Dipole Magnetic Field Research Articles

Earthward‐Tailward Asymmetry of Plasma Temperature in Reconnection Outflow in Earth's Magnetotail

AbstractTo explore the asymmetry in ion and electron heating at Earth's magnetotail at mid‐tail distances ( −30 ), we analyze near‐simultaneous observations of reconnection outflows from two opposite sides of reconnection sites at those distances using Magnetospheric Multiscale (MMS) and Acceleration, Reconnection, Turbulence and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) data. We report a pronounced temperature asymmetry between the earthward and tailward reconnection outflows. The asymmetry is more significant for electrons than for ions: Earthward moving ions are only three times hotter than tailward ones, but earthward moving electrons are 5–20 times hotter than tailward ones. The closed field‐line topology on the earthward side of the reconnection region, as opposed to the open topology on the tailward side, is likely a critical contributor to this asymmetry. These findings cast light on the underlying mechanisms of particle heating and energization in magnetotail reconnection, highlighting the significant role of Earth's dipolar magnetic field. This study offers insights for refining magnetic reconnection models, emphasizing the importance of incorporating realistic magnetic field topologies to accurately simulate the heating and energization processes observed in space plasma environments.

MeerKAT observations of pair-plasma induced birefringence in the double pulsar eclipses

ABSTRACT PSR J0737−3039A/B is unique among double neutron star systems. Its near-perfect edge-on orbit causes the fast spinning pulsar A to be eclipsed by the magnetic field of the slow spinning pulsar B. Using high-sensitivity MeerKAT radio observations combined with updated constraints on the system geometry, we studied the impact of these eclipses on the incident polarization properties of pulsar A. Averaging light curves together after correcting for the rotation of pulsar B revealed enormous amounts of circular polarization and rapid changes in the linear polarization position angle, which occur at phases where emission from pulsar A is partially transmitted through the magnetosphere of pulsar B. These behaviours confirm that the eclipse mechanism is the result of synchrotron absorption in a relativistic pair-plasma confined to the closed-field region of pulsar B’s truncated dipolar magnetic field. We demonstrate that changes in circular polarization handedness throughout the eclipses are directly tied to the average line of sight magnetic field direction of pulsar B, from which we unambiguously determine the complete magnetic and viewing geometry of the pulsar.

Energetics of Buchdahl stars and the magnetic Penrose process

Buchdahl star is the most compact object without an event horizon and is an excellent candidate for a black hole mimicker. Unlike black holes, rotating Buchdahl star can be over-extremal with respect to the black hole, sustaining a larger spin. We show that it can also develop an ergosphere above the threshold spin β>1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta > 1/\\sqrt{2}$$\\end{document}, which allows extraction of its rotational energy. Electromagnetic field around Buchdahl star is also expected to differ from that of black hole in both strength and topology. In this paper, we explore the energetics of Buchdahl star focusing on the magnetic Penrose process in the two magnetic field configurations, i.e., uniform and dipole. Below the threshold spin, Buchdahl star is expected to be quiet, while above the threshold it can be much more efficient than the black hole if a dipolar magnetic field is developed on its surface.

Comprehensive investigations on spectral and temporal features of GX 5−1 using AstroSat observations

ABSTRACT Comprehensive spectrotemporal analyses of the Z-type neutron star low-mass X-ray binary GX 5−1 were performed using 10 broad-band observations from AstroSat/Soft X-ray Telescope and Large Area X-ray Proportional Counter (LAXPC) instruments. The LAXPC-20 hardness–intensity diagram showed horizontal and normal branches (HBs and NBs) of the Z track which exhibited secular motion. The time-averaged spectra in the energy range 0.7–25.0 keV could be fitted with the model combination – $\tt {constant}\, \times \, \tt {tbabs}\, \times \, \tt {edge}\, \times \, \tt {edge}\, \times \, \tt {thcomp}\, \times \, \tt {diskbb}$. This yielded $\Gamma \, \sim$ 2, $kT_{\mathrm{ e}}\, \sim$ 3.3 keV, and $F_{\mathrm{ disc}}$/$F_{\mathrm{ total}}\, \sim$ 0.8 indicating the soft/intermediate spectral state of the source during the observations. Flux-resolved spectral analysis revealed a positive correlation between $kT_{\mathrm{ in}}$ and $F_{\mathrm{ bol}}$. However, a negative correlation was observed between them in one of the NBs. Time-averaged temporal analysis revealed multiple HB oscillations (HBOs) and NB oscillations (NBOs), and peaked noise components in the $\sim$5–50 Hz range. Furthermore, flux-resolved temporal analysis showed that the frequency of the HBOs correlates positively whereas the strength of HBOs correlates negatively with $F_{\mathrm{ bol}}$, indicating their probable origin from the accretion disc. In contrast, the frequency and strength of NBOs remain fairly constant with $F_{\mathrm{ bol}}$, suggesting that they originate from a different region in the system. Using the relativistic precession model along with highest frequency of the HBO, the upper limits of the magnetic dipole moment ($\mu$) and field strength (B) at the poles of the neutron star in the system were found to be 25.60$\times \, 10^{25}$ G cm3 and 3.64$\times \, 10^{8}$ G, respectively, for $k_{\mathrm{ A}}$ = 1.

