On the presence of electric currents in the solar atmosphere

An elementary analysis based on Ampére's Law is given to separate the general magnetic field above the photosphere into two parts B=B ₁+B ^*. The field B ₁ is a potential field due to electric currents below the photosphere. The field B ^* is produced by electric currents above the photosphere combined with the induced mirror currents. By symmetry, B ^* has a set of field lines lying entirely in the plane z = 0 taken to be the photosphere. This set of field lines can be constructed from given vector magnetograph measurements and represents all the information on the electric currents above the photosphere that a magnetograph can provide. Theoretical illustrations are given and the implications for data analysis are discussed.     

Morphological classification of new galaxies with a UV excess

The results of a morphological classification of 580 galaxies with a UV excess, included in the lists in [M. A. Kazarian, Astrofizika,15, 5 (1979); ibid.,15, 193 (1979); M. A. Kazarian and É. S. Kazarian, ibid.,16, 17 (1980); ibid.,18, 512 (1982); ibid.,19, 213 (1983)], are presented. For this we have developed a set of symbols, using the types E, S, and Ir introduced by Hubble, as well as symbols introduced by other authors and us. This set enabled us to make the morphological classification. Direct photographs obtained on the 2.6-m and 6-m telescopes were used to classify 141 of the galaxies (over 24%), while Palomar Atlas charts were used for the remaining 439 galaxies. These galaxies were divided into two groups based on classification conditions, and data on each group are given in Tables 1 and 2, respectively. The results for each group, given in Table 3, show that with the transition from early types, such as C and E, to later types, such as S and Ir, the relative number of galaxies going into one group (Table 1), in which the classification was based on direct photographs, increases in comparison with the number going into the other group (Table 2).Translated from Astrofizika, Vol. 39, No. 3, pp. 431–439, July–September, 1996.     

Modeling the Resistive MHD by the Cese Method

In this paper, the Space–Time Conservation Element and Solution Element (CESE) method is applied to 2.5-dimensional resistive magnetohydrodynamics (MHD) equations in Cartesian coordinates, with the purpose of modeling the magnetic reconnection study. To show the validity and capacity of its application to MHD reconnection problem, spontaneous fast reconnection and magnetic reconnection in multiple heliospheric current sheets are studied, which show good consistency with those obtained formerly by other authors. In order to assess the ∇ ⋅ B = 0 constraint numerically, the contours and evolution of ∇ ⋅ B are analyzed. The numerical results tell us that the CESE numerical scheme not only has good numerical resolution but also can keep the divergence-free condition for magnetic fields in the reconnection problems during the evolutionary process without any special treatment.     

Does IMF By induce the cusp field-aligned currents?

A well established correlation exists between the IMF B_y and the cusp field-aligned and horizontal currents (Wilhjelm et al., 1978). The northern and southern cusp currents may be parts of one large scale current system (D'Angelo, 1980) flowing mainly at the magnetopause and driven by the z-component of the solar wind electric field. Primdahl and Spangslev (1981) suggested that the large scale current system seems to shield out the IMF B_y from the interior of the magnetosphere. This paper proposes that the currents are induced by the change of sign of B_y at the IMF sector boundary crossings, and argues that the time constant for decay of the currents may well be one week or larger. The percentage errors in inferring the IMF sector polarity from the Godhavn H magnetogram increases with increasing time since the last sector boundary crossing. This is in accordance with a steady decay of the induced currents. Finally experimental tests are proposed to demonstrate the feasability of and possibly distinguish between the mechanisms.     

