A review of lunar and planetary magnetic field measurements using space probes.
Magnetic dipole moments of moon, Mars and Venus using space probes, discussing solar wind near- earth planetary field interaction measurements
SOLAR WIND↗
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Theoretical study of NH2 - Potential curves, transition moments, and photodissociation cross sections
Photodissociation cross sections from the ground state of NH2 have been calculated using a pseudodiatomic model. The potential curves needed in these calculations, functions of one NH bond length, were obtained by ab initio MCSCF calculations on the five lowest doublet states of NH2 using a contracted Gaussian basis set of double zeta quality augmented by polarization and Rydberg functions. Transition dipole moments between the ground and excited states were evaluated using MCSCF wave functions.
Saxon, R. P.↗
Large-scale Cosmic-ray Anisotropies with 19 yr of Data from the Pierre Auger Observatory
Results are presented for the measurement of large-scale anisotropies in the arrival directions of ultra–high-energy cosmic rays detected at the Pierre Auger Observatory during 19 yr of operation, prior to AugerPrime, the upgrade of the observatory. The 3D dipole amplitude and direction are reconstructed above 4 EeV in four energy bins. Besides the established dipolar anisotropy in R.A. above 8 EeV, the Fourier amplitude of the 8–16 EeV energy bin is now also above the 5σ discovery level. No time variation of the dipole moment above 8 EeV is found, setting an upper limit to the rate of change of such variations of 0.3% yr$^{−1}$ at the 95% confidence level. Additionally, the results for the angular power spectrum are shown, demonstrating no other statistically significant multipoles. The results for the equatorial dipole component down to 0.03 EeV are presented, using for the first time a data set obtained with a trigger that has been optimized for lower energies. Finally, model predictions are discussed and compared with observations, based on two source emission scenarios obtained in the combined fit of spectrum and composition above 0.6 EeV.
79 ASTRONOMY AND ASTROPHYSICS↗
Nuclear Structure Studies for Schiff Moment Enhancement
One of the major open questions in modern physics is the origin of the matter-antimatter asymmetry observed in the universe. While the Standard Model contains sources of charge-parity (CP) violation, they appear insufficient to explain the observed dominance of matter over antimatter. As a result, searches for additional sources of CP violation are an important area of contemporary nuclear and particle physics. Atomic electric dipole moments (EDMs) provide sensitive probes of CP-violating interactions. In heavy nuclei, the observable atomic EDM can be enhanced through the presence of a nuclear Schiff moment, which arises from CP-violating nuclear forces and nuclear structure effects. The review paper Nuclear Schiff Moments and CP Violation by Jonathan Engel provides an overview of the theoretical framework connecting CP violation, nuclear structure, and Schiff moments. The long-term goal of this project is to contribute to the identification and characterization of nuclei that may exhibit enhanced Schiff moments. Such nuclei are often associated with strong octupole correlations or low-energy parity-doublet structures that can amplify CP-violating effects. This report summarizes progress made during the initial phase of the project, including a survey of candidate isotopes and preparation for nuclear-structure calculations using the HFODD code.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
On the 2018 Outburst of the Accreting Millisecond X-Ray Pulsar Swift J1756.9-2508 As Seen with NICER
