Dipole Magnetic Field Research Articles

Statistical relations between spectropolarimetric observables and the polar strength of the stellar dipolar magnetic field

Global magnetic fields of early-type stars are commonly characterised by the mean longitudinal magnetic field 〈Bz〉 and the mean field modulus 〈B〉, derived from the circular polarisation and intensity spectra, respectively. Observational studies often report a root mean square (rms) of 〈Bz〉 and an average value of 〈B〉. In this work, I used numerical simulations to establish statistical relationships between these cumulative magnetic observables and the polar strength, Bd, of a dipolar magnetic field. I show that in the limit of many measurements randomly distributed in rotational phase, 〈Bz〉rms = 0.179−0.043+0.031 Bd and 〈B〉avg = 0.691−0.023+0.020 Bd. The same values can be recovered with only three measurements, provided that the observations are distributed uniformly in the rotational phase. These conversion factors are suitable for ensemble analyses of large stellar samples, where each target is covered by a small number of magnetic measurements.

Comparison of Solar Wind Interaction with Mars and Earth: Energy Transfer

Using a global magnetohydrodynamics numerical simulation, this work compares the interaction of the solar wind with Mars and Earth from the perspective of energy transfer under north–south interplanetary magnetic fields (IMFs). Mars lacks a global dipole magnetic field like Earth’s and instead has a small-scale crustal magnetic field near highlands in the southern hemisphere. Unlike Earth’s magnetopause reconnection (at the subsolar point or tail under a southward IMF, or behind the cusp under a northward IMF), the reconnection of the Martian magnetic pileup boundary (MPB) occurs near solar zenith angle (SZA) ≈ 45° (SZA ≈ 30° and 60°) for a southward (northward) IMF, resulting in asymmetric energy transfer between the northern and southern hemispheres. The Martian outflow of mechanical energy appears near SZA ≈ 45° (SZA ≈ 30° and 60°) under a southward (northward) IMF, accompanied by an inflow due to the process of “solar wind pickup.” For energy transfer across the MPB, whether the IMF is northward or southward, the input of electromagnetic energy is twice as large as the input of mechanical energy, which is similar to Earth’s magnetopause for a southward IMF, but opposite to it for a northward IMF. The energy transfer rate of the MPB is slightly higher in a northward IMF than in a southward one, whereas the energy transfer rate of Earth’s magnetopause is far higher in a southward IMF than in a northward one.

Dyonium induced fermion number violation

Dyonium induced fermion number violation is studied in a SU(2)L×U(1)Y gauge theory with a doublet Higgs field. Dyonium is a generalization of Nambu's monopolium, having finite sized pair of dyon and anti-dyon, connected with a thin string under the linear plus Coulomb force.1This is a follow-up of the author's paper on monopolium induced neutrino mass (including the lepton and baryon number violations), studied with a SO(10) Grand Unified model in 1983. To fulfill the requirement from the chiral anomaly or its index theorem, an electric field should be excited in parallel to the dipole magnetic field. This crucial dynamical problem, not fully answered then, has been solved, by considering not monopolium but dyonium.The fermionic zero modes in the dyonium background fields are necessary in evaluating the transition rate of the fermion number violation processes. Their Dirac equation can be reduced to a single component partial differential equation, similar to the renormalization group equation, which may be useful to estimate the reaction rates.

Particles with magnetic dipole moment orbiting magnetized Schwarzschild black holes: Applications to orbits of hot-spots around Sgr A*

We study the circular motion of particles with magnetic dipole moment around Schwarzschild black holes immersed in external asymptotically uniform and dipolar magnetic field configurations and calculate the orbital velocity of the particles. We assume that the flares observed around supermassive black hole Sagittarius (Sgr) A* detected by the GRAVITY ESO collaboration (on May 27, July 22, and July 28, 2018) are magnetized compact objects, in particular, neutron stars (NSs) and white dwarfs (WDs). Also, we apply orbital and luminosity data from (three) flares to explore the possible role of magnetic interaction on hot spots’ dynamics. First, we found the mass range of SgrA* using the orbital data in the absence of external magnetic fields as M=(3−6.3)M⊙. It is also found that, for magnetized particles that can be in the hot spot’s orbits, the magnetic coupling parameter β has to take values less than 0.13 and 0.25 in the cases of external dipolar and uniform magnetic fields, respectively. The critical values for the surface magnetic fields, mass, and radius of magnetized NSs and WDs are found to be candidates for the hot-spot objects. Finally, we found upper and lower limits for the surface magnetic field, radius, and rotating period of the NSs and WDs, using the luminosity data of the hot spots.

