The Earth’s magnetic field as it is measured by low-Earth orbit satellites such as
Swarm
and CHAMP results from the superposition of internal and external source fields overlapping in time and in ...space. The Earth’s lithospheric field is one of the weakest sources detectable from space and its accurate description requires treatments of rapidly-varying magnetic fields generated by current systems in the ionosphere and magnetosphere. In this paper, we review methods most commonly used in geomagnetism to identify and then to correct for the external perturbation fields at satellite altitudes. We document the pros and cons of Fourier Filtering, polynomial and Spherical Harmonics analyses, Singular Spectral Analysis (SSA) and Line-levelling techniques. The difficulties are illustrated with an application of the methods on a common set of real
Swarm
magnetic field measurements and with a discussion on the differences between lithospheric field models obtained with each treatment. We finally discuss some perspectives for improvements of external field correction techniques relying on statistical or more explicit assumptions about the geographical distribution as well as the shape and strengths of the external magnetic field structures.
Unique information about the dynamo process acting at Jupiter can be inferred by modeling and interpreting its magnetic field. Using the fluxgate magnetometer measurements acquired during the 4 years ...of the Juno mission, we derive a magnetic field model which describes simultaneously the main field and the secular variation (SV) up to spherical harmonic degrees 16 and 8, respectively. Apart from the Earth's, this is the first time another planetary magnetic field along with its time variation is described to such a high degree. We use properties of the power spectrum of the static field to infer the upper boundary of the dynamo convective region at 0.830 ± 0.022 Jupiter radius. The SV and correlation times are relatively comparable to the Earth's and indicate that the field is dominated by advection. The field and SV morphologies suggest zonal as well as non‐zonal deep fluid motions.
Plain Language Summary
The interior of Jupiter can be described broadly as a dense core surrounded by fluids, dominantly hydrogen and helium. The hydrogen‐rich metallic fluid generates the strongest planetary magnetic field in the Solar System. Modeling and interpreting this field gives essential information about the dynamo process inside Jupiter. We use the Juno mission data throughout 4 years (or, 28 orbits) to derive an internal magnetic field and secular variation (SV) model using spherical harmonic functions. We compute a magnetic field model to degree 16 for its static part, and model its temporal variation to degree 8. The power spectrum of the magnetic field model is used to investigate the radius of the dynamo region. We infer that the convective region has an upper boundary at 0.830 ± 0.022 Jupiter radius. The strength of the annual change of field is relatively comparable to the Earth's. The slope of the SV timescales indicates that the dynamo is dominated by advective effects. The SV displays a maximum near the equator with a bi‐polar structure in agreement with zonal drift of the Great Blue Spot. However, numerous small scale SV structures suggest that the flow at the interior is complex involving both zonal and non‐zonal features.
Key Points
Magnetic field of Jupiter is modeled from Juno's first 4 years of observations
A degree 16 magnetic field model and degree 8 secular variation model are derived
The model indicates a dynamo not far from the surface and complex motions deep inside Jupiter
Observations of the geomagnetic field taken at Earth’s surface and at satellite altitude are combined to construct continuous models of the geomagnetic field and its secular variation from 1957 to ...2020. From these parent models, we derive candidate main field models for the epochs 2015 and 2020 to the 13th generation of the International Geomagnetic Reference Field (IGRF). The secular variation candidate model for the period 2020–2025 is derived from a forecast of the secular variation in 2022.5, which results from a multi-variate singular spectrum analysis of the secular variation from 1957 to 2020.
Mercury is characterized by a very peculiar magnetic field, as it was revealed by the MESSENGER mission. Its internal component is highly axisymmetric, dominated by the dipole, and very weak. This in ...turns leads to a very dynamic magnetosphere. It is known that there exist relationships between the internally generated field and the external field, although their dynamics are complex. In this study we derive steady and time‐varying spherical harmonic models of Mercury's magnetic field using MESSENGER measurements and interpret these models both in terms of correlated features and of the internal structure of Mercury. The influence of the hemispheric data distribution of MESSENGER is evaluated to grant the robustness of our models. We find a quadrupole‐to‐dipole ratio of 0.27 for the steady magnetic field. The time‐varying models reveal periodic and highly correlated temporal variations of internal and external origins. This argues for externally inducing and internally induced sources. The main period is 88 days, the orbital period of Mercury around the Sun. There is no measurable time lag between variations of external and internal magnetic fields, which place an upper limit of 1 S/m for the mantle conductivity. Finally, the compared amplitudes of external and internal time‐varying field lead to an independent (from gravity studies) estimate of the conductive core radius, at 2,060 ± 22 km. These analyses will be further completed with the upcoming BepiColombo mission and its magnetic field experiment, but the presented results already lift the veil on some of the magnetic oddities at Mercury.
