Magnetic Dipole Axis Research Articles

Field induced by an axial magnetic dipole in the presence of two fused superconducting spheres: Analytic solution

An exact solution for a magnetostatic boundary value problem involving two fused (overlapping) spheres placed in a field generated by an axial magnetic point dipole is constructed based on the image method. The basic idea is illustrated for two unequal superconducting spheres intersecting with a vertex angle π/2 and the analytical solution for the scalar magnetic potential satisfying the Neumann boundary condition at the surface is derived. The image solution for a dipole-twin-sphere configuration consists of three image dipoles—one inside each sphere and the third inside a pseudo-/virtual sphere—all located at the respective inverse points inside the superconducting two-sphere assembly. The levitation force acting on the two-sphere superconducting surface is also calculated for the overlapping geometry. These exact results can be used as a benchmark for testing numerical algorithms for overlapping spherical superconductors. Our simple approach also offers clues for solving the Neumann boundary value problem for vertex angles π/n, n is an integer, and other related superconducting geometries.

Daily variations of auroral kilometric radiation observed by STEREO

Daily variations of terrestrial auroral kilometric radiation (AKR) are considered; an effect that is detected in STEREO/WAVES data. It has been found that the intensities of the AKR emitted from Northern and Southern sources are modulated with a period of ∼24 hours. The occurrence frequency of the AKR has been shown to be strongly dependent on the orientation of the rotating oblique magnetic dipole of the Earth relative to the Sun. AKR is found to occur more often and emit in a broader frequency range when the axis of the terrestrial magnetic dipole in the given hemisphere is oriented toward the nightside. We suggest that the observed ∼24 h variations of AKR are connected with diurnal changes of the ambient plasma density in the auroral region.

Global plate motion frames: Toward a unified model

Plate tectonics constitutes our primary framework for understanding how the Earth works over geological timescales. High‐resolution mapping of relative plate motions based on marine geophysical data has followed the discovery of geomagnetic reversals, mid‐ocean ridges, transform faults, and seafloor spreading, cementing the plate tectonic paradigm. However, so‐called “absolute plate motions,” describing how the fragments of the outer shell of the Earth have moved relative to a reference system such as the Earth's mantle, are still poorly understood. Accurate absolute plate motion models are essential surface boundary conditions for mantle convection models as well as for understanding past ocean circulation and climate as continent‐ocean distributions change with time. A fundamental problem with deciphering absolute plate motions is that the Earth's rotation axis and the averaged magnetic dipole axis are not necessarily fixed to the mantle reference system. Absolute plate motion models based on volcanic hot spot tracks are largely confined to the last 130 Ma and ideally would require knowledge about the motions within the convecting mantle. In contrast, models based on paleomagnetic data reflect plate motion relative to the magnetic dipole axis for most of Earth's history but cannot provide paleolongitudes because of the axial symmetry of the Earth's magnetic dipole field. We analyze four different reference frames (paleomagnetic, African fixed hot spot, African moving hot spot, and global moving hot spot), discuss their uncertainties, and develop a unifying approach for connecting a hot spot track system and a paleomagnetic absolute plate reference system into a “hybrid” model for the time period from the assembly of Pangea (∼320 Ma) to the present. For the last 100 Ma we use a moving hot spot reference frame that takes mantle convection into account, and we connect this to a pre–100 Ma global paleomagnetic frame adjusted 5° in longitude to smooth the reference frame transition. Using plate driving force arguments and the mapping of reconstructed large igneous provinces to core–mantle boundary topography, we argue that continental paleolongitudes can be constrained with reasonable confidence.