Plasmoids and Magnetic Field Dipolarizations During Juno's First 47 Orbits: Is Ion Acceleration Always Observed in the Dipolarizations?

AbstractPlasmoids and magnetic field dipolarizations are reconnection‐related phenomena often resulting in reconfiguration of the magnetic field and energetic particle acceleration in planetary magnetotail. Building on the work of Blöcker et al. (2023) (10.1029/2023JA031312), we selected seven specific events from their magnetic field dipolarization analysis, each exhibiting distinct ion dynamics during the time interval of the magnetic field dipolarizations. To gain further insights into the understanding why certain events were associated with ion intensity variations while others were not, we analyzed plasma moments, specifically ion flow velocity and density, for these selected events. Our findings revealed that certain magnetic field dipolarizations within our database exhibit sub‐Alfvénic flows and lack the properties typically associated with reconnection‐related magnetic field dipolarizations. These magnetic field dipolarizations also do not accelerate ions. Furthermore, we present a survey of Jovian plasmoids and magnetic field dipolarizations during the first 47 orbits of Juno. Applying Juno magnetic field data, we identified 119 magnetic field dipolarizations and 94 plasmoids within a local time range of 18:00–06:00. The majority of plasmoids were detected in the predawn sector, whereas magnetic field dipolarizations were observed closer to Jupiter and were not limited to a specific local time. Combining the statistics of plasmoids and dipolarizations is useful for contextualizing them within the framework of reconnection.

A necessary condition for breakeven in dipole-confined plasmas

We have derived a necessary condition for the achievement of breakeven in axisymmetric plasmas with zero toroidal field and confined by a dipole magnetic field (B. Lehnert, Nature, vol. 181, 1958, p. 4605; A. Hasegawa, Comments Plasma Phys. Control. Fusion, vol. 11, no. 3, 1987). Excellent MHD stability, high values of $\beta$ (up to $26$ %) and good confinement properties awaken the interest of private investors after years of neglect due to lack of public funding and competing alternative lines of research like the tokamak. Starting from a requirement of self-consistency between the balances of momentum and energy in a dipole-confined, two-species plasma and assuming a Maxwellian distribution function for ions and electrons, we derive a necessary condition for breakeven. This condition is more stringent than the Lawson criterion because of the lack of a stabilizing toroidal field. For a given current flowing across the toroidal coil internal to the plasma, the crucial factor at stake is the ratio between the radius of the main toroidal coil and the radius of the vacuum chamber.

Gyrokinetic linear simulation of feedback instability in dipole magnetosphere

We perform a novel linear simulation of the feedback instability by applying a gyrokinetic model to the magnetosphere, where the geomagnetic field is modeled by a dipole magnetic field. In order to avoid huge numerical calculation costs, the effect of the fluctuating mirror force is neglected. It is found that kinetic effects, such as the finite Larmor radius effect and the electron Landau damping, strongly stabilize the feedback instability and form a peak in the perpendicular wave number spectrum of the growth rate. During the linear growth, it is observed that electron free energy has a much larger value than the electromagnetic field perturbation energy. Since such large electron free energy may lead to electron heating and acceleration, it is important to understand its generation mechanism. Analyses based on the energy conservation reveal that the coupling of the non-uniformity of the equilibrium fields along the geomagnetic field and the fluctuating electron distribution gives rise to thermodynamic power generating the electron free energy. A fine velocity space structure around an average Alfvén velocity of the fluctuating electron distribution mainly contributes to drive the thermodynamic power.

