Global magnetohydrostatic fields in stellar atmosphere

Abstract

The equilibrium properties of the magnetic field of an axisymmetric star are studied. A family of analytical solutions to the magnetohydrostatic equations is found, which are used to model the slow evolution of the field through a series of equilibria.

Firstly, a model is set up for a force-free dipole-like field, which has a toroidal field component; it is found that, as such a field is twisted up, a critical point is reached, at which the field topology changes. If the twist is increased beyond this point, there is no physically reasonable equilibrium. Next, an untwisted magnetostatic dipole-like field is studied, with an increasing pressure differential between pole and equator. A critical point again occurs when the pressure differential becomes too large. Finally a force-free quadrupole-like field is modelled, which is being twisted up, for example by differential rotation; this has similar properties to the dipole-like field. In each case, it is suggested that, when the critical point is reached, the field will no longer evolve smoothly, but will change catastrophically to a new stable, releasing energy. Such an event could represent the onset of a stellar flare or some other dynamic stellar process.     

Reversal sequence in a multiple scale dynamo mechanism

We investigate the temporal evolution of the magnetic dipole field intensity of the Earth through a multiscale dynamo mechanism. On a large range of spatio-temporal scales, the helical motions of the fluid flow are given by a schematic model of a fully developed turbulence. The system construction is symmetric with respect to left-handed and right-handed cyclones. The multiscale cyclonic turbulence coupled with a differential rotation (schematic ω dynamo) or alone (schematic ² dynamo) is the ingredient of the loop through which poloidal and toroidal fields are built from one another. Two kinds of reaction of the magnetic field on the flow are considered: the presence of a magnetic field first favours a larger-scale organization of the flow, and, second, impedes this flow by the effect of growing Lorentz forces. We obtain the general features of the geomagnetic field intensity observed over geological times and describe a general mechanism for reversals, excursions and secular variation. The mechanism happens to keep a memory during the chrons and loose it during the events (excursions and inversions).     

Magnetic field structure in differentially rotating discs

Abstract

In order to gain a better understanding of the processes that may give rise to non-axisymmetric magnetic fields in galaxies, we have calculated field decay rates for models with a realistic galactic rotation curve and including the effects of a locally enhanced turbulent magnetic diffusivity within the disc. In all cases we have studied, the differential rotation increases the decay rate of non-axisymmetric modes, whereas axisymmetric ones are unaffected. A stronger magnetic diffusivity inside the disc does not lead to a significant preference for non-axisymmetric modes. Although Elsasser's antidynamo theorem has not yet been proved for the present case of a non-spherical distribution of the magnetic diffusivity, we do not find any evidence for the theorem not to be valid in general.     

Temporal–compositional trends over short and long time-scales in basalts of the Big Pine Volcanic Field, California

Primitive basaltic single eruptions in the Big Pine Volcanic Field (BPVF) of Owens Valley, California show systematic temporal–compositional variation that cannot be described by simple models of fractional crystallization, partial melting of a single source, or crustal contamination. We targeted five monogenetic eruption sequences in the BPVF for detailed chemical and isotopic measurements and ⁴⁰Ar/³⁹Ar dating, focusing primarily on the Papoose Canyon sequence. The vent of the primitive (Mg# = 69) Papoose Canyon sequence (760.8 ± 22.8 ka) produced magmas with systematically decreasing (up to a factor of two) incompatible element concentrations, at roughly constant MgO (9.8 ± 0.3 (1σ) wt.%) and Na₂O. SiO₂ and compatible elements (Cr and Ni) show systematic increases, while ⁸⁷Sr/⁸⁶Sr systematically decreases (0.7063–0.7055) and ε_Nd increases (− 3.4 to − 1.1). ¹⁸⁷Os/¹⁸⁸Os is highly radiogenic (0.20–0.31), but variations among four samples do not correlate with other chemical or isotopic indices, are not systematic with respect to eruption order, and thus the Os system appears to be decoupled from the dominant trends. The single eruption trends likely result from coupled melting and mixing of two isotopically distinct sources, either through melt-rock interaction or melting of a lithologically heterogeneous source. The other four sequences, Jalopy Cone (469.4 ± 9.2 ka), Quarry Cone (90.5 ±17.6 ka), Volcanic Bomb Cone (61.6 ± 23.4 ka), and Goodale Bee Cone (31.8 ± 12.1 ka) show similar systematic temporal decreases in incompatible elements. Monogenetic volcanic fields are often used to decipher tectonic changes on the order of 10⁵–10⁶ yr through long-term changes in lava chemistry. However, the systematic variation found in Papoose Canyon (10⁰–10² yr) nearly spans that of the entire volcanic field, and straddles cutoffs for models of changing tectonic regime over much longer time-scales. Moreover, ten new ⁴⁰Ar/³⁹Ar ages combined with chemistry from all BPVF single eruption sequences show the long-term trend of BPVF evolution comprises the overlapping, temporal–compositional trends of the monogenetic vents. This suggests that the single eruption sequences contain the bulk of the systematic chemical variation, whereas their aggregate compositions define the long-term trend of volcanic field evolution.     