Nonlinear Force-Free Modeling of Coronal Magnetic Fields Part I: A Quantitative Comparison of Methods

We compare six algorithms for the computation of nonlinear force-free (NLFF) magnetic fields (including optimization, magnetofrictional, Grad–Rubin based, and Green's function-based methods) by evaluating their performance in blind tests on analytical force-free-field models for which boundary conditions are specified either for the entire surface area of a cubic volume or for an extended lower boundary only. Figures of merit are used to compare the input vector field to the resulting model fields. Based on these merit functions, we argue that all algorithms yield NLFF fields that agree best with the input field in the lower central region of the volume, where the field and electrical currents are strongest and the effects of boundary conditions weakest. The NLFF vector fields in the outer domains of the volume depend sensitively on the details of the specified boundary conditions; best agreement is found if the field outside of the model volume is incorporated as part of the model boundary, either as potential field boundaries on the side and top surfaces, or as a potential field in a skirt around the main volume of interest. For input field (B) and modeled field (b), the best method included in our study yields an average relative vector error E_n = 〈 |B−b|〉/〈 |B|〉 of only 0.02 when all sides are specified and 0.14 for the case where only the lower boundary is specified, while the total energy in the magnetic field is approximated to within 2%. The models converge towards the central, strong input field at speeds that differ by a factor of one million per iteration step. The fastest-converging, best-performing model for these analytical test cases is the Wheatland, Sturrock, and Roumeliotis (2000) optimization algorithm as implemented by Wiegelmann (2004).     

On discontinuous plasma flows in the vicinity of reconnecting current sheets in solar flares

The question about the interpretation of numerical experiments on magnetic reconnection in solar flares is considered. A correspondence between the standard classification of magnetohydrodynamic discontinuities and the parameters characterizing the mass flux through a discontinuity and the magnetic field configuration has been established within a classical formulation of the problem on discontinuous magnetohydrodynamic flows. A pictorial graphical representation of the relationship between the angles of the magnetic field vector relative to the normal to the discontinuity plane on both its sides has also been found. The relations between the parameters of a two-dimensional discontinuous flow have the simplest form in a frame of reference where the magnetic field lines (B) are parallel to the matter velocity (u)—the deHoffmann-Teller frame. The question about the transformation of the magnetic field configuration when passing to a “laboratory” frame of reference where (v · B) ≠ 0, i.e., an electric field is present, is considered in this connection. The result is applied to the analytical solution of the problem on the magnetic field structure in the vicinity of a reconnecting current sheet obtained previously by Bezrodnykh et al. The regions of nonevolutionary shocks are shown to appear near the endpoints of a current sheet with reverse currents.     

Rocket measurements of electric fields,electron density and temperature during different phases of auroral substorms

On 27 January 1979, three rocket payloads were launched from Kiruna, Sweden into different phases of two successive auroral substorrns. Among other experiments, the payloads carried the RIT double probe electric field experiments providing electric field, electron density and temperature data which are presented here. These data supported by rocket particle observations are discussed mainly in association with ground-based observations (magnetometer, TV) and very briefly with GEOS electric field data. The motions of the auroral forms as obtained from auroral pictures are compared with $\text{E × B}\text{/B}{}^2$ drifts and the currents calculated from the rocket electric field and density measurements with the equivalent current system deduced from ground-based magnetometer data (Scandinavian Magnetometer Array).     

Light curves analysis of AB Andromedae

The new B and V light curves of the eclipsing variable AB And obtained during 1979 are analysed. Frequency Domain techniques is used and new geometric and photometric elements are given.     

Electric current helicity in the solar atmosphere

In the theories of solar magnetism, kinetic and magnetic helicities, which arise as a consequence of the rotation of the Sun, play a key role. The dynamo for the main field is assumed to operate in the convection zone. The solar rotation also may be the ultimate cause for the generation of dc electric currents in the atmosphere, needed as the energy source for flares. Then in the atmosphere the electric current helicity, H _C = B · × B, which is a pseudo-scalar quantity, should be antisymmetric about the equatorial plane. An inspection of 16 active regions, for which H _C has been estimated by using extrapolation of measured photospheric magnetic fields, leads to the result that the electric current helicity is predominantly negative in the northern and positive in the southern hemisphere. The helicity of the large-scale currents generated according to standard dynamo theory by the alpha effect in the convection zone is just opposite in sign. Current generation due to rotational motions of sunspots and other magnetic elements in accordance with the global differential rotation, i.e., counter-clockwise in the northern and clockwise in the southern hemisphere, however, can explain the rule found. Also in some alternative dynamo models for the global field, in which the dynamo operates at the base of the convection zone, the large-scale current helicity generated by the alpha effect has the sign needed.     