Deflection of charged signals in a dipole magnetic field in Kerr background

This paper investigates charged particle deflection in a Kerr spacetime background with a dipole magnetic field, focusing on the equatorial plane and employing the weak field approximation. We employ the Jacobi–Randers metric to unify the treatment of the gravitational and electromagnetic effects on charged particles. Furthermore, we utilize the Gauss–Bonnet theorem to calculate the deflection angle through curvature integrals. The difference between the prograde and retrograde deflection angles is linked to the non-reversibility of metrics and geodesics in Finsler geometry, revealing that this difference can be considered a Finslerian effect. We analyze the impact of both gravitomagnetic field and dipole magnetic field on particle motion and deflection using the Jacobi–Randers magnetic field. The model considered in this paper exhibits interesting features in the second-order approximation of (M/b), i.e., the ratio between the spacetime mass and impact parameters. When qμ=2MaE\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q\\mu =2MaE$$\\end{document}, where q,E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q,\\,E$$\\end{document} are the charge and asymptotic energy of the charged particle and μ,a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu ,\\,a$$\\end{document} are the dipole magnetic moment and spacetime spin, the Jacobi–Randers metric possesses reversible geodesics, leading to equal prograde and retrograde deflection angles. In this case, the gravitomagnetic field and dipole magnetic field cancel each other out, distinguishing it from scenarios involving only the gravitomagnetic field or the dipole magnetic field. We also explore the magnetic field’s impact on gravitational lensing of charged particles.

A quantitative explanation of the cyclotron-line variation in accreting magnetic neutron stars of super-critical luminosity

Context. Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering feature (CRSF) in their X-ray spectra. Cyclotron lines are believed to be generated in the radiative shock in the accretion column. High-luminosity NSs show a smooth anti-correlation between the cyclotron-line centroid (ECRSF) and X-ray luminosity (LX). Aims. It has been pointed out that the observed ECRSF − LX smooth anti-correlation in high-luminosity NSs is in tension with the theoretically predicted one, if the radiative shock is the site of cyclotron-line formation. The shock height increases approximately linearly with luminosity, while the dipolar magnetic field drops as the cubic power of distance, thereby implying that the cyclotron-line energy ought to decrease significantly when the luminosity increases by, say, an order of magnitude, which is contrary to observations. Since there is no other candidate site for the cyclotron-line formation, we re-examine the predicted rate of change of the cyclotron-line energy with luminosity at the radiative shock, taking a closer look at the Physics involved. Methods. We developed a purely analytical model describing the overall dependence of the observed cyclotron energy centroid on the shock front’s height, including both the relativistic boosting and the gravitational redshift effects in our considerations. The relativistic boosting effect is due to the mildly relativistic motion of the accreting plasma upstream with respect to the shock’s reference frame. Reults. We find that the cyclotron-line energy varies with (a) the shock height due to the dipolar magnetic field, (b) the Doppler boosting between the shock and bulk-motion frames, and (c) the gravitational redshift. We show that the relativistic effects noticeably weaken the predicted ECRSF − LX anti-correlation. We use our model to fit the data of the X-ray source V0332+53 that exhibits a weak negative correlation and demonstrate that the model fits the data impressively well, thereby alleviating the tension between observations and theory. Conclusions. The reported weak anti-correlation between cyclotron-line centroid and X-ray luminosity in the supercritical accretion regime may be explained by the combination of the variation of the magnetic-field strength along the accretion column, the effect of Doppler boosting, and the gravitational redshift. As a result of these effects, the actual magnetic field on the surface of the neutron star may be a factor of ∼2 larger than the naively inferred value from the observed CRSF.

Circular Polarization of Simulated Images of Black Holes

Models of the resolved Event Horizon Telescope (EHT) sources Sgr A* and M87* are constrained by observations at multiple wavelengths, resolutions, polarizations, and time cadences. In this paper, we compare unresolved circular polarization (CP) measurements to a library of models, where each model is characterized by a distribution of CP over time. In the library, we vary the spin of the black hole, the magnetic field strength at the horizon (i.e., both SANE and magnetically arrested disk or MAD models), the observer inclination, a parameter for the maximum ion–electron temperature ratio assuming a thermal plasma, and the direction of the magnetic field dipole moment. We find that Atacama Large Millimeter/submillimeter Array (ALMA) observations of Sgr A* are inconsistent with all edge-on (i = 90°) models. Restricting attention to the MAD models favored by earlier EHT studies of Sgr A*, we find that only models with magnetic dipole moment pointing away from the observer are consistent with ALMA data. We also note that in 26 of the 27 passing MAD models, the accretion flow rotates clockwise on the sky. We provide a table of the means and standard deviations of the CP distributions for all model parameters, along with their trends.

