Magnetic field of the solar wind

Relationship between the geoefficiency of the solar flares as well as of the active regions passing the central meridian of the Sun and the configuration of the large scale solar magnetic field is studied.It is shown that if the tangential component of the large scale magnetic field at the active region or at the flare region is directed southwards, that region and that flare produce geomagnetic storm. In case when the tangential magnetic field is directed northward, the active region and the flares occurring at that region do not cause any geomagnetic disturbance.An index of the geoefficiency of the solar flares and of the active regions is proposed.     

Nonlinear Force-Free Reconstruction of the Global Solar Magnetic Field: Methodology

We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on the theory of force-free electrodynamics and applies directly to the reconstruction of the solar coronal magnetic field for a given distribution of the photospheric radial field component. The method works as follows: we start with any initial magnetostatic global field configuration (e.g. zero, dipole), and along the boundary surface we create an evolving distribution of tangential (horizontal) electric fields that, via Faraday’s equation, give rise to a respective normal-field distribution approaching asymptotically the target distribution. At the same time, these electric fields are used as boundary condition to numerically evolve the resulting electromagnetic field above the boundary surface, modeled as a thin ideal plasma with non-reflecting, perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear force-free configuration that satisfies the given normal-field distribution on the boundary. This is different from existing methods relying on a fixed boundary condition – the boundary evolves toward the a priori given one, at the same time evolving the three-dimensional field solution above it. Moreover, this is the first time that a nonlinear force-free solution is reached by using only the normal field component on the boundary. This solution is not unique, but it depends on the initial magnetic field configuration and on the evolutionary course along the boundary surface. To our knowledge, this is the first time that the formalism of force-free electrodynamics, used very successfully in other astrophysical contexts, is applied to the global solar magnetic field.     

The Magnetic Field at the Inner Boundary of the Heliosphere Around Solar Minimum

STEREO A and B observations of the radial magnetic field between 1 January 2007 and 31 October 2008 show significant evidence that in the heliosphere, the ambient radial magnetic field component with any dynamic effects removed is uniformly distributed. Based on this monopolar nature of the ambient heliospheric field we find that the surface beyond which the magnetic fields are in the monopolar configuration must be spherical, and this spherical surface can be defined as the inner boundary of the heliosphere that separates the monopole-dominated heliospheric magnetic field from the multipole-dominated coronal magnetic field. By using the radial variation of the coronal helmet streamers belts and the horizontal current – current sheet – source surface model we find that the spherical inner boundary of the heliosphere should be located around 14 solar radii near solar minimum phase.     

Possible relations between the rotational axis of the Earth's inner core and the magnetic dipole axis

The geomagnetic field is maintained by amagnetohydrodynamic dynamo process within the liquid outer core. The distribution of the associated electric currents is modified if the outer core is bounded by electrically conducting material. Then, eddy currents and the related magnetic fields are generated within these regions. In particular, the relative rigid rotation of the inner core produces a secondary magnetic field, which is superimposed on the dynamo field. The angle between the dipole axis of the total field and the rotational axis of the inner core is an important quantity needed for the theory of polar motion of the Earth. This angle is investigated for a broad spectrum of angular velocities of the inner core. To simplify the mathematical procedure, we model the dynamo field using an axisymmetric field generated by a system of electric currents within the outer core. The conductivity of the mantle is neglected. We find that the position of the dipole axis depends on the angular velocity of the inner core as well as on the distribution of the current system within the outer core. Coincidence of both axes can be reached if the angular velocity is high enough and if the current system is concentrated within a thin sheet near the outer core-inner core boundary.     