Ancient magnetic field determinations on selected chondritic meteorites

Paleofield intensity determinations involving a comparison of the stable natural remanence (NRM) component with a laboratory thermoremanence (TRM) were carried out on nine chondrites selected in Brecher and Fuhrman (1979a, this issue, hereafter called Paper I), as well as on two manifestly unsuitable controls. To judge their reliability: (1) heat-alteration was monitored by comparing saturation coercivity spectra before and after heating; and (2) the NRM and TRM intensity and stability were compared to those of residual magnetization following zero-field cooling (TRM₀) from above the Curie point of kamacite (Ni---Fe). The latter criterion separates the role of an external magnetic field (of 0.43 Oe) at cooling from intrinsic contributions to magnetic grain alignments, due to accretionary, metamorphic or shock-oriented petrofabrics.

In some chondrites (e.g., Brownfield, H3B; Holyoke, H4C; Farley, H5A), a surprisingly large (10% NRM) and stable TRM₀ proved so similar to NRM and TRM, that sizeable spurious “paleofields” — comparable to paleointensities obtained — were derived by the standard method for zero-field cooling. In other chondrites, with negligible TRM₀ (1% of NRM) and irregular AF demagnetization curves, more reliable paleofield strengths in the range 0.01–0.09 Oe were obtained (e.g., Cavour, H6C). These seem representative of magnetic fields at the end of metamorphism intervals (10⁷ years after accretion) and/or at post-shock cooling. Thus, field strengths obtained from ordinary chondrites are typically weaker (by factors of 10–100) than those reliably determined from carbonaceous chondrites and ureilites, suggesting temporal decay of nebular magnetic fields, from the end of accretion until the end of metamorphism and early catastrophic-collisional stages.     

Dislocation microstructures in naturally deformed silicate garnets

Dislocation microstructures of naturally deformed silicate garnets and olivines in garnet-peridotites and silicate garnets in eclogites from four localities have been observed with a transmission electron microscope (TEM) to clarify the dislocation characteristics of silicate garnets. We have obtained the following results: (1) dislocation densities of garnets in all the garnet-peridotites (ρ = 10⁵−10⁷ cm⁻²) are always nearly an order of magnitude lower than those of co-existing olivines; (2) dislocation densities of garnets in eclogites (ρ = 10⁵−10⁸ cm⁻²) which are embedded in garnet-peridotites are almost an order of magnitude higher than those of garnets in the surrounding garnet-peridotites; (3) the dominant Burgers vector, b, of mainly edge dislocations in garnet is 100 for specimens with dislocation density ρ = 10⁵−10⁶ cm⁻², while b=1/2111 for specimens with ρ = 10⁷−10⁸ cm⁻². Result (1) indicates that the observed dislocations in garnets were formed by plastic deformation under the same stresses as for co-existing olivines, and that there is a similar relationship between applied stress and dislocation density for garnets as for olivines. Result (2) suggests that the stress concentration occurred around eclogites embedded in garnet-peridotites, and the resulting differential stress in garnets in eclogites was further elevated by the interlocking of neighboring hard garnet grains. Finally, result (3) indicates that the dominant Burgers vector of mainly edge dislocations in garnet changes from 100 to 1/2111 with increasing applied differential stress.     