Polarization perspectives on Hercules X-1: further constraining the geometry

ABSTRACT We conduct a comprehensive analysis of the accreting X-ray pulsar, Hercules X-1, utilizing data from Imaging X-ray Polarimetry Explorer (IXPE) and Nuclear Spectroscopic Telescope Array. IXPE performed five observations of Her X-1, consisting of three in the Main-on state and two in the Short-on state. Our time-resolved analysis uncovers the linear correlations between the flux and polarization degree as well as the pulse fraction and polarization degree. Geometry parameters are rigorously constrained by fitting the phase-resolved modulations of Cyclotron Resonance Scattering Feature and polarization angle with a simple dipole model and Rotating Vector Model, respectively, yielding roughly consistent results. The changes of χp (the position angle of the pulsar’s spin axis on the plane of the sky) between different Main-on observations suggest the possible forced precession of the neutron star crust. Furthermore, a linear association between the energy of Cyclotron Resonance Scattering Feature and polarization angle implies the prevalence of a dominant dipole magnetic field, and their phase-resolved modulations likely arise from viewing angle effects.

Theoretical Analysis of the RX J0209.6−7427 X-Ray Spectrum during a Giant Outburst

We model the spectral formation occurring in the binary X-ray pulsar (XRP) RX J0209.6−7427 during the 2019 super-Eddington outburst. Using a theoretical model previously developed by the authors, we are able to produce spectra that closely resemble the phase-averaged X-ray spectra observed using the Nuclear Spectroscopic Telescope Array and Insight-HXMT during low- and high-luminosity states of the outburst, respectively. The theoretical model simulates the accretion of fully ionized gas in a dipole magnetic field and includes a complete description of the radiation hydrodynamics, matter distribution, and spectral formation. Type II X-ray outbursts provide an opportunity to study accretion over a large range of luminosities for the same neutron star. The analysis performed here represents the first time both the outburst low and high states of an accretion-powered XRP are modeled using a physics-based model rather than standard phenomenological fitting with arbitrary mathematical functions. We find that the outer polar cap radius remains constant and the column is more fully filled with increasing luminosity, Comptonized bremsstrahlung dominates the formation of the phase-averaged X-ray spectrum, and a negative correlation exists between cyclotron centroid energy and luminosity, as expected. The super-Eddington nature of the outburst is rendered possible owing to the low scattering cross section for photons propagating parallel to the magnetic field. We also find that emission through the column top dominates in both the low and high states, implying that the pulse profiles should have a roughly sinusoidal shape, which agrees with observed properties of ultraluminous XRPs.

Study of Electron Energy Distribution Function, Transport Parameters and Instability Analysis of Argon Plasma confined by a Dipole Magnet

This theoretical study is to investigate production and properties of plasma confined by a dipole magnet. A cylindrical permanent magnet (N40 grade) having a surface magnetic field of nearly 1Tesla is simulated to create a dipole magnetic field. Plasma is created by electron cyclotron resonance heating. Heating is accomplished using microwaves operating in continuous mode at 2.45 GHz and electron cyclotron resonance. The investigation is performed in systems of cylindrical geometries at varying pressures (0.5 mTorr – 1.5 mTorr). The electron temperature lies in the range of 1 - 5 eV, is hotter near the magnets and follows a downstream fashion throughout the region.Electron Energy Distribution Function (EEDF) growth investigation throughout the region was done to understand the role of magnetic field confinement. The EEDF was calculated numerically from steady state Boltzmann equation, considering plasma follows druyvesteyn distribution. Followed by analysing transport parameters such as diffusion coefficient, drift velocity, mobility, and recombination rates in plasma. A comparative study for all plots gave been done with respect to pressure. The instability analysis of elastic collisional frequency with inelastic collisions, real frequency and growth factor with wave vector has been also listed in the study.

Role of partial stable stratification on fluid flow and heat transfer in rotating thermal convection