Photovisual light curve and photometric elements of the eclipsing nucleus of the planetary nebula Abell 63

The firstV-photoelectric light curve (on theUBV system) of the eclipsing variable UU Sagittae (constituting the central star of a faint planetary nebula Abell 63) was obtained in 1979 with the 74 in. reflector at the Kottamia station of Helwan Observatory in Egypt, and analysed for the photometric elements of the system. Some of the geometrical elements obtained by us differ significantly from those previously deduced by Bondet al. (1978) from theirB-light curve secured in 1976; but there is no reason to suspect from this that any physical change has taken place in the system between 1976 and 1979.The most significant feature of the light curve of UU Sge (in both colours) is the large amplitude of the reflection effect exhibited between minima, as well as the fact that the secondary minimum appears to be almost wholly due to an eclipse of reflected light. This, combined with the depths of the alternate minima observed in both colours, leads us to conclude that the effective temperature of the O-type component is probably not much higher than 30 000 K, while that of the secondary component is not less than 6000 K (corresponding to a subgiant of spectral class close to G0).     

Isothermal magnetostatic atmospheres

An investigation of a family of isothermal magneto-static atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is carried out. The distributed current in the model J is directed along the x-axis where x is the horizontal ignorable coordinate. The current J is taken proportional to the square of the magneto-static potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of solution examples are displayed depending on the four free parameters in the solutions. Three of these parameters determine the source currents for the potential field solution of the family, whereas the fourth parameter determines the magnitude of the distributed current. The solutions illustrate the contribution of the anisotropic J × B force (B, magnetic field induction), the gravitational force, and gas pressure gradient to the force balance.     

Coronal magnetic-field model with non-spherical source surface

Previous global models of coronal magnetic fields have used a geometrical construction based on a spherical source surface because of requirements for computational speed. As a result they have had difficulty accounting for (a) the tendency of full magnetohydrodynamic (MHD) models to predict non-radial plasma flow out to r 10r and (b) the appreciable magnitude, 3, of B _r , (the radial component of B) consistently observed at r 1 AU. We present a new modelling technique based on a non-spherical source surface, which is taken to be an isogauss of the underlying potential field generated by currents in or below the photosphere. This modification of the source surface significantly improves the agreement between the geometrical construction and the MHD solution while retaining most of the computational ease provided by a spherical source surface. A detailed comparison between the present source-surface model and the MHD solution is made for the internal dipole case. The resulting B field agrees well in magnitude and direction with the coronal B field derived from the full MHD equations. It shows evidence of the slightly equatorward meridional plasma flow that is characteristic of the MHD solution. Moreover, the B field obtained by using our non-spherical source surface agrees well with that observed by spacecraft in the vicinity of the Earth's orbit. Applied to a solar dipole field with a moment of 1 G-r ³ , the present model predicts that B _r at r 1 AU lies in the range of 1–2 and is remarkably insensitive to heliomagnetic latitude. Our method should be applicable also to more general (i.e., more realistic) configurations of the solar magnetic field. Isogauss surfaces for two representative solar rotations, as calculated from expansions of observed photospheric magnetic-field data, are found to show large and significant deviations from sphericity.     