We report on the coherent timing analysis of the 182 Hz accreting millisecond X-ray pulsar SwiftJ1756.92508during its 2018 outburst as observed with the Neutron Star Interior Composition Explorer (NICER). Combiningour NICER observations with Rossi X-ray Timing Explorer observations of the 2007 and 2009 outbursts, we alsostudied the long-term spin and orbital evolution of this source. We find that the binary system is well describedby a constant orbital period model, with an upper limit on the orbital period derivative of Pb < 7.4 ´ 10-13 ss1.Additionally, we improve upon the source coordinates through astrometric analysis of the pulse arrival times,finding R.A.=17h56m57 18±0 08 and decl.=25°0627 8±3 5, while simultaneously measuring thelong-term spin frequency derivative as n = -7.3 ´ 10-16 Hzs1. We briefly discuss the implications of thesemeasurements in the context of the wider population of accreting millisecond pulsars. We reported on the coherent timing analysis of the 2018 outburst of Swift J1756 as observed with NICER. Consistent with analyses of the previous outbursts (Krimm et al. 2007b; Patruno et al. 2010), we find that the X-ray pulsations have energy dependent amplitudes; the fractional amplitude of the fundamental increases with energy, whereas the fractional amplitude of the harmonic shows a slight decline with energy. This energy dependent behavior is not unusual in AMXPs (Patruno & Watts 2012) and can be interpreted in terms of the thermal emission from the stellar hotspot and reprocessing in the accretion column (e.g., Gierliński et al. 2002; Ibragimov & Poutanen 2009). The pulse arrival times of the 2018 outburst are well described by a timing model consisting of a circular orbit with a constant spin frequency. The pulse phases with respect to this model do not show spurious residuals with time or orbital phase, and no evidence is found that the pulse arrival times exhibit an additional delay associated with passing through the gravitational well of the companion star (Shapiro delay). We note, however, that the expected Shapiro delay is given as (Shapiro et al. 1971) Equation (5) where Φ is the orbital phase, G is the gravitational constant, c is the speed of light, and i is the inclination. Even for the maximum allowed companion mass, ${M}_{C}=0.030\,{M}_{\odot }$ (Krimm et al. 2007b, but see Section 4.2 for more details) and an inclination of 90°, the largest delay we can expect is only 4 μs. As this time-delay is smaller than the uncertainty on our phase residuals by nearly two orders of magnitude (see Figure 1), we are not sensitive to Shapiro delays in Swift J1756. Comparing our measurements for the 2018 outburst with those of the 2007 and 2009 outbursts as observed with RXTE, we analyzed the long-term evolution of this source. We found that the binary system is consistent with having a constant orbital period and that the pulsar shows a spin frequency derivative of $\dot{\nu }=-7.3\times {10}^{-16}\,\mathrm{Hz}\,{{\rm{s}}}^{-1}$. 4.1. Spin-down Evolution The long-term spin frequency derivative measured in Swift J1756 is of the same order as the spin frequency derivatives measured in other AMXPs (Hartman et al. 2008; Patruno 2010; Riggio et al. 2011). This frequency change is most likely driven by the neutron star's loss of rotational energy. If so, then the spin-down luminosity is given as Equation (6) where I represents the neutron star moment of inertia. The long-term spin-down of a neutron star is usually assumed to be dominated by the braking torque associated with a spinning magnetic field. Assuming this mechanism is responsible for the observed spin-down in Swift J1756, we can compute the magnetic dipole moment as (Spitkovsky 2006) Equation (7) where α is the misalignment angle between the rotational and magnetic poles. Considering α = 0°–90°, we then find a magnetic field strength of $B\simeq (4\mbox{--}6)\times {10}^{8}$ G at the stellar magnetic poles. This magnetic field strength estimate is in line with those obtained for other accreting millisecond pulsars (see Mukherjee et al. 2015 and references therein). 4.2. Orbit Evolution The observed long-term binary evolution of Swift J1756 is consistent with this source having a constant orbital period and a lower limit on the evolutionary timescale of Equation (8) Binary evolution theory predicts that systems of this type evolve due to angular momentum loss through gravitational radiation (Kraft et al. 1962; Rappaport et al. 1982; Verbunt 1993). For conservative mass transfer, the binary period derivative is given by di Salvo et al. (2008), Equation (9) where MNS is the neutron star mass, $q={M}_{C}/{M}_{\mathrm{NS}}$ is the binary mass ratio, and −1/3 < n < 1 is the mass–radius index of the companion star. Depending on the source inclination, Krimm et al. (2007b) derived a companion mass of ${M}_{C}\,=0.007\mbox{--}0.022\,{M}_{\odot }$ for a neutron star mass of 1.4 ${M}_{\odot }$. For a neutron star mass of 2.2 ${M}_{\odot }$, the allowed range increased to ${M}_{C}=0.009\mbox{--}0.030\,{M}_{\odot }$. In both cases, they assumed an upper limit on the inclination of i < 85°, motivated by the fact that Swift J1756 does not show eclipses in its light curve. Accounting for the extreme cases of stellar masses and n, the binary may either be contracting or expanding. In either case, however, the rate of change is limited to $| {\dot{P}}_{b}| \lesssim 7\times {10}^{-14}$ s s−1, which is well below the upper limit obtained in this work. Although the binary evolution timescale we obtain for Swift J1756 is consistent with theory, it is worth noting that this is not generally true for low-mass X-ray binaries (see Patruno et al. 2017, for a comprehensive discussion). The AMXP SAX J1808.4–3658, in particular, has been found to evolve on a much shorter timescale, with a first derivative on the orbital period of $3.5\times {10}^{-12}$ s s−1 (Hartman et al. 2008; Patruno et al. 2012; Sanna et al. 2017a). Two models have been proposed to explain this discrepancy: highly nonconservative mass transfer due to irradiation of the companion star by the pulsar (di Salvo et al. 2008; Burderi et al. 2009), and spin–orbit coupling in the companion star (Hartman et al. 2008, 2009). While the latter depends on the companion star, and may vary from source to source, the former should operate in all AMXPs (see also Patruno 2017; Sanna et al. 2017c), including Swift J1756. The spin-down luminosity impinging on the companion star can be estimated as Equation (10) where ${\dot{E}}_{\mathrm{abl}}$ is the ablation luminosity, RL2 is the Roche lobe radius of the companion (Eggleton 1983), and a the binary separation. The irradiation fraction is $f={\dot{E}}_{\mathrm{abl}}/{\dot{E}}_{\mathrm{sd}}$, which, accounting for the range of allowed neutron star and companion masses, evaluates to f = 0.15%–0.35%. The associated mass loss for the companion is given by Equation (11) such that, assuming an efficiency of η = 100%, ${\dot{M}}_{C}\,\sim -3\times {10}^{-10}\,{M}_{\odot }$ yr−1. The effect of this mass loss on the orbital period follows through the relation (Frank et al. 2002) Equation (12) giving a period derivative due to mass loss of ${\dot{P}}_{b,\mathrm{ML}}\,=5\times {10}^{-12}$ s s−1. This value is well above our limit on the period derivative. Hence, in order for this mechanism to be consistent with our observations of Swift J1756, the efficiency at which the companion star converts the incident luminosity into mass loss must be η < 15%. This value is very different from the 40% required in SAX J1808.4–3658 (Patruno et al. 2016) and is instead in line with the <5% efficiency determined for IGR J00291+5934 (Patruno 2017). This work was supported by NASA through the NICER mission and the Astrophysics Explorers Program, and made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC). P.B. was supported by an NPP fellowship at NASA Goddard Space Flight Center. D.A. acknowledges support from the Royal Society.
Bult, Peter↗
The Varying Core Magnetic Field from a Space Weather Perspective
This paper summarizes recent advances in our understanding of geomagnetism, and its relevance to terrestrial space weather. It also discusses specific core magnetic field features such as the dipole moment decay, the evolution of the South Atlantic anomaly, and the location of the magnetic poles that are of importance for the practice of space weather.
Core Field↗
Magnetohydrodynamic Turbulence and the Geodynamo
Recent research results concerning forced, dissipative, rotating magnetohydrodynamic (MHD) turbulence will be discussed. In particular, we present new results from long-time Fourier method (periodic box) simulations in which forcing contains varying amounts of magnetic and kinetic helicity. Numerical results indicate that if MHD turbulence is forced so as to produce a state of relatively constant energy, then the largest-scale components are dominant and quasistationary, and in fact, have an effective dipole moment vector that aligns closely with the rotation axis. The relationship of this work to established results in ideal MHD turbulence, as well as to models of MHD turbulence in a spherical shell will also be presented. These results appear to be very pertinent to understanding the Geodynamo and the origin of its dominant dipole component. Our conclusion is that MHD turbulence, per se, may well contain the origin of the Earth's dipole magnetic field.
