Effect of drift-resonance broadening on radial diffusion in the magnetosphere

In the quasilinear theory of magnetospheric radial diffusion caused by fluctuating electrostatic (E) or magnetic (B) fields, the diffusion coefficientD _LLis proportional to the spectral density of E or B at the particle drift frequency ₃/2. Since ₃ varies withL at fixedM andJ (adiabatic invariants), the drift resonance =₃ can be maintained only transiently, and therefore is not perfectly sharp. Its bandwidth ^* is approximately (16D _LL /L ²₃)^1/3₃. In magnetospheric radial diffusion caused mainly by electrostatic fluctuations, the value of ^*₃ typically exceeds 0.4 for particle energiesE40 keV. However, the numerical value ofD _LLis correctly given (within 1% in all cases) by quasilinear theory because the spectrum of E is rather flat at resonance frequencies for which the bandwidth is an appreciable fraction of ₃. (Numerical conclusions are based on a quasilinear model forD _LLused successfully by Cornwall in 1972.)     

Slow rotational perturbations of Friedmann universes

In this work the rotational perturbations of the Friedmann universes are investigated. In the general case where none of the terms including (r, t) are neglected, for perfect fluid, the field equations belonging to the perturbed metric give =(t). In this case, since the condition =0 can be accomplished by a coordinate transformation, the solutions of the field equations reduce to those of the classical Friedmann equations. For this reason, the approximate solutions obtained by other authors become formal solutions without physical interest.     

Phase relation between the poloidal and toroidal solar-cycle general magnetic fields and location of the origin of the surface magnetic fields

The phase relation of the poloidal and toroidal components of the solar-cycle general magnetic fields, which propagate along isorotation surfaces as dynamo waves, is investigated to infer the structure of the differential rotation and the direction of the regeneration action of the dynamo processes responsible for the solar cycle. It is shown that, from the phase relation alone, (i) the sign of the radial gradient of the differential rotation (/r) can be determined in the case that the radial gradient dominates the differential rotation, and (ii) the direction of the regeneration action can be determined in the case that the latitudinal gradient (/) dominates the differential rotation. Examining the observed poloidal and toroidal fields, it is concluded that (i) the / should dominate the differential rotation, and (ii) the determined sign of the regeneration factor (positive [negative] in the northern [southern] hemisphere) describing the direction of the regeneration action requires that the surface magnetic fields should originate from the upper part of the convection zone according to the model of the solar cycle driven by the dynamo action of the global convection.     

On the reconstruction of the nonlinear force-free coronal magnetic field from boundary data

Using a simple model in which the corona is represented by the half-space domain = {z > 0} and the photosphere by the boundary plane = {z = 0}, we discuss some important aspects of the general problem of the reconstruction of the magnetic field B in a small isolated coronal region from the values of the vector B¦ measured by a magnetograph over its whole basis. Assuming B to be force-free in : (i) we derive a series of relations which must be necessarily satisfied by the boundary field B¦ , and then by the magnetograph data if the force-free assumption is actually correct; (ii) we show how to extract directly from the measured B¦ some useful informations about the energy of B in and the topological structure of its field lines; (iii) we present a critical discussion of the two methods which have been proposed so far for computing effectively B in from B¦ .     

Two-dimensional stochastic motions and the problem of differential rotation

This paper deals with the spatial dependence of the angular velocity in a rotating turbulent fluid sphere. The original turbulence unaffected by the global rotation is assumed to be two-dimensional where the stochastic force field producing the turbulence does not possess a radial component. By using results of earlier papers we proceed to the treatment of a rotational rate, , no longer small compared to _c (frequency of turbulent mode). It is shown that for _c the angular velocity increases with increasing radius but no latitudinal dependence exists. Contrary to this, for 2 _c an equatorial acceleration is possible and related to negativity of the two-dimensional eddy viscosity. Furthermore, the outer layers rotate faster than the inner ones. These findings coincide with Gilman's numerical results. Ward's observations, as well as the characteristic scales of supergranulation and giant cells, suggest the presence of negative two-dimensional eddy viscosity on the Sun.     

Distribution of polarization and intensity of radiation across the stellar disk and numberical values of atmospheric characteristics governing this distribution

Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT _eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT _eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT _eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk.     

The interaction of matter and radiation in the hot model of the Universe,II

Heating of the primaeval plasma prior to the epoch of recombination results in distortions in the Rayleigh-Jeans region of the microwave relic radiation spectrum (1–60 cm, or more exactly =2.5_–7/8 cm). The present observational data allow limits to be set to such energy injection from which follow upper limits to (a) the amount of antimatter in the universe; (b) the parameters of primaeval turbulence; and (c) the adiabatic fluctuation spectrum for small masses (M<10¹¹ M ).If the heating takes place prior to the epocht=10_1012/5 sec (and in particular at the annihilation of electron-positron pairs atT10⁸–10¹⁰ K,t<300 sec), no observable distortions are expected in the relic radiation spectrum. Here =/_crit is the dimensionless average density of matter in the universe.Translated from the Russian by D. F. Smith.     