Key Points
We model Mercury's magnetic field with spherical harmonics
We analyze time‐varying external (inducing) and internal (induced) magnetic fields
We estimate Mercury's core size at 2,060 km
Aims. The Sun shows strong variability in its magnetic activity, from Grand minima to Grand maxima, but the nature of the variability is not fully understood, mostly because of the insufficient ...length of the directly observed solar activity records and of uncertainties related to long-term reconstructions. Here we present a new adjustment-free reconstruction of solar activity over three millennia and study its different modes. Methods. We present a new adjustment-free, physical reconstruction of solar activity over the past three millennia, using the latest verified carbon cycle, 14C production, and archeomagnetic field models. This great improvement allowed us to study different modes of solar activity at an unprecedented level of details. Results. The distribution of solar activity is clearly bi-modal, implying the existence of distinct modes of activity. The main regular activity mode corresponds to moderate activity that varies in a relatively narrow band between sunspot numbers 20 and 67. The existence of a separate Grand minimum mode with reduced solar activity, which cannot be explained by random fluctuations of the regular mode, is confirmed at a high confidence level. The possible existence of a separate Grand maximum mode is also suggested, but the statistics is too low to reach a confident conclusion. Conclusions. The Sun is shown to operate in distinct modes – a main general mode, a Grand minimum mode corresponding to an inactive Sun, and a possible Grand maximum mode corresponding to an unusually active Sun. These results provide important constraints for both dynamo models of Sun-like stars and investigations of possible solar influence on Earth’s climate.
•First quasi-hemispheric magnetic field model based on the entire MESSENGER’s mission lifetime.•First regional model in the Northern hemisphere of Mercury to the spatial resolution of about 900km ...downward continued to the core-mantle boundary.•First order separation of internal and external fields at Mercury over the Northern hemisphere.•A new estimate for the internal axial quadrupole to axial dipole ratio of 0.27 was derived.
This paper presents the first regional model of the magnetic field of Mercury developed with mathematical continuous functions. The model has a horizontal spatial resolution of about 830km at the surface of the planet, and it is derived without any a priori information about the geometry of the internal and external fields or regularization. It relies on an extensive dataset of the MESSENGER’s measurements selected over its entire orbital lifetime between 2011 and 2015. A first order separation between the internal and the external fields over the Northern hemisphere is achieved under the assumption that the magnetic field measurements are acquired in a source free region within the magnetospheric cavity. When downward continued to the core-mantle boundary, the model confirms some of the general structures observed in previous studies such as the dominance of zonal field, the location of the North magnetic pole, and the global absence of significant small scale structures. The transformation of the regional model into a global spherical harmonic one provides an estimate for the axial quadrupole to axial dipole ratio of about g20/g10=0.27. This is much lower than previous estimates of about 0.40. We note that it is possible to obtain a similar ratio provided that more weight is put on the location of the magnetic equator and less elsewhere.
We recently proposed a technique able to represent the spatial variations of the magnetic field at regional scales. However, we pointed out that these preliminary developments were not suited for the ...complete representation of the geomagnetic field. In this paper, we propose a complete revision, the revised spherical cap harmonic analysis (R‐SCHA), which introduces slight changes in order to rectify the previous shortcomings. In addition, some discussions shed a new light on the former spherical cap harmonic analysis (SCHA) and help us to demonstrate its deficiencies and approximations. We finally show that R‐SCHA now fully satisfies the natural properties of potential fields. R‐SCHA also yields analytical relationships with the spherical harmonics. Taking advantage of the mathematical equivalence of both representations, we explore the relevance of fundamental concepts like spectrum, minimum wavelength, or internal/external field separation. We conclude that these concepts are misleading and must be handled with care in regional modeling. A prime goal being the ability of R‐SCHA to represent real data sets, we also investigate and illustrate the effect of finite series expansions. A norm for the regularization of the inverse problem is proposed as well. The conclusions drawn in this paper allow us to validate the method and to assert that the present proposal is suited for modeling and studying the lithospheric magnetic field from ground to satellite altitudes at regional scales.