Analysis of geodynamo equations by means of perturbation theory

Abstract

Perturbation theory methods are developed for the kinematic geodynamo equations. The vector Green's function is constructed for the unperturbed equation, which includes the axisymmetric differential rotation. While investigating the perturbation series, we consider a special case in which the decay rates of the axisymmetric toroidal and poloidal dipoles are degenerate. For a number of models within the framework of the theory developed, estimates are given for generation conditions and for observed characteristics of the geomagnetic field.     

U,U andTh in seawater

We have developed techniques to determine²³⁸U,²³⁴U and²³²Th concentrations in seawater by isotope dilution mass spectrometry. U measurements are made using a²³³U²³⁶U double spike to correct for instrumental fractionation. Measurements on uranium standards demonstrate that²³⁴U/²³⁸U ratios can be measured accurately and reproducibly.²³⁴U/²³⁸U can be measured routinely to ± 5‰ (2σ) for a sample of 5 × 10⁹ atoms of²³⁴U (3 × 10⁻⁸ g of total U, 10 ml of seawater). Data acquisition time is 1 hour. The small sample size, high precision and short data acquisition time are superior to-counting techniques.²³⁸U is measured to ± 2‰ (2σ) for a sample of 8 × 10¹² atoms of²³⁸U ( 3 × 10⁻⁹ g of U, 1 ml of seawater).²³²Th is measured to ± 20‰ with 3 × 10¹¹²³²Th atoms (10⁻¹⁰ g²³²Th, 1 1 of seawater). This small sample size will greatly facilitate investigation of the²³²Th concentration in the oceans. Using these techniques, we have measured²³⁸U,²³⁴U and²³²Th in vertical profiles of unfiltered, acidified seawater from the Atlantic and²³⁸U and²³⁴U in vertical profiles from the Pacific. Determinations of²³⁴U/²³⁸U at depths ranging from 0 to 4900 m in the Atlantic (7°44′N, 40°43′W) and the Pacific (14°41′N, 160°01′W) Oceans are the same within experimental error (± 5‰,2σ). The average of these²³⁴U/²³⁸U measurements is 144 ± 2‰ (2σ) higher than the equilibrium ratio of 5.472 × 10⁻⁵. U concentrations, normalized to 35‰ salinity, range from 3.162 to 3.281 ng/g, a range of 3.8%. The average concentration of the Pacific samples (31°4′N, 159°1′W) is 1% higher than that of the Atlantic (7°44′N, 40°43′W and 31°49′N, 64°6′W).²³²Th concentrations from an Atlantic profile range from 0.092 to 0.145 pg/g. The observed constancy of the²³⁴U/²³⁸U ratio is consistent with the predicted range of²³⁴U/²³⁸U using a simple two-☐ model and the residence time of deep water in the ocean determined from¹⁴C. The variation in salinity-normalized U concentrations suggests that U may be much more reactive in the marine environment than previously thought.     

Magnetotelluric measurements in Antarctica

During austral summer 1984–1985 magnetotelluric measurements were carried out in North Victoria Land, Antarctica. The magnetic field was measured by a three-component fluxgate magnetometer. Copper screens (50 cm × 50 cm) were used as electrodes for recording the electric field, connected to a two channel electrograph with an input impedance of 10¹² ω. Analogue data are digitized with 12 bit resolution by a data acquisition system. 1 Mb of solid state CMOS-RAM memory was used to store the data in the field until it could be played back onto 3.5 inch floppy discs during station control. All equipment is designed for low power consumption. In the field it is supplied by a battery, which is charged by solar panels. Time series of measured data are presented. The influence of the polar electrojet (PEJ) on the source fields is clearly seen by comparing 24-h time series with the position of the auroral oval at different times of the day. Despite the clear effect of the PEJ in the data, the calculated apparent resistivity and phase curves seem to be rather uninfluenced. Initial interpretations have led to a typical continental resistivity distribution, showing decreasing resistivity with increasing depth.     