Slowly rotating cosmological viscous fluid Universe

The perturbation by a spherical rotating shell is investigated in a homogeneous and isotropic cosmological model of viscous fluid distribution to first order in angular velocity (r, t) of matter and the metric rotation function (r, t) which is uniform and non-uniform the exact solutions for (r, t) are obtained for all cosmological models. The physical properties of these solutions are discussed.     

Comments on ‘outward transport of angular momentum...’ by E. M. Drobyshevski

Drobyshevski's effect for maintaining the equatorial acceleration of the Sun is characterized to be of order/R where represents the eddy size andR the solar radius. The weakness of this mechanism is, therefore, not surprising.Furthermore we have discussed the idea of replacing the two-dimensional eddy tubes by spherical eddy configurations. We can state here that a theory which is linear in the rotational rate and uses the radial direction as the only source (besides) of anisotropy cannot explain the observed phenomenon of differential rotation.     

Structure of the martian north polar cap and vernal hood system at L s 61‡–66‡ of the 1995 apparition

The boundary and internal structure of the north polar deposits and polar hood vernal remnant on Mars have been mapped at L _s 61–66 on the hemisphere centered on longitude = 0, using images obtained in Feb–Mar 1995 with the Swedish Vacuum Solar Telescope on La Palma. On red light images, several internal rifts, including the historically well documented Rima Tenuis and Rima Hyperborea, as well as an internal, long absent, annular rift were mapped. The ground cap was asymmetric with a mean boundary at 72 N for = 270, increasing to 77 N at = 90. Images in green light showed the locations of high opacity hood clouds, including an extensive outflow to 67 N at 100. The state of the cap and hood is compared with the findings of previous studies and the historical significance of the annular rift structure is discussed. It is concluded, based on the structure of the deposited laminae, that the north polar climate was nearly, or possibly slightly milder than, normal at the northern hemisphere spring season studied.     

The cosmological model of Brans-Dicke theory

We use the generalized Brans-Dicke theory, in which the Pauli metric is identified to be the physical space-time metric, to study the Universe in different epochs. Exact analytical expressions for dilaton field , cosmological radiusR and density parameter are obtained fork=+1,0,–1 Universe in the radiation-dominated epoch. For matter dominated Epoch, exact analytical expressions for Hubble parameterH, cosmological radius, dilaton field, deceleration factorq, density parameter and the gravitational coupling of the ordinary matter are obtained for the flat Universe. Other important results are: (1) the density parameter is always less than unity for the flat Universe because the dilaton field plays a role as an effective dark matter, and (2) the new Brans-Dicke parameter must be larger than 31.75 in order to consistent with the observed data.     

Cyclotron waves in the solar wind

Cyclotron waves in the solar wind near 1 AU with frequencies well below the electron cyclotron frequency and wavelengths much larger than the electron cyclotron radius but less than the proton cyclotron radius are considered. The cyclotron radii are defined from parallel thermal velocity of electron component and proton component with respect to the interplanetary magnetic field. No LH cyclotron waves are found to propagate for _p < 0, where _p 1 –T _p/T _p is the temperature anisotropy of the proton component with respect to the interplanetary magnetic field. The damping or growth of RH cyclotron waves is found to depend on the frequency range and the temperature anisotropy of the proton component. The RH cyclotron waves are damped in the frequency range _r | _p | _p for _p < 0, where _p is the proton cyclotron frequency. RH cyclotron instabilities occur in the frequency range | _p | _p > _r > | _p | _p /(1– _r ) for _p < 0. The marginal state is at _r =| _p | _p .Abstract presented at theInternational Symposium on Solar-Terrestrial, São Paulo, Brazil, 17–22 June, 1974     

Isothermal self-similar blast wave theory of supernova remnants driven by relativistic gas pressure