Characteristic of the radiation field in low earth orbit and in deep space

The radiation exposure in space by cosmic radiation can be reduced through careful mission planning and constructive measures as example the provision of a radiation shelter, but it cannot be completely avoided. The reason for that are the extreme high energies of particles in this field and the herewith connected high penetration depth in matter. For missions outside the magnetosphere ionizing radiation is recognized as the key factor through its impact on crew health and performance.In absence of sporadic solar particle events the radiation exposure in Low Earth orbit (LEO) inside Spacecraft is determined by the galactic cosmic radiation (protons and heavier ions) and by the protons inside the South Atlantic Anomaly (SAA), an area where the radiation belt comes closer to the earth surface due to a displacement of the magnetic dipole axes from the Earth's center. In addition there is an albedo source of neutrons produced as interaction products of the primary galactic particles with the atoms of the earth atmosphere. Outside the spacecraft the dose is dominated by the electrons of the horns of the radiation belt located at about 60° latitude in Polar Regions. The radiation field has spatial and temporal variations in dependence of the Earth magnetic field and the solar cycle. The complexity of the radiation field inside a spacecraft is further increased through the interaction of the high energy components with the spacecraft shielding material and with the body of the astronauts.In interplanetary missions the radiation belt will be crossed in a couple of minutes and therefore its contribution to their radiation exposure is quite small, but subsequently the protection by the Earth magnetic field is lost, leaving only shielding measures as exposure reduction means. The report intends to describe the radiation field in space, the interaction of the particles with the magnetic field and shielding material and give some numbers on the radiation exposure in low earth orbits and in interplanetary missions.

Effects of thermally heterogeneous structure in the lowermost mantle on the geomagnetic field strength

We have conducted a study of numerical dynamos in a rapidly rotating spherical shell with prescribed non-uniform heat-flux patterns at the outer boundary to examine effects of thermal structure at the core–mantle boundary (CMB) on the geodynamo, especially on the magnetic field strength. Large heat-flux heterogeneity with equatorial symmetry enhances strength of the dipolar magnetic field for a sufficiently small Ekman number, whereas that with equatorial anti-symmetry does not change the strength but affects the tilt of the magnetic dipole axis. The thermal wind induced by heat-flux heterogeneity at the CMB has strong influence on the flow structure and on the magnetic field intensity. These results suggest that thermally heterogeneous structure of the lowermost mantle might give rise to an anomalously strong geomagnetic field such as that during the Cretaceous Normal Superchron.

The energy loss of a rotating magnetized neutron star

The analysis of observations of pulsar B1931+24 shows that the mechanism of the spin-down of a rotating magnetized neutron star is due to the plasma generation in its magnetosphere and, consequently, the radio emission generation. The unique observation of the switch on and switch off of this pulsar allows us to distinguish between the energy loss in the absence of radio emission (the magnetodipole radiation) and the current loss due to the rotation energy expenditure to the relativistic plasma generation and acceleration in the pulsar magnetosphere. The inclination angle χ , the angle between the rotation axis and the magnetic dipole axis, can be stationary for this pulsar, χ = χ st. From observations and theory it follows that χ st = 59 ◦ .

Monopole-charged Pulsars and Relevant Issues

An aligned pulsar whose rotation axis and magnetic dipole axis are parallel should be positively charged. We consider the electromagnetic field both inside and outside the star under a specific condition and derive the total charge of a pulsar. The statistical relation between the pulsar's rotation energy loss rate (or the period derivative) and the period may imply that the millisecond radio pulsars with small periods could be low-mass bare strange stars.

Recovery of the global magnetic field configuration of 78 Virginis from StokesIQUVline profiles

The surface magnetic field configuration of the Ap star HD 118022 (78 Vir) has been reconstructed in the framework of the magnetic charge distribution (MCD) method from the analysis of Stokes IQUV spectra obtained using the MuSiCoS spectropolarimeter at Pic du Midi Observatory. Magnetically-sensitive Fe ii lines were primarily employed in the analysis, supposing that iron is evenly distributed over the stellar surface. We show that the Stokes IQUV profile shapes and variations of 78 Vir can be approximately fit assuming a global magnetic field configuration described by a slightly decentered, inclined magnetic dipole of polar surface intensity approximately 3.3 kG. The derived inclinations of the stellar rotational axis to the line of sight i = 24 ± 5 ◦ as well as to the magnetic dipole axis β = 124 ± 5 ◦ are in good agreement with previous .

