rotation law and S(r) are known, then the solution of the energy equation, performed in this paper in the framework of the ML formalism, leads to a knowledge of the Reynolds stresses, convective fluxes, and meridional motions. The ML-formalism is an extension of the mixing length theory to rotating convection zones, and the calculations also involve the azimuthal momentum equation, from which an expression for the meridional motions in terms of the Reynolds stresses can be derived. The meridional motions are expanded as U _r(r,)=P ₂(cos)₂(r)/r ²+P ₄(cos)₄(r)/r ² +..., and a corresponding equation for U (r,). Here is the polar angle, is the density, and P ₂(cos), P ₄(cos) are Legendre polynomials. A good approximation to the meridional motion is obtained by setting ₄(r)=–H₂(r) with H–1.6, a constant. The value of ₂(r) is negative, i.e., the P ₂ flow rises at the equator and sinks at the poles. For the value of H obtained in the numerical calculations, the meridional motions have a narrow countercell at the poles, and the convective flux has a relative maximum at the poles, a minimum at mid latitudes and a larger maximum at the equator. Both results are in agreement with the observations.     

Multiple expansion of the tidal potential

The Earth tidal deformation causes an additional gravitational potential. Its effect on the Moon orbital motion has been studied by several authors.In this contribution, we develop this additional potential without specifying the inertial frame chosen.For this purpose, we use the properties of the representation of rotation groups in 3 dimensions space. We finally obtain the interaction potential between the distorted Earth and the Moon which is a necessary preliminary to the study of the evolution of the Earth-Moon system.Nomenclature T.R.O Tide raising object - (, , ) Spherical coordinates of the T.R.O. - (J, _E ) Earth spin axis orientation. _E is the longitude of the ascending node of Earth's equator on thexy-plane - (a ,I ,e , , ,M ) Elliptics elements of the T.R.O     

The loss-cone driven instability for Langmuir waves in an unmagnetized plasma

Analytic and numerical results are presented for the growth rate of Langmuir waves due to a loss-cone distribution of energetic electrons. The effect of the magnetic field on the wave-particle interaction is ignored, and the resonance condition is described in terms of a resonance hyperboloid in momentum space. The collisional evolution of a distribution of magnetically trapped electrons is followed numerically to show how a gap distribution develops. The growth is most favorable for an intermediate sized loss cone ( 45 °) and a gap distribution in which the mean energy of the suprathermal electrons is much larger than the thermal energy of the background electrons. It is plausible that loss-cone gap distributions do develop in the solar corona, and that they should lead to second harmonic plasma emission weakly polarized in the x-mode.     

Рассеяние света на анизотропных частицах

, — . , , . , , .