Dynamos with a flat α-effect distribution

Abstract

In order to obtain a better insight into the excitation conditions of magnetic fields in flat objects, such as galaxies, we have calculated critical dynamo numbers of different magnetic field modes for spherical dynamos with a flat α-effect distribution. A simple but realistic approximation formula for the rotation curve is employed. In most cases investigated a stationary quadrupole-type solution is preferred. This is a consequence of the flat distribution of the α-effect. Non-axisymmetric fields are in all cases harder to excite than axisymmetric ones. This seems to be the case particularly for flat objects in combination with a realistic rotation curve for galaxies. The question of whether non-axisymmetric (bisymmetric) fields, which are observed in some galaxies, can be explained as dynamos generated by an axisymmetric αω-effect is therefore still open.     

Bifurcations in Spherical MHD Models

A series of numerical studies on the behaviour of magnetic fields and motions in a spherical body of an electrically conducting incompressible fluid have been carried out. The magnetic field was assumed to be maintained by a given electromotive force inside the body and to continue as a potential field in outer space. In view of the motion an external forcing was taken into account, and boundary conditions were considered which correspond to a stress-free surface. The stability of several steady states has been studied as well as the evolutions starting from unstable states. In this paper a configuration with a poloidal magnetic field and a differential rotation, both symmetric about the same axis, is considered. This configuration is stable only for sufficiently small Hartmann numbers but evolves, if disturbed, in the case of larger Hartmann numbers toward a non-axisymmetric state. In this case the well-known symmetrization effect of differential rotation in magnetic fields is destroyed.     

On the strength of electric currents and zonal magnetic fields at the top of the Earth''s core: Methodology and preliminary estimates

A new method is described for estimating: (a) the meridional electric current density, j_θ, (b) the vertical growth rate of the zonal magnetic field, ∂B_φ/∂r, or its scale-height, B_φ/∂B_φ/∂r) and (c) the vertical growth rate of the vertical current density, ∂j_r/∂r, at a few isolated points on the top surface of the Earth's core from observations of the internal geomagnetic field at the Earth's surface. The theoretical technique rests on combining unaccelerated, gravitationally-driven Boussinesq fluid dynamics of the core with frozen-flux electromagnetism, the mantle being treated as a spherically symmetric insulator.

Insertion into this theory of main field models for epochs 1965, 1975 leads to preliminary values for these quantities of magnitude: (a) j_θ 1 A/m², (b) ∂B_φ/∂r 10⁻⁶ T/m or B_φ/(∂B_φ/∂r) 10 m, (c) ∂j_r/∂r 10⁻⁶ A/m³. Some geophysical implications of these estimates are discussed.     

Martian mantle mineralogy investigated by the Lu–Hf and Sm–Nd systematics of shergottites