Current Flows in Pulsar Magnetospheres

The global structure of current flows in pulsar magnetosphere is investigated, with rough calculations of the circuit elements. It is emphasized that the potential of the critical field lines (the field lines that intersect the null surface at the light cylinder radius) should be the same as that of interstellar medium, and that pulsars whose rotation axes and magnetic dipole axes are parallel should be positively charged, in order to close the pulsar's current flows. The statistical relation between the radio luminosity and pulsar's electric charge (or the spindown power) may hint that the millisecond pulsars could be low-mass bare strange stars.

On the Spin‐up/Spin‐down Transitions in Accreting X‐Ray Binaries

Accreting X-ray binaries display a wide range of behaviors. Some of them are observed to spin up steadily, others to alternate between spin-up and spin-down states, sometimes superimposed on a longer trend of either spin-up or spin-down. Here we interpret this rich phenomenology within a new, simple model of the disk-magnetosphere interaction. Our model, based on the simplest version of a purely material torque, accounts for the fact that when a neutron star is in the propeller regime, a fraction of the ejected material does not receive enough energy to completely unbind, and hence falls back into the disk. We show that the presence of this feedback mass component causes the occurrence of multiple states available to the system for a given, constant value of the mass accretion rate * from the companion star. If the angle χ of the magnetic dipole axis with respect to the perpendicular to the disk is larger than a critical value χcrit, the system eventually settles in a cycle of spin-up/spin-down transitions for a constant value of * and independent of the initial conditions. No external perturbations are required to induce the torque reversals. The transition from spin-up to spin-down is often accompanied by a large drop in luminosity. The frequency range spanned in each cycle and the timescale for torque reversals depend on *, the magnetic field of the star, the magnetic colatitude χ, and the degree of elasticity regulating the magnetosphere-disk interaction. The critical angle χcrit ranges from ~25° to 30° for a completely elastic interaction to ~40°-45° for a totally anelastic one. For χ ≲ χcrit, cycles are no longer possible and the long-term evolution of the system is a pure spin-up. We specifically illustrate our model in the cases of the X-ray binaries GX 1+4 and 4U 1626-67.

The global magnetic field configuration of 78 Virginis: Modeling from line profiles in all 4 Stokes parameters

The surface magnetic field configuration at the Ap star 78 Vir is reconstructed in the framework of the magnetic charge description (MCD) method from the analysis of Stokes IQUV spectra obtained using the MuSiCoS spectropolarimeter at Pic du Midi Observatory. Only the magnetically-sensitive Fe ii lines were employed in the analysis, supposing that iron is evenly distributed over the surface of 78 Vir. A stellar atmosphere model with T eff = 9250 K, log( g ) = 4.5 provides the best fit to the majority of lines analysed at the level of χ 2 = 1.68÷6.30. We show that the global magnetic field structure of 78 Vir can be well-described by a slightly decentered magnetic dipole. The derived inclinations of the stellar rotational axis to the line of sight i = 24° as well as to the magnetic dipole axis β = 125° agree reasonably well with previous estimations by other authors, whereas the sky-projected position angle of the stellar rotation axis Ω ~ 110°, increasing clockwise toward the north celestial pole, is determined here for the first time.

Orientations of Spin and Magnetic Dipole Axes of Pulsars in the J0737-3039 Binary Based on Polarimetry Observations at the Green Bank Telescope

We report here the first polarimetric measurements of the pulsars in the J0737-3039 binary neutron star system using the Green Bank Telescope. The data suggest that the primary star (pulsar A) has a wide hollow cone of emission, which is an expected characteristic of the relatively open magnetosphere given its short spin period, and that pulsar A has a small angle between its spin and magnetic dipole axes, 4° ± 3°. This geometry suggests that pulsar A's wind pressure on pulsar B's magnetosphere will depend on orbital phase. This variable pressure is one mechanism for the variation of flux and profile shape of pulsar B with respect to the orbital phase that has been reported. The response of pulsar B to the pulsar A wind pressure will also depend on the particular side of its magnetosphere facing the wind at the spin phase when pulsar B is visible. This is a second possible mechanism for variability. We suggest that pulsar B may have its spin axis aligned with the orbital angular momentum owing to pulsar A's wind torque that contributes to its spin-down. Monitoring the pulsars while geodetic precession changes spin orientations will provide essential evidence to test detailed theoretical models. We determine the rotation measures of the two stars to be -112.3 ± 1.5 and -118 ± 12 rad m-2.