Relationship between Powerful Flares and Dynamic Evolution of the Magnetic Field at the Solar Surface

Powerful flares are closely related to the evolution of the complex magnetic field configuration at the solar surface. The strength of the magnetic field and speed of its evolution are two vital parameters in the study of the change of magnetic field in the solar atmosphere. We propose a dynamic and quantitative depiction of the changes in complexity of the active region: E=u×B, where u is the velocity of the footpoint motion of the magnetic field lines and B is the magnetic field. E represents the dynamic evolution of the velocity field and the magnetic field, shows the sweeping motions of magnetic footpoints, exhibits the buildup process of current, and relates to the changes in nonpotentiality of the active region in the photosphere. It is actually the induced electric field in the photosphere. It can be deduced observationally from velocities computed by the local correlation tracking (LCT) technique and vector magnetic fields derived from vector magnetograms. The relationship between E and ten X-class flares of four active regions (NOAA 10720, 10486, 9077, and 8100) has been studied. It is found that (1) the initial brightenings of flare kernels are roughly located near the inversion lines where the intensities of E are very high, (2) the daily averages of the mean densities of E and its normal component (E _n) decrease after flares for most cases we studied, whereas those of the tangential component of E (E _t) show no obvious regularities before and after flares, and (3) the daily averages of the mean densities of E _t are always higher than those of E _n, which cannot be naturally deduced by the daily averages of the mean densities of B _n and B _t.     

Basic concepts in the electrodynamics of the auroral ionosphere

Equations governing the large-scale electrodynamic processes in the auroral ionosphere are systematically discussed and the limits to drawing conclusions from incomplete sets of equations are evaluated. The vectors of electic current density,j, and electric field,E, are expressed as explicit functions of the densities, pressures and velocities of the constituents of the ionosphere.The equation div (·E)=0 is an identity satisfied by any solution of the full set of equations governing the problem and cannot be treated as a differential equation forE in which the components of the conductivity tensor are given parameters. The concept of the height-integrated conductivities and the conclusions based on it are inconsistent with the equations of momentum balance for the ionospheric constituents.The global structure of the auroral ionosphere is determined by the state of equilibrium between the pressure gradients, the inertial forces and thej×B-force associated with the auronal electrojets flowing along the auroral oval. The time-averaged, global, electric field is directed across the auroral oval. Its value is substantially affected by the motions of neutral particles. The velocity vector of the neutrals has a substantial component directed across the oval.     

Axially Symmetric Cosmic Strings in a Scalar-Tensor Theory

Axially symmetric cosmological models with cosmic string source are obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A113, 467, 1985). The models obtained give us axially symmetric geometric (Nambu) string, p-string and Reddy string (Astrophys. Space Sci. 286, 2003b) in Saez-Ballester theory. Some physical properties of the models are also discussed.     

Fourier techniques for an analysis of eclipsing binary light curves: IV

The aim of the present paper is to establish two further series expansions (alternative to those given in Demircan, 1979a, b, c), for the observed light changes of eclipsing binary system. The coefficients of these expansions have also been expressed in the form of general series expansions in terms of the eclipse elementsr _1.2,i andL ₁ of the spherical model on which all other distorted models may be based (Kopal, 1975, 1976) in an analysis in the frequency-domain.     