Influence of accelerated particles on the large-scale magnetic field in young supernova remnants

We offer a possible explanation for the observational data on the magnetic-field structure in young supernova remnants (SN 1006, Tycho, Kepler, Cas A) that have been obtained by analyzing the polarizations of electromagnetic radiation in the radio, infrared, and other wavelength ranges. The authors of observational works interpret these data as evidence that the ordered magnetic-field component is predominantly radial, but it can be much smaller in amplitude than the stochastic field component that accounts for the bulk of the total magnetic energy. We calculate the magnetic field in supernova remnants by taking into account the shock compression of the primary field and the generation of a large-scale magnetic field by the particles accelerated at the shock front. The assumption that the field in the supernova remnant is the explosion-compressed primary field near the star is inconsistent with observational data, because the tangential (relative to the shock front) field component perpendicular to the radius must prevail in this case. However, allowing for the generation of an additional magnetic field by the electric current of the particles accelerated by a strong shock front leads us to conclude that the field components parallel to the front are suppressed by accelerated particles by several orders of magnitude. Only the component perpendicular to the front remains. Such a field configuration for uniform injection does not lead to the generation of an additional magnetic field, and, in this sense, it is stable. This explains the data on the radial direction of the ordered field component. As regards the stochastic field component, we show that it is effectively generated by accelerated particles if their injection into acceleration at the shock front is nonuniform along the front. Injection nonuniformity can be caused by upstream density nonuniformities. A relative density nonuniformity of the order of several percent is enough for an observable magnetic field with scales on the order of the density nonuniformity scales to be generated.     

On the Influence of a Large-scale Magnetic Field on Turbulent Motions in an Electrically Conducting Medium

This paper deals with turbulent motions in a homogeneous incompressible electrically conducting medium in the presence of a magnetic field which is on average homogeneous and stationary. Using a model in which the turbulence is produced by a stochastic body force, and supposing a weak interaction between motion and magnetic field, a method is developed for calculating the pair correlation tensor of the velocity field from that occuring in a zero magnetic field. As an example, the pair-correlation tensor for a homogeneous stationary turbulence, which is isotropic and mirror-symmetric for zero magnetic field, is determined. With obvious assumptions on the correlation for zero field, two results are obtained. Firstly, the turbulent velocity is reduced by the magnetic field, the component parallel to the field, however, less than those perpendicular to it. Secondly, the correlation length parallel to the field turns out to be greater than the one perpendicular to it, indicating a tendency towards two-dimensional motion. Finally, the possibility of special situations is briefly discussed in which the turbulent velocity is enhanced by the magnetic field, and the anisotropies of the velocity components and the correlation lengths are opposite to those above.     

On some problems concerning the calculation of the form of the magnetopause and the electric field on the magnetopause in the framework of the continuum medium model

In order to understand the reason of the existence of the electric field in the magnetosphere, and for the theoretical evaluation of its value, it is necessary to find the solution of the problem of determination of the magnetosphere boundary form in the frameworks of the continuum medium model which takes into account part of the magnetospheric plasma movement in supporting the magnetospheric boundary equilibrium. A number of problems for finding the distribution of the pressure, the density, the magnetic field and the electric field on the particular tangential discontinuity is considered in the case when the form of discontinuity is set (the direct problem) and a number of problems for finding the form of the discontinuity and the distribution of the above-mentioned physical quantities on the discontinuity is considered when the law of the change of the external pressure along the boundary is set (for example, with the help of the approximate Newton equation). The problem which is considered here, which deals with the calculation of the boundary form and with the calculation of the distribution of the corresponding physical quantities on the discontinuity of the 1st kind for the compressible fluid with the magnetic field with field lines which are perpendicular to the plane of the flow in question, concerns the last sort of problems. The comparison of the results of the calculation with the data in the equatorial cross-section of the magnetosphere demonstrates that the calculated form of the boundary, the value of the velocity of the return flow and the value of the electric field on the magnetopause, agree satisfactorily with the observational data.     