Modeling the Accretion Stream in Polars

I present a summary of my dissertation research into a method of modeling the accretion stream in magnetic cataclysmic variables known as polars. Polars are interacting binary stars in which the primary star is a magnetic white dwarf with a surface field strength 10 MG. Material is accreted from a low-mass main-sequence secondary star and funneled by the magnetic field onto the white dwarf surface. The standard, simple picture of the accretion stream has two regions: the ballistic path where the magnetic forces are negligible and the magnetically controlled path where the material is forced to flow along the magnetic field lines onto the white dwarf surface. The “coupling” point is located where the gas stream transitions from the ballistic path to the magnetically controlled path. The stream is assumed to be a thin tube with a cylindrically symmetric density distribution. This simple picture, however, is unable to explain the complex features often seen in polar observations. In order to develop a better understanding of the complex accretion streams, a more detailed model is needed. My models solve for the three-dimensional stream geometry and provide the density distribution and gas velocity throughout the stream from the L1 point to the white dwarf surface. In order to solve for the detailed stream structure without resorting to simplified geometries, we must employ computationally intensive algorithms such as smoothed particle hydrodynamics (SPH). SPH treats a continuous gas as a superposition of extended segments of the gas, referred to as particles. The hydrodynamic equations can then be approximated by summations over the particles. In my SPH models, the gas particles are released from the L1 boundary and then allowed to flow under the influence of the gravitational, rotational, and thermodynamic forces. These initial models use the common assumption that the magnetic pressure is negligible as long as the ram pressure of the gas is higher. Once the magnetic pressure on a particle exceeds the ram pressure, the particle “couples” and is forced to flow along the magnetic field lines. The SPH method has been applied to a “reference system” that has system parameters typical of what is found in known polars. The reference system results are in general agreement with the standard, simplified model of the accretion stream but show considerably more detail. Interesting features include the coupling region and the impact region on the white dwarf surface. The coupling region is significantly extended, approximately 11 white dwarf radii long. The low-density edges of the stream couple to the field lines first, while the higher density core of the stream is able to penetrate farther into the magnetosphere of the white dwarf. In addition, because of the orientation of the magnetic dipole axis to the stream, the edge of the stream closest to the dipole will begin to couple before the far edge. The resulting shape is an asymmetric cone. The basic structure in the coupling region is projected down to the white dwarf surface at the impact region. Material from the stream impacts the surface in an arc shape offset from the dipole axis. One end of the arc, corresponding to the material that coupled from the core of the stream, has a much higher density than material impacting along the remainder of the arc. The arc is more accurately described as a V shape with two wings extending out from the high-density core region. The impacting density drops off along these wings, which are also asymmetric. In addition to the stream geometry described above, the reference SPH model reveals another feature not seen in the standard simple accretion-stream model. While the vast majority of the gas in the stream flows away from the L1 point along the ballistic stream, a small fraction of the material is predicted to be controlled by the magnetic field immediately and couple to the lines directly at the L1 point. This small amount of material would flow along a distinct path and impact the white dwarf away from the main arc-shaped impact region. The initial reference model work was supplemented with additional SPH models that explore the effects of various system parameters on the accretion stream. In particular, the magnetic field strength, mass-transfer rate, dipole orientation, and stream temperature were varied. As expected, the coupling position depends upon the mass-transfer rate and magnetic field strength. The stream temperature, which is assumed to be isothermal, does not significantly affect the coupling position but does affect the width of the accretion stream. The dipole orientation naturally affects the geometry of the magnetically confined path and impact location on the white dwarf but shows