Chemical heterogeneities in the Martian mantle are believed to result from the crystallization of a magma ocean in the first 100 million years of its history. Shergottite meteorites from Mars are thought to retain a compositional record of such early differentiation and the resulting mineralogy at different depths. The coupled ¹⁷⁶Lu–¹⁷⁶Hf and ¹⁴⁷Sm–¹⁴³Nd isotope systematics in 9 shergottites are used here to investigate these issues. Three compositional groups in the shergottites display distinct isotope systematics. One group, commonly termed as depleted, is characterized by positive ¹⁷⁶Hf_i from + 46.2 to + 50.4 and ¹⁴³Nd_i from + 36.2 to + 39.1. Another, termed as enriched, has negative ¹⁷⁶Hf_i = − 16.5 to − 13.2 and ¹⁴³Nd_i = − 7.0 to − 6.5. The third group is intermediate between the depleted and enriched groups with positive ¹⁷⁶Hf_i = + 30.0 to + 33.4 and ¹⁴³Nd_i = + 16.9. Together, they describe mixing curves between ¹⁷⁶Hf/¹⁷⁷Hf, ¹⁴³Nd/¹⁴⁴Nd, Lu/Hf, and Sm/Nd, implying that they sample two distinct sources in the Martian mantle. All shergottites are characterized by (Sm/Nd)_source < (Sm/Nd)_sample, but (Lu/Hf)_source > (Lu/Hf)_sample. This decoupling can be explained by two successive partial melting episodes in the depleted shergottite source and localized in the Martian upper mantle. The genesis of shergottites can be modeled using non-modal equilibrium partial melting in a source initially composed of 60% olivine, 21% clinopyroxene, 9% orthopyroxene, and 10% garnet, with degrees of partial melting of 8.8% and 3.9%, respectively, for the two successive events. The enriched end-member of the shergottite mixing curve is best modeled by late-stage quenched residual melt resulting from the crystallization of a magma ocean. The depleted shergottite source may be modeled as a mixture of cumulates and residual melt, as convection in the Martian magma ocean is expected to reduce the incompatible trace element heterogeneity in the final solidified layers. Consequently, equilibrium crystallization is preferred to model the crystallization of the Martian magma ocean. The models that best explain the shergottite data are those where the magma ocean is at a depth of at least 1350 km in Mars.     

Review of the geomagnetic secular variations on the historical time scale

In view of the classification of the geomagnetic field into its axisymmetric and non-axisymmetric parts, studies of geomagnetic secular variations on the historical time-scale are reviewed. The westward drift of the geomagnetic field, which is one of the most conspicuous features of its secular variation, is examined first. The non-axisymmetric field during the past several hundred years can be well approximated by the superposition of two constant-magnitude fields, a standing and a drifting field, whose lifetimes are supposed to be longer than 1000 years. It is pointed out that the sectorial term of the non-dipole standing field is small compared with the drifting one. The lack of the n = M = 2 term of the standing field is particularly remarkable.

On the other hand, the equatorial dipole field is likely to consist of two components which are both drifting. One drifts westwards with a normal velocity and the other eastwards with a small velocity.

Besides the pronounced westward drift in an east-west direction, the poleward movements of particular foci of the secular variation are noted. This may, however, be related to the rapid growth of the axisymmetric quadrupole field.

The time variation of the dipole field is briefly examined. As far as the data on the historical time scale are concerned, an antiparallel relationship seems to exist between the variations in the dipole and the quadrupole field. As the dipole moment decreases, the magnitude of the quadrupole moment increases. Finally, characteristic oscillation periods of the dipole field are examined. Although the data are few, a 60–70-year period, a 400–600-year and a 8000-year period emerge as the dominant periods.     

“Andesitic water”: a phantom of the isotopic evolution of water-silicate systems. Comment on “Isotopic shifts in waters from geothermal and volcanic systems along convergent plate boundaries and their origin” by W.F. Giggenbach

On account of the low porosity of the lithosphere, intracrustal fluids behave very differently from surface fluids, in that they are changing their geochemical and isotopic labels according to the geological environment. Given a heat source, meteoric waters can be supplied plentifully and their rates of throughput in geothermal systems are sufficiently high to exhaust the compositional signals of a given rock buffer. In contrast, fluids exsolved from magma, and subducted fluids, would be supplied at less than about one tenth of the meteoric rate over the life time of a system. Based on up-to-date flow models, the isotopic evolution of meteoric water interacting with crustal rock follows a curved to L-shaped track in the δD versus δ¹⁸O plot. Instantaneous (present-day) tie-lines between recharge and discharge are secants of such tracks and can have a range of slopes. At the start of an interaction, waters have δD and δ¹⁸O values approaching equilibrium with the original rock composition (water “W1”). Using known hydrogen isotope fractionation factors, W1 values generally plot in the region of “andesite” or “andesitic” waters of various authors. Since the W1 waters have δD values that are on average more positive, and also less variable than those of the meteoric recharges, most tracks and tie-lines have positive slopes, and the plotting of a large number of tie-lines will produce a focus on the field of W1 waters, regardless of the original water source.     

