On diffusion of the tangential fluctuations of the geomagnetic field through the mantle

In this paper we develop a statistical approach to resolve the transport problem for the tangential fluctuations of the geomagnetic field in the mantle. For the sake of simplicity we treat the mantle as a thick layer of vacuum and assume in addition that only a radial component of the magnetic field of the core penetrates through the core-mantle boundary. These assumptions allow us to find exact expressions for the tangential field components throughout the mantle. By using such expressions we construct a correlation tensor of tangential components and then, since the mantle is thick enough, study its asymptotic properties on the Earth surface. Incidentally, the correlation tensor trace happens to be equal to the correlation function of the radial component that was obtained by Pilipenko and Sokoloff (1992). Indeed, we provide a simple boundary problem which initially describes the diffusion functions. We also pay a special attention to transformation properties of the correlation tensor and find here some interesting analogies with secular variation data of the geomagnetic field     

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.     

The outer core rotation about an inclined axis from geomagnetic secular variations (Mitteilungen des Zentralinstituts für Physik der Erde,Nr. 1832)

Non-axisymmetric motions of the outer core of the Earth are important for the dynamo problem and the excitation of the decade variations of the polar motion. The components of the vector of a rigid rotation of the outer core about an inclined axis were estimated by a first-order approximation of the frozen- field theory of the geomagnetic secular variation from 1903.5 to 1975.5. The trends and quasi-periodic constituents of these quantities were computed. It was shown that the position and time behaviour of the rotational pole of the outer core differ considerably from the well-know co-ordinates of the dipole axis. Some periods of the equatorial components of the rotational vector are comparable with those of the axial component previously derived for a pure axial rotation. Additionally, the time behaviour of the pole path shows events like the well-known Markowitz wobble but naturally with other extent. These and other results suggested that the investigations are worth to be continued in future by some physical interpretations.     

Magnetic field of solar prominences: The procedure of radio observations

The first successful radio astronomical results of measurements of the magnetic field of solar prominences are presented. The accuracy of polarization and magnetic field observations is 3 · · 10⁻⁴ and 2 G, respectively. The observations were made by the 22-meter radio telescope of the Crimean Astrophysical Observatory at wavelengths of 8 and 13.5 mm. It has been found that the value of the magnetic fields coincides with the optical one (from 7 to 30 G), but the image of radio polarization differs from the intensity.     

Planetary dynamos: effects of electrically conducting flows overlying turbulent regions of magnetic field generation

A fully three-dimensional, nonlinear, time-dependent, multi-layered spherical kinematic dynamo model is used to study the effect on the observable external magnetic field of flow in an electrically conducting layer above a spherical turbulent dynamo region in which the α effect generates the magnetic field. It is shown that the amplitude and structure of an observable planetary magnetic field are largely determined by the magnitude and structure of the flow in the overlying layer. It is also shown that a strong-field planetary dynamo can be readily produced by the effect of an electrically conducting flow layer at the top of a convective core. The overlying layer and the underlying convective region constitute a magnetically strongly coupled system. Such overlying layers might exist at the top of the Earth's core due to chemical or thermal causes, in the cores of other terrestrial planets for similar reasons, and in Saturn due to the differentiation of helium from hydrogen. An electrically conducting and differentially rotating layer could exist above the metallic hydrogen region in Jupiter and affect the jovian magnetic field similar to the overlying layers in other planets. Lateral temperature gradients resulting in thermal winds drive the flow in the overlying layers. All planetary magnetic fields could be maintained by similar turbulent convective dynamos in the field-generation regions of planets with the differences among observable magnetic fields due to different circulations in the overlying electrically conducting layers.     

Average anisotropy characteristics of high energy cosmic ray particles and geomagnetic disturbance index Ap

The average characteristics of the diurnal and semi-diurnal anisotropy of cosmic ray intensity at relativistic energies have been obtained by using data from the worldwide grid of neutron monitor for the period 1989 to 1996. The complex behaviour of the diurnal amplitudes and time of maxima (phase) and its association with the Ap index on a long-term and day-to-day basis have been studied. Even though the general characteristics, on a yearly average basis, have not changed significantly during this period, both the diurnal and semi-diurnal amplitudes and phases vary significantly, besides significant changes being observed for different interplanetary conditions on a short-term basis. It is found that the relationship between the Ap index and the diurnal vector is out of phase during the period 1991 to 1995. On a long-term basis, the correlation of diurnal variation with Ap index has been found to vary during the solar cycle. On a short-term basis, it has been observed that the high Ap days are usually associated with higher amplitudes with phase shifted to earlier hours.     

Lines of force of the geomagnetic field in space

The lines of force of the geomagnetic field at various latitudes and longitudes in the northern hemisphere are approximately traced to their intersections with the earth's surface in the southern hemisphere, using an electronic computer and the first nine Gauss coefficients. Those lines leaving the average northern auroral zone are traced to their intersection of the geomagnetic field with the earth's surface. These points of intersection are found to be very nearly at the average southern auroral zone deduced from auroral observations and from magnetic measurements of disturbance. It is concluded, therefore, that the geomagnetic field has stability and a simple character even at distances as great as about 6 earth radii above the earth, measured in the equatorial plane, even during auroral displays. It is also concluded that solar streams at such times do not seriously distort the field lines connecting the auroral zones.     