Radio Polarization of the Young High–Magnetic‐Field Pulsar PSR J1119−6127

We have investigated the radio polarization properties of PSR J1119� 6127, a recently discovered young radio pulsar with a large magnetic field. Using pulsar-gated radio imaging data taken at a center frequency of 2496 MHz with the Australia Telescope Compact Array, we have determined a rotation measure for the pulsar of +842 � 23 rad m � 2 . These data, combined with archival polarimetry data taken at a center frequency of 1366 MHz with the Parkes telescope, were used to determine the polarization characteristics of PSR J1119� 6127 at both frequencies. The pulsar has a fractional linear polarization of � 75% and � 55% at 1366 and 2496 MHz, respectively, and the profile consists of a single, wide component. This pulse morphology and high degree of linear polarization are in agreement with previously noticed trends for young pulsars (e.g., PSR J1513� 5908). A rotating vector (RV) model fit of the position angle of linear polarization over pulse phase using the Parkes data suggests that the radio emission comes from the leading edge of a conal beam. We discuss PSR J1119� 6127 in the context of a recent theoretical model of pulsar spin-down, which can in principle be tested with polarization and timing data from this pulsar. Geometric constraints from the RV fit are currently insufficient to test this model with statistical significance, but additional data may allow such a test in the future. Subject headings: polarization — pulsars: individual (PSR J1119� 6127) — radio continuum: stars — stars: neutron Pulsar polarimetry is one of the keys to understanding the process and geometry of radio emission from pulsars. In the rotating vector (RV) model (Radhakrishnan & Cooke 1969) the polarization of pulsar radio emission is linked to the emission geometry in such a way that as the pulsar rotates, the axis of linear polarization is aligned with the projected direction on the sky of the pulsar’s magnetic dipole axis. The pulsar’s emission geometry itself may be described by two angles, each measured from the pulsar’s angular

Dynamo mechanism in a rotating spherical shell: competition between magnetic field and convection vortices

A strong axial magnetic dipole field with magnetic energy 15 times larger than the kinetic energy of thermal convection is realized by a direct numerical simulation of the magnetohydrodynamic equation of an electrically conducting Boussinesq fluid in a rotating spherical shell which is driven by a temperature difference between the outer and inner boundaries against a gravity force pointed towards the system centre. Cyclonic and anticyclonic convection vortices are generated and play a primary role in the magnetic field intensification. The magnetic field is enhanced through the stretching of magnetic lines in four particular parts of the convection fields, namely inside anticyclones, between cyclones and their western neighbouring anticyclones at middle as well as low latitudes, and between anticyclones and the outer boundary. A ‘twist-turn’ loop of intense magnetic flux density is identified as a fundamental structure which yields dominant contributions both to the toroidal and poloidal components of the longitudinally averaged magnetic field. Various types of competitive interaction between the magnetic field and convection vortices are observed. Among these, a creation-and-annihilation cycle in a statistically equilibrium state is particularly important. It is composed of three sequentially recurrent dynamical processes: the generation of convection vortices by the Rayleigh–Bénard instability, the growth of anticyclones and the intensification of magnetic field by a concentrate-and-stretch mechanism, and the breakdown of vortices by the Lorentz force followed by diminution of the magnetic field. The energy transfer from the velocity to the magnetic fields takes place predominantly in this dynamical cycle.

An Asymptotic Solution for Boundary - Layer Fields Near a Convex Impedance Surface

—An analytic representation for fields (E, H) that, for wavenumber k, satisfies the Maxwell equations to order k -2/3 within a suitably-defined boundary-layer neighborhood is provided for the case of a general doubly-curved convex impedance surface. This solution is an ansatz construct obtained via heuristic modification of a residue-series solution to a corresponding circular-cylinder canonical problem with an infinitesimal axial magnetic dipole excitation. The field components are in the form of creeping-ray modal series written as functions of geodesic-polar and normal coordinates (s, , n) appropriate to the vicinity of a general convex surface. Adaptation of the canonical solution to the general case begins with a transformation from the native cylindrical (p, φ, z) coordinates of the canonical solution to a system ( p, c, s) defined by cylinder-surface geodesics. The transformed canonical solution is further modified by replacement of corresponding factors deriving from the metric and curl operators in the (p, c, s) and (s, , n) systems, and by pervasive application of a substitution previously employed in a more limited way by Pathak and Wang. The physical content of the substitution process is that the creeping-ray attenuation along the geodesics occurs independently of the surface normal curvature transverse to the geodesic direction.