The liquid iron core of the Earth undergoes vigorous convection driven by thermal and compositional buoyancy. The dynamics of convective fluid motions and heat transfer in such conditions are determined by background rotation, geometrical symmetry, and thermal interactions across the boundaries. In this study, rotating thermal convection in a horizontal fluid layer is considered to understand the fluid flow characteristics in the Earth's outer core focusing on the regions close to the rotational axis. The effects of a partial stable stratification on fluid flow and heat transfer are investigated to ascertain the physical significance of thermal core–mantle interaction on geomagnetic field generation driven by core fluid motion. It is found that even with non-linear evolution, convective instabilities retain the fundamental characteristics of linear onset modes. Mildly supercritical regimes lead to near laminar flows with the transition to turbulent convection occurring for strongly driven convection around 50–100 times enhanced buoyancy. Axial symmetry breaking and preferential damping of small-scale vortical structures are the hallmark of penetrative convection. Rapid rotation sustains small-scale helical flows in stable regions, a necessary ingredient for the sustenance of Earthlike dipolar magnetic fields. Coherent flow structures for strongly turbulent convection are obtained using reduced-order modeling. The overall total heat transfer is suppressed (up to 25%) due to the stable stratification although convective efficiency is enhanced (up to 30%) in the unstable regions favored by rapid rotation. Flow suppression is overcome under strong buoyancy forces, a relevant dynamical regime for deep-seated dynamo action in the Earth's core.

Electron Resonant Interaction With Coherent ULF Waves: Hamiltonian Approach

AbstractElectron resonant interaction with ultra‐low‐frequency (ULF) waves is considered to be a driver of electron radial transport in Earth’s inner magnetosphere. Traditional concept of such interaction assumes the electron slow diffusive scattering by a broad‐band ULF spectrum, but recent spacecraft observations reported a possibility for electrons to resonate nonlinearly with intense coherent ULF waves. This study proposes a theoretical model describing the main elements of such nonlinear resonant interactions. We implement a Hamiltonian approach to describe equatorial electron motion in a dipole magnetic field and electric ULF wavefield and demonstrate the ULF‐electron interactions has two basic nonlinear resonant regimes: phase bunching and phase trapping. Finally, we discuss possible applications of the proposed theoretical approach and the importance of ULF‐electron nonlinear resonances.

Errors in average strength estimates of sedimentary rock masses in South Yakutia based on geometric induction sounding data

The probabilistic model developed to describe the engineering and geological conditions for the operation of buildings and infrastructure in the city of Neryungri has been verified. The model is a power-function equation which correlates, by regression relationships, laboratory-determined compressive strength of saturated frozen sandstone samples with attenuation of the high-frequency harmonic field of a vertical magnetic dipole in warm permafrost composed of sandstone. The attenuation values were obtained by geometric electromagnetic induction sounding at a frequency of 1.125 MHz. The model verification was conducted at a fixed frequency on a section of the Amur-Yakutsk Railway located at a significant distance from Neryungri. The railway here is underlain by low-temperature dolomite masses. The statistical analysis indicates that the relative errors of the dolomite saturated strength estimates from the geometric EM induction data with a 73.0% probability do not exceed 20%. With this level of accuracy close to that of laboratory tests according to GOST 25100–2020, it is reasonable to suggest that the probabilistic model can be used region-wide in southern Yakutia to predict saturated strength of foundation materials composed of sandstone and dolomite. It can provide an effective solution for market-based construction and mining industries, as increasing anthropogenic and climatic impacts are anticipated to cause thawing and saturation of sedimentary rock masses.

Plug-and-Play latent feature editing for orientation-adaptive quantitative susceptibility mapping neural networks

Quantitative susceptibility mapping (QSM) is a post-processing technique for deriving tissue magnetic susceptibility distribution from MRI phase measurements. Deep learning (DL) algorithms hold great potential for solving the ill-posed QSM reconstruction problem. However, a significant challenge facing current DL-QSM approaches is their limited adaptability to magnetic dipole field orientation variations during training and testing. In this work, we propose a novel Orientation-Adaptive Latent Feature Editing (OA-LFE) module to learn the encoding of acquisition orientation vectors and seamlessly integrate them into the latent features of deep networks. Importantly, it can be directly Plug-and-Play (PnP) into various existing DL-QSM architectures, enabling reconstructions of QSM from arbitrary magnetic dipole orientations. Its effectiveness is demonstrated by combining the OA-LFE module into our previously proposed phase-to-susceptibility single-step instant QSM (iQSM) network, which was initially tailored for pure-axial acquisitions. The proposed OA-LFE-empowered iQSM, which we refer to as iQSM+, is trained in a simulated-supervised manner on a specially-designed simulation brain dataset. Comprehensive experiments are conducted on simulated and in vivo human brain datasets, encompassing subjects ranging from healthy individuals to those with pathological conditions. These experiments involve various MRI platforms (3T and 7T) and aim to compare our proposed iQSM+ against several established QSM reconstruction frameworks, including the original iQSM. The iQSM+ yields QSM images with significantly improved accuracies and mitigates artifacts, surpassing other state-of-the-art DL-QSM algorithms. The PnP OA-LFE module’s versatility was further demonstrated by its successful application to xQSM, a distinct DL-QSM network for dipole inversion. In conclusion, this work introduces a new DL paradigm, allowing researchers to develop innovative QSM methods without requiring a complete overhaul of their existing architectures.