Shebalin, John V.↗
A Passive Gravitational Attitude Control System for Satellites
It is shown how the gravity-gradient effect may be utilized to design a long-lived, earth-pointing satellite attitude control system which requires no fuel supplies, attitude sensors or active control equipment. This two-body system is provided with a magnetic hysteresis damper which effectively damps out oscillations (librations) about the local vertical. The long rods, which must be extended in space from coiled up metal tapes, provide the required large moments of inertia and possess adequate rigidity and sufficient strength to endure the rigors of the extension process. The system is compatible with the requirements of multiple satellite launchings from a single last-stage vehicle. Analysis indicates that the gravitational torques are sufficient to keep the disturbing effects of solar radiation pressure, residual magnetic dipole moments, orbit eccentricity, rod curvature, eddy currents, and meteorite impacts within tolerable limits. It is believed that the high-performance, earth-pointing system described and analyzed in this paper represents an essential step in the development of high-capacity communications satellites requiring long life.
GRAVITY↗
A search for the dipole anisotropy of the Cosmic x ray background
X ray data was analyzed which was obtained by the HEAO-1 A2 satellite in order to look for large scale structure in the Cosmic X ray Background. The dipole moment of the x ray background is deltaI/I = (1.87 + or - .34)x 10(exp -2) in a direction, declination = 3.6 + or - 9.4 deg and right ascension = 15.9 + or - .2 hr. This implies a velocity of the Earth with respect to the background of 409.2 + or - 74.4 km/s in the same direction. Comparatively, measurements of the dipole anisotropy of the Cosmic Microwave Background imply a velocity of 369.2 + or - 4 km/s in a direction, declination = 6 + or - 1 deg and right ascension = 11.2 + or - .1 hr. Quoted errors are statistical only. The disparity between the velocities of the x ray dipole and microwave dipole may be due to residual structure in the x ray sky or as yet undiscovered systematic errors.
Evans, Tom↗
Theory of global thermoremanent magnetization of planetary lithospheres in dipole fields of internal origin
A model is presented for the global thermoremanent magnetization of spherical lithospheres which cool in the presence of central dipole fields. Reversals and intensity variations of the field are incorporated in this model, which is applicable to bodies whose interiors have remained above the Curie point throughout their evolution. The model demonstrates that even considering Runcorn's (1975) magnetostatics theorems for spherical shells, a nonzero magnetic permeability and a finite cooling rate in the lithosphere permit the acquisition of a sizable global remanent dipole moment, which would be detectable by external measurements after the magnetizing field has disappeared. Preliminary application of this model to Mercury, Venus, and Mars suggests that only the combination of a nonreversing ancient source field with a surface value near 1 Oe plus a sizable concentration (about 1% by volume) of ferromagnetic material in their crusts could produce remanent planetary dipole fields as large as those measured by spacecraft. On the other hand, if ancient reversing dynamos existed in these planets, it is unlikely that large planetary-scale fields like those observed at Mercury could be due to remanence in their crusts, irrespective of their composition.
Srnka, L. J.↗
On the search for an intrinsic magnetic field at Venus
Magnetic field observations obtained by the Pioneer Venus orbiter at low altitude are now available for two sets of orbits in the Venus wake. Data from these 130 orbits are examined for possible surface correlated features or any intrinsic magnetic moment. No surface correlated magnetic fields are observed, but the threshold for the detectability of such fields at Venus is about an order of magnitude greater than at the moon. A surface feature of 10 deg extent would have to create an anomaly of at least 5 gammas at 200 km to be detected in the Pioneer Venus data. Using measurements averaged in 72 10 x 10 deg bins, a planetary magnetic dipole moment of 0.87 + or - 3.00 x 10 to the 21st gauss-cu cm is obtained. Thus the upper limit of the present day Venus moment is less than 4 x 10 to the -5th of the terrestrial moment.