Joule heating of Io's ionosphere by unipolar induction currents

The unexpectedly large scale height of Io's ionosphere (Kliore, A., et al., 1975, Icarus24, 407–410) together with the relatively large molecular weight of the likely principal constituent, SO₂ (Pearl, J., et al., 1979, Nature280, 755–758), suggest a high ionospheric temperature. Electrical induction in Io's ionosphere due to the corotating plasma bound to the Jovian magnetosphere is one possible source for attainment of such high temperatures. Accordingly, unipolar induction models were constructed to calculate ionospheric joule heating numerically. Heating rates produced by highly simplified models lie in the range 10^?9 to 10^?8 W/m³. These heating rates are lower than those determined from uv photodissociative heating models (Kumar, S., 1980, Geophys. Res. Lett.7, 9–12) at low levels in the ionosphere but are comparable in the upper ionosphere. The low electrical heating rate throughout most of the ionosphere is due to the power limitation imposed by the Alfvén wings which complete the electrical circuit (Neubauer, F.M., 1980, J. Geophys. Res.85, 1171–1178). Contrary to the pre-Voyager calculations of Cloutier, P. A., et al. (1978, Astrophys. Space Sci.55, 93–112), our numerical results show that the J × B force density due to unipolar induction currents in the ionosphere is much less than the gravitational force density when the combined mass of the neutral species is included. The binding and coupling of the ionosphere is principally due to the relatively dense (possibly localized) neutral SO₂ atmosphere. In regions where the ions and neutrals are collisionally coupled the ionosphere will not be stripped off by the J × B forces. However at a level above that (to which the ions move by diffusion only) the charged species would be removed. Thus there appears to be no need to postulate the existence of an intrinsic Ionian magnetic field as suggested by Kivelson, M. G., et al. (79, Science 205, 491–493) and Southwood, S. J., et al. (1980, J. Geophys. Res., in press) in order to retain the observed ionosphere.     

Abundance calibration and evolution of GiantHii Regions

We present a self-consistent method to determine abundance and evolutionary status for GiantHii Regions (GHR) as well as the nominal temperature of the ionizing cluster and the ionization parameter. We define the ionization parameter-free plane [,R ₂₃] (Vilchez and Pagel, 1988) where observations are compared with the prediction of photoionization models, in order to obtain the abundance and evolutionary status for a given GHR. This new method allows us to re-calibrate the empirical relationship (R ₂₃, O/H) by Pagelet al. (1979) up to abundances three times solar. The effects of evolution of GHR on their observed spectra are explained in terms of the cooling down of the ionizing population and some evolutionary tracks are presented.     

Response of the polar cap boundary and the current system to changes in IMF observed from the Magsat satellite in the southern hemisphere during summer

The magnetic field vector residuals observed from the Magsat satellite have been used to obtain the dependence of the polar cap boundary and the current system on IMF for quiet and mildly disturbed conditions (K_p ⩽ 3 +). The study has been carried out for the summer months in the Southern Hemisphere. “Shear reversals” (SRs) in vector residuals indicative of the infinite current sheet approximation of the field-aligned currents (FACs) indicate roughly the polar cap boundary or the poleward boundary of the plasma sheet. This is also the poleward edge of the region 1 FACs. The SR is defined to occur at the latitude where the vector goes to minimum and changes direction by approximately 180°.It is found that SRs mainly occur when the interplanetary magnetic field (IMF) has a southward-directed B_z- component and in the latitude range of about 70°–80°. SRs in the dusk sector occur predominantly when the azimuthal component B_y is positive and in the dawn sector when B_y is negative, irrespective of the sign of B_z These results agree with the known merging process of IMF with magnetopause field lines. When SRs occur on both dawn and dusk sectors, the residuals over the entire polar cap are nearly uniform in direction and magnitude, indicating negligible polar currents. Similar behaviour is observed during highly disturbed conditions usually associated with large negative values of B_z.Forty-one Magsat orbits with such SRs are quantitatively modelled for preliminary case studies of the resulting current distribution. It is found that SRs, in the plane perpendicular to the geomagnetic field, for the current vectors and the magnetic vector residuals (perturbations relative to the unperturbed field) occur at almost the same latitudes. The electrojet intensities range from 1.2 × 10⁴ to 6.5 × 10⁵ A (amperes). A preliminary classification of polar cap boundary crossings characterized by vector rotations rather than SRs also shows that they tend to occur mainly for negative B_z.     

Electromagnetic fields satisfying the condition B ∧ (∇ ∧ B)=0

It is proved that (1) electromagnetic fields with electric and magnetic components parallel to one another are solutions of Maxwell's equations; (2) the equationB(B)=0 (B is the magnetic field) is gauge and relativistically-invariant for systems of reference moving with velocityv/c=EB(1+v ²/c ²)/(E ²+B ²).