Simulating the Ring Current Proton Dynamics in Response to Radial Diffusion by Ultra‐Low‐Frequency (ULF) Waves

AbstractRadial diffusion (RD) induced by ULF waves can contribute to particle acceleration and scattering. Past global simulations that incorporate RD often use dipole magnetic fields, which could not realistically reveal the role of RD. To better understand the effects of RD and identify whether a background magnetic field model matters in understanding the ring current dynamics in response to RD, we simulate a storm event with different magnetic configurations using a global kinetic ring current model. Results indicate that RD can effectively diffuse protons of hundreds of keV to inner regions (L ∼ 3.5), especially in recovery phase. Comparisons with in‐situ observations demonstrate that simulations with TS05 overall capture both the intensity and variations of proton fluxes with the aid of RD, whereas that with a dipole field significantly overestimates low‐L region fluxes. This study implies adopting realistic magnetic fields is important for correctly interpreting the role of RD.

Characterizing the dynamical magnetosphere of the extremely slowly rotating magnetic O9.7 V star HD 54879 using rotational modulation of the Hα profile

AbstractThe magnetic field in the O9.7 V star HD 54879 has been monitored for almost a decade. Spectropolarimetric observations reveal a rather strong mean longitudinal magnetic field that varies with a period of about 7.41 years. Observations in the H line show a variation with the same period, while the H line shows only little variation. Assuming the periodic variation to be caused by a slow rotation and a dipolar magnetic field, we find a magnetic field strength of 2 kG at the magnetic poles. With the relatively low mass loss rate of year−1, this star is a case of extremely strong magnetic confinement. Both theoretical arguments and numerical simulations indicate the presence of an extended disk of increased gas density in the equatorial plane of the magnetic field, where gas from the line‐driven stellar wind is trapped. This disk is likely to be the origin of the observed H emission, which peaks together with the strongest line‐of‐sight magnetic field. The profile of the H line is resolved in several components and shows a remarkable variability with the rotation period.

Reversals and Large-Scale Variations of the Geomagnetic Field: Similarities and Differences

It is shown that during reversals in geodynamo models the minimum amplitudes of the
 dipole, quadrupole and octupole coincide. Since the characteristic time of the reversal is
 close to the oscillations of the large-scale geomagnetic field, a similar analysis was carried
 out for the minima of the amplitude of the dipole magnetic field over the past 100 thousand
 years. It turned out that in this case such synchronization also occurs. It can be assumed
 that reversals and large scale variations of the geomagnetic field between the reversals have
 a lot in common. The wavelet analysis carried out indicates that the concept of the main
 geodynamo cycle is very arbitrary: the period of oscillation can vary from 8-10 thousand
 years to 20-30 thousand for a dipole. Analysis of the evolution of the Mauersberger spectrum
 allows us to conclude that magnetic field fluctuations observed at the Earth’s surface are
 associated with the transfer of the magnetic field to the surface of the liquid core and can
 hardly be described by functions periodic in time.

Exploring slip effects of ferrofluid film flow over a slanted rough surface

We examined the influences of slip parameters on the velocity and thermal characteristics of a ferrofluid film of fixed thickness. The flow is generated on a rough and inclined whirling surface that is positioned in an external magnetic (dipole) field. The similarity transformation reduces the model equations (continuity, momentum, energy and concentration), and the solution of the normalized coupled ordinary differential equations is carried out through the finite element process. The influences of slip effects, Brownian motion, thermophoresis and a heat source on the velocity (radial, tangential and axial), gravity (drainage, induced), temperature profile and concentration profile are determined. The tangential flow and temperature are both decreased by an increase in the velocity slip parameter, whereas drainage, induced, radial and axial flows are increased. Enlarging the thermal slip parameter decreases the temperature. Improving slip parameters (velocity and thermal) also improves the concentration profile. Both Nusselt and Sherwood numbers are found to improve on improving the velocity slip parameter, while they decrease on decreasing the thermal slip parameter. The results and insights from this work could be applied to a wide range of medicinal fields, such as targeted medication therapy and delivery, tissue engineering, etc. as well as different industrial processes including coating, lubrication, heat transfer, etc.