Russell, C. T.↗
Excitation and tunneling spectra of a fractional quantum Hall system in the thin-cylinder limit
Here, the excitations of fractional quantum Hall effect (FQHE) states have been largely inaccessible to experimental probes until recently. New electron scanning tunneling microscopy (STM) results from Hu et al. [Nat. Phys. 21, 716 (2025)] show promise in detecting and identifying these excited states via the local density of states (LDOS) spectrum. On a torus, there exists a mapping from the lowest Landau level states to a 1D lattice with a Hamiltonian that features dipole moment conservation. In this work, we apply perturbation theory starting from the thin-cylinder limit (𝐿 𝑥 → ∞, 𝐿 𝑦 < 𝑙 𝐵 for torus dimensions 𝐿 𝑥 and 𝐿 𝑦 and magnetic length 𝑙 𝐵 ) to obtain an analytical approach to the low-lying neutral and charged excitations of the 𝜈 = 1/3 FQHE state. Notably, in the thin cylinder, we can systematically enumerate all the low-lying excitations by the patterns of “dipoles” formed by the electron occupation pattern on the 1D lattice. We find that the thin-cylinder limit predicts a significant dispersion of the low-lying neutral excitations but sharpness of the LDOS spectra, which measure charged excitations. We also discuss connections between our work and several different approaches to the FQHE STM spectra, including those using the composite fermion theory. Numerical exact diagonalization beyond the thin-cylinder limit suggests that the energies of charged excitations remain largely confined to a narrow range of energies, which in experiments might appear as a single peak.
Adhidewata, Jyesta M. [University of California, B↗
A test of the galactic origin of gamma-ray bursts
Models in which gamma-ray bursters are young neutron stars may be difficult to reconcile with the apparently isotropic distribution of observed bursts. To justify this statement, the distribution of old neutron stars in the Galaxy was calculated by integrating numerically some 90,000 orbits in the Galactic gravitational potential for up to 10 to the 10th yr. Other calculations included the dipole moment in the angular distribution of neutron stars as a convenient measure of their concentration toward the Galactic center, the quadrupole moment in their angular distribution as a convenient measure of their concentration toward the Galactic plane, and the average value of V/Vmax as a convenient measure of the radial distribution of neutron stars. Models that require accretion from a cold circumstellar disk or from a close companion are only marginally consistent with the isotropic distribution of the observed bursts. Models that require accretion of interstellar matter are ruled out due to a very strong dipole anisotropy. Models that suggest the Galactic halo origin of gamma-ray bursts are briefly discussed. The GRANAT and GRO missions should provide evidence for or against the association of gamma-ray bursts with the Galactic disk neutron stars.
Paczynski, Bohdan↗
The magnetic moment of Venus - Venera-4 measurements reinterpreted
Venera-4 magnetic-field measurements made during that spacecraft's descent through the atmosphere of Venus are reexamined using three models for the interaction of the solar-wind with the planet. The first model assumes the existence of just the interplanetary and planetary magnetic fields; the second admits the presence of a magnetosheath and a current layer, but assumes that the magnetosheath field is spatially uniform between the planet and the bow shock; the third assumes shielding of the planetary field from the magnetosheath field by a current layer. All three models are found to yield a strong altitude dependence for the magnitude of the planetary field, suggesting that the intrinsic magnetic dipole moment of Venus may exceed that of both Mars and Mercury. It is concluded that a Venusian surface field of 30 gammas is a plausible interpretation of the Venera-4 measurements.-
Russell, C. T.↗
Limits on the possible intrinsic magnetic field of Venus
Magnetic field measurements obtained by the Pioneer Venus orbiter at low altitudes in the solar wind wake region are examined for possible surface-correlated features and any possible intrinsic magnetic moment. The field variations observed in the wake do not resemble those expected for a solar wind interaction with even a weak intrinsic magnetic field. Little orbit-to-orbit persistence of features is found in the magnetic records. The magnetic field measurements in the wake are averaged in 10 deg x 10 deg bins to minimize the effects of external field sources. In these 37 bins, the average fields appear to be randomly oriented and consistent with zero mean in the region mapped. Using these 37 averaged vector fields, a maximum intrinsic magnetic dipole moment is obtained of 4.3 + or - 2.0 x 10 to the 21st G cu cm, approximately an order of magnitude less than previous estimates. It is noted that a more conservative estimate of the probable error of the mean is 5.5 x 10 to the 21st G cu cm. The Pioneer Venus measurements are thus consistent with zero planetary moment. The present measurements are found to be far below estimates made on the basis of angular momentum, the so-called magnetic Bode's law, and far below the dynamo scaling law of Busse.