Application of the Method of Matched Asymptotic Expansions to the radial oscillations of a magnetic cylinder

This study deals with the singular character of the perturbation introduced into the eigenvalue problem of the linear and adiabatic oscillations of a gaseous configuration by a magnetic field that is non-zero on the boundary surface of the configuration. This singular character implies that a regular perturbation scheme cannot yield uniformly valid expansion for the eigenfunctions.This investigation considers the application of the Method of Matched Asymptotic Expansions (M.M.A.E.) to the latter singular perturbation problem in order to obtain uniformly valid expansions for the eigenfunctions and first-order expressions for the eigenfrequencies. As an illustrative example, the M.M.A.E. is applied to the eigenvalue problem of the linear, radial, and adiabatic oscillations of a homogeneous cylindrical plasma with a constant longitudinal magnetic field.     

Quasi-Alfvén oscillations of magnetic surfaces

A system of equations has been derived for the modes of free oscillation of the magnetosphere when it is regarded as an adiabatic magnetic dipole trap filled with cold inhomogeneous plasma. The limiting case of infinite longitudinal conductivity corresponding to the assumption that the electric field is orthogonal to the geomagnetic field has been studied. The boundary at the ionosphere is supposed to be perfectly conducting.The eigenmode spectrum has been found to have discrete and continuous components. The eigenmodes of the discrete component correspond to quasi-magnetosonic modes and the eigenmodes of the continuous component to quasi-Alfvén modes.Assuming the magnetosphere to be axisymmetric, a general expression in the form of a Frobenius series has been derived for quasi-Alfvén oscillations of magnetic shells near resonant magnetic surfaces.     

Geomagnetic field variation during winter storm at localized southern and northern high latitude

This paper presents the effect of geomagnetic storm on geomagnetic field components at Southern (Maitri) and Northern (Kiruna) Hemispheres. The Indian Antarctic Station Maitri is located at geom. long. 66.03° S; 53.21° E whereas Kiruna is located at geom. long. 67.52° N; 23.38° E. We have studied all the geomagnetic storms that occurred during winter season of the year 2004–2005. We observed that at Southern Hemisphere the variation is large as compared to the Northern Hemisphere. Geomagnetic field components vary when the interplanetary magnetic field is oriented in southward direction. Geomagnetic field components vary in the main phase of the ring current. Due to southward orientation of vertical component of IMF reconnection takes place all across the dayside that transports plasma and magnetic flux which create the geomagnetic field variation.     

An important statistical consideration,and the effect of the interplanetary magnetic field on the quiet time variation of the geomaganetic field

We present an analysis of some interplanetary and geomagnetic field data and at the same time attempt to show that erroneous conclusions may be drawn if the effects of autocorrelation are not taken into account in standard least squares regression methods. We found the following conclusions survived the autocorrelation corrections to simple correlation tests (i) that the directed z component of the interplanetary magnetic field (IMF) affects the first few Fourier terms in the daily variation of the vertical component of the quiet geomagnetic field (ii) ΣK_p correlates with the daily mean magnitude of the IMF.     

Description of the coastal effect at equatorial latitudes with applications to the Peruvian and Nigerian zones

The problem of the electromagnetic induction produced by a localized and an extended ionospheric current near an ocean coast, over a mantle of infinite conductivity, has been reduced to the solution of an integral equation where the induced current density appears in an implicit form. This formalism is applied to calculate the field induced by the geomagnetic daily variation due to the presence of the ocean at the Peruvian and Nigerian equatorial zones.     

Optimal dynamos in the cores of terrestrial exoplanets: Magnetic field generation and detectability

A potentially promising way to gain knowledge about the internal dynamics of extrasolar planets is by remote measurement of an intrinsic magnetic field. Strong planetary magnetic fields, maintained by internal dynamo action in an electrically conducting fluid layer, are helpful for shielding the upper atmosphere from stellar wind induced mass loss and retaining water over long (Gyr) time scales. Here we present a whole planet dynamo model that consists of three main components: an internal structure model with composition and layers similar to the Earth, an optimal mantle convection model that is designed to maximize the heat flow available to drive convective dynamo action in the core, and a scaling law to estimate the magnetic field intensity at the surface of a terrestrial exoplanet. We find that the magnetic field intensity at the core surface can be up to twice the present-day geomagnetic field intensity, while the magnetic moment varies by a factor of 20 over the models considered. Assuming electron cyclotron emission is produced from the interaction between the stellar wind and the exoplanet magnetic field we estimate the cyclotron frequencies around the ionospheric cutoff at 10 MHz with emission fluxes in the range 10⁻⁴-10⁻⁷ Jy, below the current detection threshold of radio telescopes. However, we propose that anomalous boosts and modulations to the magnetic field intensity and cyclotron emission may allow for their detection in the future.     