Magnetic field of a neutron star with a superconducting quark core in the CFL-phase

The Ginzburg-Landau equations are derived for the magnetic and gluomagnetic gauge fields in the color superconducting core of a neutron star containing a CFL-condensate of diquarks. The interaction of the diquark CFL-condensate with the magnetic and gluomagnetic gauge fields is taken into account. The behavior of the magnetic field in a neutron star is studied by solving the Ginzburg-Landau equations taking correct account of the boundary conditions, including the gluon confinement conditions. The magnetic field distribution in the quark and hadronic phases of a neutron star is found. It is shown that a magnetic field generated in the hadronic phase by the entrainment effect penetrates into the quark core in the form of quark vortex filaments because of the presence of screening Meissner currents. __________ Translated from Astrofizika, Vol. 50, No. 1, pp. 87–98 (February 2007).     

The equatorial shape and gravity field of Mercury from MESSENGER flybys 1 and 2

On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0-90°E, is greater than that seen during flyby 2 in the longitude range 180-270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field, C_2,2, is well determined and correlates with the equatorial shape. The S_2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J₂, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C_2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment (C_m/C), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.     

Interaction within the ionosphere in the presence of geomagnetic field

Field intensities within the ionospheric medium during nonlinear transient processes due to interactions among different modes of propagation have been derived taking into consideration the influence of geomagnetic field. The expression for angular distribution of power during wave propagation has also been evaluated.     

Motion of the Earth's inner core and related variations of polar motion and the rotational velocity

Correlations between the geomagnetic field parameters and polar motion were explained using the hypothesis of an inner core motion. For a number of periodic constituents of both phenomena it could be proved that this model works well. Secular variations of polar motion caused by inner core dynamics are in the same order of magnitude as the secular variation of the pole derived from pole coordinates of the International Latitude Service (ILS).     

The compressed geomagnetic field as a function of dipole tilt

The currents on the precisely calculated magnetosphere surface previously reported have been integrated with the same accuracy as used in the surface calculation to give the magnetic field at 688 points within the magnetosphere for each of eight surfaces for the tilt of the Earth's dipole in steps of 5° between 0° and 35°. The magnetic fields have then been used to fit the coefficients of a 35 term spherical harmonic expansion of the scalar magnetic potential representing the field by the method of least squares fit. The coefficients for each of the eight surfaces were then represented as a power series in dipole tilt angle, λ so that the complete field can be given very conveniently for any λ. For λ = 0, the first two coefficients g₁₀ and g₂₁ are the dominant terms and the azimuthally dependent term g₂₁ is 30 per cent less than that calculated by Mead and Midgley from older less accurate surface and field calculations.     

The neutrino in the primordial magnetic field

We discuss the evolution of the massive Dirac particle in the cosmic magnetic field. The magnetic field makes the space metric anisotropic. By solving the Dirac equation we obtain the apparent magnetic moment of the neutrino in the cosmic magnetic field.     

On the role of the motion of the photospheric footpoints of the magnetic field lines

By means of a simple relation between the velocity v of the fluid particle and the velocity v_f of the photospheric footpoint of the magnetic field line v_z and B_z being respectively the components of v and the magnetic field B normal to the photospheric surface, it is shown formally that through the phtospheric surface the transport of all the quantities attributed to the magnetic field, such as the magnetic flux, the magnetic energy and the helicity, is independent of v_z, and v_f is the only kinematical quantity on which the transport depends. In addition, in the neighborhood of the neutral line the velocity v_l of the moving curve of constant B_z is found to be equal approximately to the component of v or v_f in the direction of v_l. Since v_l can be measured or extimated, so can the components of v and v_f near the neutral line.     

On the vertical electric component of the geomagnetic pulsation field

The existence of a close correlation between the atmospheric electric field and geomagnetic pulsations in the range of Pc 2–4 is demonstrated experimentally and theoretically (from the horizontal propagation of pulsations). The need to take this into account in any geological-geophysical interpretation of experimental data is stressed.     

Magnetic Flux Imbalance of the Solar and Heliospheric Magnetic Fields

A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B _z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B _z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B _z component were found in temporal patterns of the cumulative sum of the IMF B _z .     

Influence of geomagnetic field on the motion of low satellites

The first aim of the present work is to compute a more accurate and recent model for the Earth’s magnetic field. The second aim is to determine the effects of the Earth’s magnetic field on the motion of a charged artificial satellite to evaluate the variations of the orbital elements of the satellite due to these effects. The magnetic field and its variation with time have been studied at different heights, longitudes and latitudes. The geomagnetic field is considered as a multiple potential field and the electrical charge of the satellite is assumed to be constant. A new computer code has been constructed to follow the components of the magnetic field in spherical harmonic models. The Gauss equations are solved numerically. The results concentrate on the computation of the numerical values of orbital perturbation for the case of a low Earth satellite. RS-1 satellite and space craft gravity probe B (GPB) are chosen as cases of studies for a detailed numerical analysis.