Russell, C. T.↗
On the determination of the Hermaean magnetic moment - A critical review
The determination of Mercury's magnetic moment from the spatially and temporally limited observations obtained by the Mariner 10 mission is dependent upon the assumed nature of both the intrinsic planetary magnetic field and that of the magnetospheric current systems. In this paper the methods that have been used for this purpose are reviewed. The results that have been obtained are then considered in comparison with the constraints placed on the planetary field by the solar wind dynamic pressures and stand-off distances inferred from the Mariner 10 magnetic field data by Slavin and Holtzer (1979) which are consistent with an effective dipole moment of 6 + or - 2 x 10 to the 22nd G cu cm. It is found that the models which fit the observations with substantial quadrupole and octupole moments are not consistent with the magnetospheric boundary conditions, presumably owing to incorrect assumptions regarding the magnetopause position, incorrect assumptions regarding solar wind dynamic pressure, and/or averaging over temporal variations in the Mariner 10 data.
Slavin, J. A.↗
Magnetic Shield Design Modeling and Validation for SWOT Spacecraft Ka-Band Extended Interaction Klystron
Two Extended Interaction Klystrons (EIKs) containing strong permanent magnets were modeled magnetically in a representative spacecraft geometry using commercial finite element modeling techniques and were validated against measurements made at varying distances. Initial modeling results for the 63 A-m2 dipole moment magnets showed that magnetic shields would be necessary in order to meet magnetic field requirements for the Surface Water and Ocean Topography (SWOT) spacecraft, which contains components that are susceptible to external DC magnetic fields. JPL and the EIK vendor proposed cold rolled steel and mu-metal as potential shield materials along with proposed thicknesses of 0.5 mm and 1.5 mm. Magnetic shields made from each of these materials were designed and modeled in software, taking highfield saturation into account. Prototype magnetic shields with these parameters were then built, measured with an existing EIK, and compared against modeling results. For single-axis field measurements along the dipole axis, modeling results were within 7 gauss of the measured values at 10 cm from the magnet, and converged to less than 1.5 gauss at distances greater than 14 cm from the magnet. Three-axis field measurements at locations of interest showed that model correlation improved to within 4 gauss at 11 cm and 2 gauss for distances ranging between 15 cm and 36 cm.
Gonzales, Edward↗
Magnetic Shield Design Modeling and Validation for SWOT Spacecraft Ka-Band Extended Interaction Klystron
Two Extended Interaction Klystrons (EIKs) containing strong permanent magnets were modeled magnetically in a representative spacecraft geometry using commercial finite element modeling techniques and were validated against measurements made at varying distances. Initial modeling results for the 63 A-m2 (amperes per square meter) dipole moment magnets showed that magnetic shields would be necessary in order to meet magnetic field requirements for the Surface Water and Ocean Topography (SWOT) spacecraft, which contains components that are susceptible to external DC (Direct Current) magnetic fields. JPL (Jet Propulsion Laboratory) and the EIK vendor proposed cold rolled steel and mu-metal as potential shield materials along with proposed thicknesses of 0.5 millimeters and 1.5 millimeters. Magnetic shields made from each of these materials were designed and modeled in software, taking high-field saturation into account. Prototype magnetic shields with these parameters were then built, measured with an existing EIK, and compared against modeling results. For single-axis field measurements along the dipole axis, modeling results were within 7 gauss of the measured values at 10 centimeters from the magnet, and converged to less than 1.5 gauss at distances greater than 14 centimeters from the magnet. Three-axis field measurements at locations of interest showed that model correlation improved to within 4 gauss at 11 centimeters and 2 gauss for distances ranging between 15 centimeters and 36 centimeters.
Gonzales, Edward↗