A two-component solar cycle

From a previous analysis of a long series of geomagnetic data, we came to the conclusion that, during 91.5% of the time, geomagnetic activity is controlled by the solar wind flow at the Earth's orbit.In this paper, we consider the flow of the solar wind plasma in a coronal field whose source is a dipole. The temporal evolution of the dipole source as well as any small scale evolution occurring in the associated coronal field topology can be closely monitored from the latitudinal distribution of the wind velocity.In the geomagnetic data series, the index Aa is closely linked to the wind velocity at the power 2.25. From this data set, we can reconstruct the behavior of the solar dipole field from 1868 onward.The main results of our analysis are as follows. The solar cycle has two distinct components, dipole and toroidal, of which the respective cycles are out of phase. The toroidal component is strongly linked, with a 5–6 yr delay, to the preceding dipole component. This finding is in contradistinction to the view that the dipole field is a result of the poleward migration of the decaying toroidal field. This result should contribute to improve our understanding of the Sun's cyclical behaviour.     

On the quasi-periodic oscillations in magnetars

We study torsional Alfvén oscillations of magnetars, that is neutron stars with a strong magnetic field. We consider the poloidal and toroidal components of the magnetic field and a wide range of equilibrium stellar models. We use a new coordinate system  ( X , Y )  , where     and     and a ₁ is the radial component of the magnetic field. In this coordinate system, the one+two-dimensional evolution equation describing the quasi-periodic oscillations (QPOs), see Sotani et al., is reduced to a one+one-dimensional equation where the perturbations propagate only along the y -axis. We solve the one+one-dimensional equation for different boundary conditions and the open magnetic field lines, that is magnetic field lines that reach the surface and there match up with the exterior dipole magnetic field as well as closed magnetic lines, i.e. magnetic lines that never reach the stellar surface. For the open field lines, we find two families of QPO frequencies: a family of 'lower' QPO frequencies which is located near the x -axis and a family of 'upper' frequencies located near the y -axis. According to Levin, the fundamental frequencies of these two families can be interpreted as the turning point of the continuous spectrum. We find that the upper frequencies are multiples of the lower ones by a constant equalling  2 n + 1  . For the closed lines, the corresponding factor is   n + 1  . By using these relations, we can explain both the lower and the higher observed frequencies in SGR 1806−20 and SGR 1900+14.     

Analysis of observations of the dwarf nova pegasi 2010

Analysis of photometric and spectroscopic observations of GSC 02197-00886 at the outburst maximum (on May 8, 2010) and at the stage of relaxation towards the quiescent (on August 4, 2010) was performed. Radiation of an optically thick accretion disc with a hot boundary layer dominates the spectra, which are consistent with the spectra of a WZ Sge-type dwarf novae. In the relaxation phase, an optically thin accretion disc with radiation in the HI and HeI emission lines is observed against the background of the absorption spectrum of a white dwarf. The parameters of GSC 02197-00886, which were determined by combining the radial velocities of the components with the assumption that the secondary component is close to mainsequence stars, differ significantly from the parameters that characterize other WZ Sge-type systems. We hypothesize that the secondary component was excited in the course of the outburst and experienced long-lasting relaxation towards the main-sequence state.     

The determination of the velocity amplitude of the total photospheric motion field

By the analysis of the profiles of 20 weak lines observed at five centre-to-limb positions on the solar disk, radial and tangential components of the velocity amplitude of the photospheric motion field are derived in the range of optical depth - 3.0 ? lgτ5 ? +0.5.