The Asymmetrical Distribution of a Dominant Motional Electric Field within the Martian Magnetosheath

Attributed to the lack of an Earth-like global intrinsic dipole magnetic field on Mars, the induced electromagnetic field environment plays a crucial role in the evolution of its atmosphere. The dominant motional electric field (EM) induced by the bulk motion of the magnetic field within the Martian magnetosheath serves to accelerate ions toward escape velocity, thereby forming a plume escape channel. However, the distribution morphology of EM itself has received limited attention in previous research. In this study, by taking advantage of the multi-fluid Hall-MHD model cooperating with the Martian crustal field model, we focus on elucidating the physical mechanisms underlying the asymmetrical distribution of EM and examining the influence of the crustal field on this asymmetry. The results obtained from the simulation conducted in the absence of the crustal field indicate that the EM is more intense within the −ZMSE magnetosheath, where EM is directed toward Mars, primarily due to its corresponding higher velocity and a stronger magnetic field at lower solar zenith angles. The Martian crustal field has the ability to enhance the local EM around the inner boundary of the magnetosheath by amplifying both the magnetic field and its associated velocity. Accordingly, these findings provide valuable insights into the asymmetric nature of EM within the Martian magnetosheath under typical quiet-time solar wind conditions.

X-ray Polarimetry of X-ray Pulsars

Radiation from X-ray pulsars (XRPs) was expected to be strongly linearly polarized owing to a large difference in their ordinary and extraordinary mode opacities. The launch of IXPE allowed us to check this prediction. IXPE observed a dozen X-ray pulsars, discovering pulse-phase dependent variation of the polarization degree (PD) and polarization angle (PA). Although the PD showed rather erratic profiles resembling flux pulse dependence, the PA in most cases showed smooth variations consistent with the rotating vector model (RVM), which can be interpreted as a combined effect of vacuum birefringence and dipole magnetic field structure at a polarization-limiting (adiabatic) radius. Application of the RVM allowed us to determine XRP geometry and to confirm the free precession of the NS in Her X-1. Deviations from RVM in two bright transients led to the discovery of an unpulsed polarized emission likely produced by scattering off the accretion disk wind.

A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437–4715

We report Bayesian inference of the mass, radius, and hot X-ray emitting region properties—using data from the Neutron Star Interior Composition ExploreR (NICER)—for the brightest rotation-powered millisecond X-ray pulsar, PSR J0437−4715. Our modeling is conditional on informative tight priors on mass, distance, and binary inclination obtained from radio pulsar timing using the Parkes Pulsar Timing Array (PPTA; Reardon et al.), and we use NICER background models to constrain the nonsource background, cross-checking with data from XMM-Newton. We assume two distinct hot emitting regions and various parameterized hot region geometries that are defined in terms of overlapping circles; while simplified, these capture many of the possibilities suggested by detailed modeling of return current heating. For the preferred model identified by our analysis, we infer a mass of M = 1.418 ± 0.037 M ⊙ (largely informed by the PPTA mass prior) and an equatorial radius of R=11.36−0.63+0.95 km, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. This radius favors softer dense matter equations of state and is highly consistent with constraints derived from gravitational wave measurements of neutron star binary mergers. The hot regions are inferred to be nonantipodal and hence inconsistent with a pure centered dipole magnetic field.

A quantum sensor for atomic-scale electric and magnetic fields

The detection of faint magnetic fields from single-electron and nuclear spins at the atomic scale is a long-standing challenge in physics. While current mobile quantum sensors achieve single-electron spin sensitivity, atomic spatial resolution remains elusive for existing techniques. Here we fabricate a single-molecule quantum sensor at the apex of the metallic tip of a scanning tunnelling microscope by attaching Fe atoms and a PTCDA (3,4,9,10-perylenetetracarboxylic-dianhydride) molecule to the tip apex. We address the molecular spin by electron spin resonance and achieve ~100 neV resolution in energy. In a proof-of-principle experiment, we measure the magnetic and electric dipole fields emanating from a single Fe atom and an Ag dimer on an Ag(111) surface with sub-angstrom spatial resolution. Our method enables atomic-scale quantum sensing experiments of electric and magnetic fields on conducting surfaces and may find applications in the sensing of spin-labelled biomolecules and of spin textures in quantum materials.