We investigate the spherically symmetric, self-similar flow behind a blast wave from a point explosion in a medium whose density varies with distance asr ^– with the assumption that the flow is both isothermal and contains a relativistic component of pressure. A self-similar solution is shown to exist only if both the blast wave speed,u _s ,and the local sound speed,w, are constant. If [(1–w ²/c ²)] lies in 1>>0, there exists a critical point in the radial distance-flow velocity plane. To be physically acceptable, the solution must pass through the origin and through the critical point and then through to the blast front; solution branches between these points exist, although a proper connection at the critical point has not been demonstrated. If <0, a continuous single-valued solution does not exist. If 2>>1, the critical point is beyond the blast curve and the flow is subsonic everywhere. For 2<<3, the critical point disappears, but a new one arises. To be physically acceptable, the flow must by-pass this new critical point. It is shown that it does. The dependence of the solutions of is non-analytic for <1, so that interpolation between neighboring values of is not permitted. We investigate the stability of these isothermal blast waves to spherically symmetric but non-self-similar perturbations. If 3>>3/2 or 0<<1, the solutions are shown to be definitively linearly unstable against short wavelength disturbances near the blast front, they are also unstable there in 3/2>>1 unless the flow meets the blast front atprecisely the velocity (normalized) of (2–1)^1/2/(3–2)^1/2. The solutions are also unstable for all in 1>>0 near the critical point. Since there is no characteristic time scale in the system, all the instabilities grow as a power law in time rather than exponentially. The existence of these instabilities implies that initial deviations do not decay and the system does not tend to a self-similar form. We conclude that isothermal self-similar blast waves do not provide a valid model for a supernova remnant driven by a relativistic gas pressure. Since the validity of the adiabatic blast wave models has elsewhere been shown to be questionable, it is doubtful whether the self-similar property can be involved at all in the case of supernova remnants. This raises serious questions of interpretation of quantities deduced for supernova remnants on the basis of the use of self-similar models.     

Theory of gravitational radiation of the (Ω,A µν )-field

Further exploration of the -field theory as first proposed by Yu (1989) is here presented to cover the equation of motion of a test particle which induces gravitational radiation. The same theory is shown to contain an exact gravitational radiation equation derived as a logical consequence of field equations without extra postulates. In this general dynamic context the theory is renamed The (,A _µ )-field Theory.     

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     

Fe XXI emission line ratios as electron temperature diagnostics for the coronae of cool stars

A method for the reconstruction of the linear force-free magnetic field in a bounded domain (as a rectangular box, ) is presented here. The Dirichlet boundary-value problem for the Helmholtz equation is solved for the B _z component specified at the boundary. Chebyshev's iteration method with the optimal rearrangement of the iteration parameters sequence was used. The solution is obtained as for the positive-definite, and for the non-sign-definite difference analogue of the differential operator ² u + ² u. Specifying two scalar functions, B _x and B _y on the intersection of the lateral part of the boundary with one selected plane z = constant, and using B _z inside the , we have found B _x and B _y throughout .The algorithm was tested with the numerical procedure which gives the analytic solution B of the linear force-free field (LFFF) equations for the dipole in a half-space. The root-mean-square deviation of the analytic solution B from the calculated B does not exceed 1.0%. Boundary conditions for the B calculation were taken as given by the analytic LFFF solution B. Comparison of B with B, which was calculated by the potential non-photospheric boundary conditions, show that they differ significantly. Thus, the specification of boundary conditions at non-photospheric boundaries of the volume under consideration is of particular importance when modeling the LFFF in a bounded volume.The algorithm proposed here allows one to use the information about magnetic fields in the corona for the modeling of LFFF in a limited domain above an active region on the Sun.     

Rapidly rotating polytropes in the post-Newtonian approximation to general relativity

The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order ⁴, where is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter = ²/2G _c and a relativity parameter, =p _c / _c C ² , wherep _c and _c are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of order ². The critical rotation parameterv _c , which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of . Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5.     

The nonlinear solar dynamo and differential rotation: A Taylor number puzzle?

We consider dynamically consistent mean-field dynamos in a spherical shell of incompressible fluid. The generation of magnetic field and differential rotation is parameterized by the - and -effects, respectively. Extending previous investigations, we include now the cases of moderate and rapid rotation in the sense that the inverse Rossby number can approach or exceed unity: This can lead to disk-shaped -contours, which are in better accordance with recent results of helioseismology than cylindrical -contours. On the other hand, in order to obtain -dynamo cycles the Taylor number has to be so large, that eventually cylindrical -contours become unavoidable (cf. Taylor-Proudman theorem). We discuss the different possibilities in a state diagram, where the inverse Rossby number and the relative correlation length are taken as the elementary parameters for mean-field dynamos.     

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.     

Electron-cyclotron maser emission from the sun and stars: Variations with plasma temperature and density

Very bright and highly circularly polarized radio bursts from the Sun, the planets, flare stars, and close binary stars are attributed to the electron-cyclotron maser instability. The mode and frequency of the dominant radiation from the maser instability is shown to be dependent on the plasma temperature and the ratio _p / _e of the plasma frequency to the electron-cyclotron frequency. For the emission from the Sun _p / _e is probably greater than 0.3 and for 0.3 < _p / _e < 2 the emission can be either in the x-mode at the second harmonic or in the o- and/or z-modes at the fundamental. For higher _p / _e , the emission moves to higher harmonics of _e with the emission being predominately in the z-mode when _p / _e > 3.Proceedings of the Workshop on RadioContinua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.