Linear Theory Analysis and One‐Dimensional Hybrid Simulations of High‐Frequency EMIC Waves in a Dipole Magnetic Field

AbstractNarrowband (Δf ≲ 0.1fcp), high‐frequency (0.9fcp ≲ f < fcp) electromagnetic ion cyclotron (EMIC) waves, or HFEMIC waves for short, are a relatively new type of EMIC waves, where fcp is the proton cyclotron frequency. Here, we investigate the instability threshold conditions and the nonlinear evolution of HFEMIC waves at parallel propagation. First, linear theory analysis is extended to a regime relevant to HFEMIC waves (parallel proton beta β‖p < 0.01). The instability threshold follows a similar anisotropy‐β‖p relation and requires a large value of anisotropy (T⊥p/T‖p ≳ 10) for wave growth. As a result of decreasing group velocity, the convective growth rate at a fixed threshold exhibits a similar inverse relation with β‖p. Heavy ions affect the instability only weakly, primarily through the introduction of stop bands. Second, we carry out one‐dimensional hybrid simulations in a parabolic background magnetic field, with initial parameters constrained by observation. Despite the narrow source region (within about ±3° latitude), HFEMIC waves can grow well above the thermal noise level due in large part to a small group velocity of HFEMIC waves. The saturation level is well within the range of observational amplitudes, and the quasilinear process primarily determines the wave evolution. Finally, we demonstrate that the present results compare favorably to the recent statistical results, thereby supporting anisotropic low‐energy protons as free energy source for HFEMIC waves.

Properties of Mars' Dayside Low‐Altitude Induced Magnetic Field and Comparisons With Venus

AbstractMars and Venus have atmospheres but lack intrinsic dipole magnetic fields. Consequently, the solar wind interaction at each planet results in the formation of an induced magnetosphere. Our work aims to compare the low‐altitude (< 250 km) component of the induced magnetic field at Venus and Mars using observations from Pioneer Venus Orbiter and Mars Atmosphere and Volatile EvolutioN. We restrict the in‐situ data from Mars to regions of weak crustal magnetism. At Venus, it has long been known the vertical structure of the induced magnetic field profiles have recurring features that enable them to be classified as either magnetized or unmagnetized. We find the induced field profiles at Mars are more varied, lack recurring features, and are unable to be classified in the same way. The solar zenith angle dependence of the low‐altitude field strength at both planets is controlled by the shape of the magnetic pileup boundary. Also, because the ionospheric thermal pressure at Venus is often comparable to the solar wind dynamic pressure, the induced fields are weaker than required to balance the solar wind by themselves. By contrast, induced fields at Mars are stronger than required to achieve pressure balance. Lastly, we find the induced fields in the magnetized ionosphere of Venus have a weaker dependence on solar wind dynamic pressure than the induced fields at Mars. Our results point to planetary properties, such as planet‐Sun distance, having a major effect on the properties of induced fields at nonmagentized planets.

Observational features of charge distribution in Earth’s inner magnetosphere

Understanding the motion of charged particles in the electromagnetic field in the inner magnetosphere is essential for space science and space weather. Charge accumulation can occur due to the dipole magnetic and convective electric fields in this region. However, until the recent Magnetospheric Multiscale (MMS) mission, there were few means to detect charge distribution in situ. We report unambiguous in situ observation of the spatial distribution of the excess charge density in the inner magnetosphere by the MMS mission. We find that a positive (negative) charge accumulates in the dusk (dawn) side inner magnetospheres, which is contrary to the long assumed overall quasi-neutrality of space plasma. These observations and results offer insight into magnetosphere–ionosphere coupling.

Rotating Massive Strangeon Stars and X-Ray Plateau of Short GRBs

Strangeon stars, which are proposed to describe the nature of pulsar-like compact stars, have passed various observational tests. The maximum mass of a non-rotating strangeon star could be high, which implies that the remnants of binary strangeon star mergers could even be long-lived massive strangeon stars. We study rigidly rotating strangeon stars in the slowly rotating approximation, using the Lennard-Jones model for the equation of state. Rotation can significantly increase the maximum mass of strangeon stars with unchanged baryon numbers, enlarging the mass-range of long-lived strangeon stars. During spin-down after merger, the decrease of radius of the remnant will lead to the release of gravitational energy. Taking into account the efficiency of converting the gravitational energy luminosity to the observed X-ray luminosity, we find that the gravitational energy could provide an alternative energy source for the plateau emission of X-ray afterglow. The fitting results of X-ray plateau emission of some short gamma-ray bursts suggest that the magnetic dipole field strength of the remnants can be much smaller than that of expected when the plateau emission is powered only by spin-down luminosity of magnetars.

The Statistical Mechanics of Ideal Magnetohydrodynamic Turbulence and a Solution of the Dynamo Problem

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’.