Closed magnetic topology in the Venusian magnetotail and ion escape at Venus

Venus, lacking an intrinsic global dipole magnetic field, serves as a textbook example of an induced magnetosphere, formed by interplanetary magnetic fields (IMF) enveloping the planet. Yet, various aspects of its magnetospheric dynamics and planetary ion outflows are complex and not well understood. Here we analyze plasma and magnetic field data acquired during the fourth Venus flyby of the Parker Solar Probe (PSP) mission and show evidence for closed topology in the nightside and downstream portion of the Venus magnetosphere (i.e., the magnetotail). The formation of the closed topology involves magnetic reconnection—a process rarely observed at non-magnetized planets. In addition, our study provides an evidence linking the cold Venusian ion flow in the magnetotail directly to magnetic connectivity to the ionosphere, akin to observations at Mars. These findings not only help the understanding of the complex ion flow patterns at Venus but also suggest that magnetic topology is one piece of key information for resolving ion escape mechanisms and thus the atmospheric evolution across various planetary environments and exoplanets.

The high count-rate self-triggering Silicon Tracking System of the CBM experiment at FAIR: Design, series assembly, upgrade options

The Compressed Baryonic Matter (CBM) experiment is a stationary target spectrometer with hadron and lepton identification. It is under construction at the Facility for Antiproton and Ion Research (FAIR) that is being realized next to the GSI grounds in Darmstadt, Germany. CBM will investigate QCD matter at highest, up to supernova core-collaps baryonic densities (Ablyazimov et al., 2017). This will be done in collisions of nuclear beams with targets at center of mass energies sNN=2.9–4.9 GeV. Because of the long beam extraction technique employed at FAIR’s SIS100 synchrotron, CBM’s data collection can be based on streaming time-stamped detector data into a compute farm. Event determination and physics analysis are performed there online, allowing for collision rates up to 10 MHz. CBM’s core tracking detector is the Silicon Tracking System, operating 8 tracking stations based on double-sided silicon microstrip sensors and self-triggering front-end electronics in a 1 Tm dipole magnetic field (Heuser et al., 2013).

The Thousand-Pulsar-Array programme on MeerKAT – XV. A comparison of the radio emission properties of slow and millisecond pulsars

ABSTRACT We use data from the MeerTime project on the MeerKAT telescope to ask whether the radio emission properties of millisecond pulsars (MSPs) and slowly rotating, younger pulsars (SPs) are similar or different. We show that the flux density spectra of both populations are similarly steep, and the widths of MSP profiles obey the same dependence on the rotational period as slow pulsars. We also show that the polarization of MSPs has similar properties to slow pulsars. The commonly used pseudo-luminosity of pulsars, defined as the product of the flux density and the distance squared, is not appropriate for drawing conclusions about the relative intrinsic radio luminosity of SPs and MSPs. We show that it is possible to scale the pseudo-luminosity to account for the pulse duty cycle and the solid angle of the radio beam, in such a way that MSPs and SPs do not show clear differences in intrinsic luminosity. The data therefore support common emission physics between the two populations in spite of orders of magnitude difference in their period derivatives and inferred, surface, dipole magnetic field strengths.

A conclusive non-detection of magnetic field in the Am star o Peg with high-precision near-infrared spectroscopy

The A-type metallic-line (Am) stars are typically considered to be non-magnetic or to possess very weak sub-G magnetic fields. This view has been repeatedly challenged in the literature; most commonly for the bright hot Am star Several studies claim to have detected 1--2 kG field of unknown topology in this object, possibly indicating a new process of magnetic-field generation in intermediate-mass stars. In this study, we revisit the evidence of a strong magnetic field in using new high-resolution spectropolarimetric observations and advanced spectral fitting techniques. We estimated the mean magnetic field strength in from the high-precision CRyogenic InfraRed Echelle Spectrograph $) measurement of near-infrared (NIR) sulphur lines. We modelled this observation with a polarised radiative transfer code, including treatment of the departures from local thermodynamic equilibrium. In addition, we used the least-squares deconvolution multi-line technique to derive longitudinal field measurements from archival optical spectropolarimetric observations of this star. Our analysis of the NIR S i lines reveals no evidence of Zeeman broadening, ruling out magnetic field with a strength exceeding 260 G. This null result is compatible with the relative intensification of Fe ii lines in the optical spectrum, taking into account blending and uncertain atomic parameters of the relevant diagnostic transitions. Longitudinal field measurements on three different nights also yield null results with a precision of 2 G. This study refutes the claims of kG-strength dipolar or tangled magnetic field in This star therefore appears to be non-magnetic, with surface magnetic field characteristics no different from those of other Am stars.

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.