     

Cluster strong lensing in the Millennium simulation: the effect of galaxies and structures along the line-of-sight

We use ray-tracing through the Millennium simulation to study how secondary matter structures along the line-of-sight and the stellar mass in galaxies affect strong cluster lensing, in particular the cross-section for giant arcs. Furthermore, we investigate the distribution of the cluster Einstein radii and the radial distribution of giant arcs. We find that additional structures along the line-of-sight increase the strong-lensing optical depth by  ∼10–25 per cent  , while strong-lensing cross-sections of individual clusters are frequently boosted by as much as  ∼50 per cent  . The enhancement is mainly due to structures that are not correlated with the lens. Cluster galaxies increase the strong-lensing optical depth by up to a factor of 2, while interloping galaxies are not significant. We conclude that these effects need to be taken into account for predictions of the giant arc abundance, but they are not large enough to fully account for the reported discrepancy between predicted and observed abundances.
Furthermore, we find that Einstein radii defined via the area enclosed by the critical curve are 10–30 per cent larger than those defined via radial surface mass density profiles. The contributions of radial and tangential arcs to the radial distribution of arcs can be clearly distinguished. The radial distribution of tangential arcs is very broad and extends out to several Einstein radii. Thus, individual arcs are not well suited for constraining Einstein radii.     

Dynamo-generated magnetic fields at the surface of a massive star

Spruit has shown that an astrophysical dynamo can operate in the non-convective material of a differentially rotating star as a result of a particular instability in the magnetic field (the Tayler instability). By assuming that the dynamo operates in a state of marginal instability, Spruit has obtained formulae which predict the equilibrium strengths of azimuthal and radial field components in terms of local physical quantities. Here, we apply Spruit's formulae to our previously published models of rotating massive stars in order to estimate Tayler dynamo field strengths. There are no free parameters in Spruit's formulae. In our models of 10- and  50-M_⊙  stars on the zero-age main sequence, we find internal azimuthal fields of up to 1 MG, and internal radial components of a few kG. Evolved models contain weaker fields. In order to obtain estimates of the field strength at the stellar surface, we examine the conditions under which the Tayler dynamo fields are subject to magnetic buoyancy. We find that conditions for Tayler instability overlap with those for buoyancy at intermediate to high magnetic latitudes. This suggests that fields emerge at the surface of a massive star between magnetic latitudes of about 45° and the poles. We attempt to estimate the strength of the field which emerges at the surface of a massive star. Although these estimates are very rough, we find that the surface field strengths overlap with values which have been reported recently for line-of-sight fields in several O and B stars.     

Spatial structure and stability of coupled Alfvén and drift compressional modes in non-uniform magnetosphere: Gyrokinetic treatment

The spatial structure and stability properties of the coupled Alfvén and drift compressional modes in a space plasma are studied in a gyrokinetic framework in a model taking into account field-line curvature and plasma and magnetic field inhomogeneity across the magnetic shells. The perturbation is found to be localized in two transparent regions, the Alfvén and drift compressional transparent regions, where the wave vector radial component squared is positive. Both regions are bounded by the resonance and cut-off surfaces, where the wave vector radial component turns into infinity and zero, respectively. An existence of the drift compressional resonance is one of the most important results of this work. It is argued that on the surface of this resonance the longitudinal and azimuthal components of the wave's magnetic field have a pole and logarithmic singularities, respectively. The instability conditions and expressions for the growth rate of the coupled modes have been obtained. In the Alfvénic transparent region, an instability occurs in the presence of the negative plasma temperature gradient. This instability does not lead to a non-stationary wave behavior: all the energy gained from the resonance particles was finally absorbed owing to any dissipation process. In a drift compressional transparent region, a necessary condition for the instability is the growth of the temperature with the radial coordinate. The growth rate is almost independent of the radial coordinate, which means that the wave energy gained from the particles cannot disappear. It will lead to an ever increasing wave amplitude, and no stationary picture for the unstable drift compressional mode is possible.