Previous models of Mercury's core magnetic field based on high altitude data from first MESSENGER flybys revealed an axisymmetric structure of the field. Here, we use low altitude MESSENGER data ...covering the entire mission period to construct spherical harmonic models based on various spatial norms. Although we find a dominantly axisymmetric field, our models nevertheless include detectable deviations from axisymmetry. These non‐axisymmetric features appear at high latitudes, resembling intense geomagnetic flux patches at Earth's core‐mantle boundary. Based on this core field morphology, we then attempt to infer Mercury's internal structure. More specifically, assuming that Mercury's high‐latitude non‐axisymmetric features are concentrated by downwellings at the edge of the planet's inner core tangent cylinder, and accounting for the presence of a stably stratified layer at the top of Mercury's core, we establish a relation between the inner core size and the thickness of the stratified layer. Considering plausible ranges, we propose that Mercury's inner core size is about 500–660 km, which corresponds to a stratified layer thickness of 880–500 km, respectively.
Plain Language Summary
Measurements of the magnetic field of Mercury taken by the MESSENGER space probe allow us to construct a model of the magnetic field generated inside Mercury. This internal field is generated within the core of Mercury by a magnetic dynamo process. This field is highly symmetric with respect to the axis of rotation, but very much weaker than Earth's magnetic field. Deviations from the axisymmetry of the field allow us to infer the internal structure of Mercury's core. A combined interpretation of Mercury's gravity field observations and our results provide a certain range for Mercury's inner core size, which is likely to be solid. We also infer the size of Mercury's dynamo and the thickness of the stratified layer above the dynamo region. We find that Mercury's inner core size is about 500–660 km, which corresponds to a stratified layer thickness of 880–500 km, respectively. The size of the dynamo region is between 680 and 900 km. This study provides new insights to the internal structure of a planet's core that are inferred from observations of its magnetic field.
Key Points
We model Mercury's internal magnetic field from MESSENGER data with spherical harmonics
Our core field model contains non‐axisymmetric features from which we make inferences of Mercury's internal structure
We estimate Mercury's inner core radius of ∼500–660 km and a corresponding thickness of a top stratified layer of ∼880–500 km
A light coating of oil is known to increase the dust holding capacity of fibrous filter media. The underlying causes for this effect were investigated by performing filtration experiments with arrays ...of nylon and stainless steel fibers (diameters of 20, 30, and 44μm) coated with precisely defined amounts of oil. The single fiber efficiency in the inertial regime (Stokes numbers >0.5) was measured as a function of dust load, using 3.5μm polystyrene and 2.1μm silica particles in combination with various types of oils (0W-30, WD-40). Additionally, the influence of an oil film on the growth of particle deposit structures was investigated by optical microscopy.
It was found that dust deposition on oily fibers occurs in two distinct stages: at first particles are immersed in the oil film without any appreciable increase in fiber efficiency. Once the film is saturated with particles, further deposition leads to quasi-normal dendritic growth typical of dust deposition on dry fibers, and a sharp increase in single fiber efficiency. The maximum packing density inside the film which is reached at the transition from particle immersion to regular growth, was approximately 46% by volume, regardless of film thickness. There were no indications of flow-induced particle rearrangement inside the film during the first stage.
Comparative measurements were also made with standard paper media containing varying quantities of oil. The oil caused an increase in dust holding capacity by factors between about 1.5 and 3 compared to dry media, due to a delayed upswing of the filter pressure drop with dust loading. The penetration of dust through the media more than doubled.
We conclude that particle immersion in the oil film is responsible for both the delayed increase in fiber efficiency and fiber drag, and that this delay is roughly proportional to the amount of oil loading.
Pre-treating filter fibers with oil delays the formation of widespread particle dendrites, as collected particles get packed tightly inside the oil films. Until the film is saturated with particles, collection efficiency and drag increase only marginally, which ultimately leads to a higher dust holding capacity of oil-treated media. Display omitted
•An oil film on filter fibers absorbs particles up to 87% of its volume.•Single fiber efficiency and drag hardly increase until the film is loaded to capacity with particles.•The high packing density of immersed particles is responsible for the increased dust holding capacity of the filter.
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