Ring simulation experiment using fine-particle plasmas

We can create a ring structure around a magnetized miniature sphere which is immersed in a fine-particle plasma and rotated around its magnetic dipole axis. Aluminum fine particles generated by a boat method acquire charges by UV light irradiation and are converted to a fine-particle plasma. When the magnetized sphere was rotated in the fine-particle plasma, a ring appeared around the equatorial plane under certain conditions. Unipolar induction can reveal some of ring creation mechanisms of the ring; that is, the rotation frequency matches a theoretical simulating condition, and the location of the ring almost fits with the peak position of potential, which is two to three times the sphere radius. This experiment reveals one of mechanisms why the outer planets such as the Saturn, have rings. It indicates the fact that the unipolar induction plays an important role for the creation of the outer planets in the early stage of the solar system formation.

Numerical simulations of aligned neutron star magnetospheres

ABSTRA C T We present detailed numerical simulations of the magnetosphere of an isolated neutron star in which the spin and magnetic dipole axes of the star are aligned. We demonstrate that stable charge distributions are always found, rather than particle outflows. A stable magnetosphere consists of a dome above the polar cap containing plasma of one charge and an equatorial belt containing plasma of the other sign: E · Ba 0 inside both of these. These are separated by a vacuum gap in which E · B ‐ 0Ora 0 instead). We show that the charge distribution used in the ‘standard’ Goldreich‐Julian pulsar model is inherently unstable: it collapses to a stable configuration that is very similar to the others illustrated here. An instructive video of this collapse is available at http://spacsun.rice.edu/,ian/. For typical pulsars, the stable solution has no particles near to the light cylinder, and if there were any there then their loss from the system would not lead to a replacement from the star (in contradiction to the explicit assumption used in the Goldreich‐Julian model). We discuss the generic effects of pair creation, in particular as an additional source of ionization in the vacuum gap. The overall effect is simply to reduce the value of E · B in the vacuum gap so that the pair-production rate drops towards zero. A dome, disc and gap geometry is still the resulting solution. In conclusion, we confirm previous studies that the aligned rotator cannot make an active pulsar.

Energetic electron beams in the duskside Jovian magnetosphere: Ulysses EPAC and HI-SCALE measurements

The Ulysses flyby of Jupiter in February 1992 provided the first opportunity to investigate the high southern latitudes of the dusk side magnetosphere. We combine measurements taken by the Ulysses energetic particle instruments EPAC and HI-SCALE and identify bi-directional, field-aligned electron beams in an energy range from 100–380 keV. The beams are detected in southern Jovigraphic latitudes of 30°–36° and occur at distances between 14 and 80 Jovian radii ( R j) from the planet. These beams have electron distributions with small pitch angles and show a 10h period. The periodic appearance of these electron beams is related to the position of the planetary magnetic dipole axis relative to the position of Ulysses. From the pitch angle distribution (PAD) of the electron beams we also identify two different regions along the Ulysses trajectory similar to ion fluxes and anisotropies discussed by Cowley et al. (1996). These regions can be characterised by broad electron PADs at higher magnetic latitudes near the planet and very pronounced beams at higher magnetic latitudes far from the planet in the buter duskside magnetosphere. For the bi-directionality of the electron PAD we discuss whether the duskside magnetosphere is magnetically open or closed favouring a mainly closed magnetosphere.

Axisymmetric excitation of a dielectric torus: Numerical solution

The article considers the mathematical model of a lens antenna in the shape of a homogeneous dielectric torus excited by an axial magnetic dipole. The boundary-value problem for an elliptical differential equation is posed and reduced by the fundamental solution method to an integral equation of 2nd kind over the torus section. A numerical algorithm is proposed, and the numerical results are compared with experimental findings.