Correlated chemical and isotopic zoning in carbonates in the martian meteorite ALH84001

The meteorite ALH84001, a sample of the ancient martian crust, contains small quantities (1%) of strongly chemically zoned carbonate. High spatial resolution (10 μm) ion microprobe analyses show that the chemical zoning is strongly correlated with variations in oxygen isotope ratios. Early formed Ca,Fe-rich cores have δ¹⁸O 7‰ increasing to 22‰ SMOW in the more Mg-rich outer cores and magnesite rims. Isolated areas of ankerite appear to be isotopically lighter with δ¹⁸O 1‰. The large range in δ¹⁸O requires a significant range in either fluid isotopic composition, or temperature, or both, in the course of the deposition sequence. Our data are inconsistent with formation of the zoned carbonates by closed system Rayleigh fractionation. There is no unique interpretation of the oxygen data, but the recent observation of existence of Δ¹⁷O excesses in the carbonate appears to rule out models which involve high temperature isotopic exchange with silicate. Comparison with terrestrial analogues suggests that ALH84001 carbonates formed in a hydrothermal system with T<400°C, and which, at least in the early stages of formation, may have involved water with δ¹⁸O < 0‰ SMOW. The later stages of deposition probably occurred at temperatures below 150°C, a conclusion which does not preclude the co-existence of thermophilic bacteria; temperatures during earlier stages of deposition are less likely to have been hospitable to bacteria.     

Establishing a chronology for lacustrine sediments using a multiple dating approach—A case study from the Frickenhauser See, central Germany

In order to establish a reliable chronology for lacustrine sediments of the Frickenhauser See (central Germany) different dating methods have been applied. A total of 17 AMS ¹⁴C dates, all within the last 2000 years, were supplemented with ¹³⁷Cs/²¹⁰Pb dating and varve counting of the uppermost sediments (131 years). The age–depth model for the Frickenhauser See has to cope with highly variable sedimentation rates and overlapping probability distributions of calibrated ¹⁴C dates. The uncertainty of calibrated ¹⁴C dates could be considerably reduced by including the stratigraphic relationship of the dated samples, the age information derived from short-lived isotopes and varve counting as well as an upper and lower limit of realistic sedimentation rates as ‘a priori’ information in the calibration procedure. Sets of possible age combinations obtained by repeated sampling from the modified probability distributions were used to calculate continuous age–depth relationships based on monotonic smoothing splines. The obtained age–depth model for the sediment record of the Frickenhauser See represents the average of over 16,000 such model runs and suggests a drastic increase in sedimentation rates from around 1–2 mm a⁻¹ (200–1000 AD) to over 25 mm a⁻¹ for the period between 1100 and 1300 AD. From then on, sedimentation rates exhibit relatively stable values around 3–9 mm a⁻¹. ‘Conventional’ age–depth models such as general polynomial regression or cubic splines either do not include the obtained age-information in a satisfying manner (the model being too “stiff”) or exhibit “swings” causing age-reversals in the model. Although the age–depth relationships obtained for monotonic smoothing splines and mixed-effect regression are generally very similar, they differ in their respective sedimentation rates as well as in their uncertainties. Mixed-effect regression resulted in much higher sedimentation rates of more than 37 mm a⁻¹. These results suggest that monotonic smoothing splines give better control of the age–depth model characteristics and are well suited in situations, where the integrity of ¹⁴C dates is high, i.e. the dated material represents the age of the respective layer.     

Methods of analyzing radio polarization data

Abstract

Methods of estimating the strength and direction of galactic magnetic fields from radio polarization measurements are reviewed. Particular attention is paid to the analysis of the Faraday rotation in order to derive the large scale magnetic field structure. Ways in which an axisymmetric spiral field structure can be observationally distinguished from a bisymmetric spiral structure are described, as are the ways in which field symmetric with respect to the galactic plane can be distinguished from those that are antisymmetric.     

用模式匹配算法研究层状各向异性倾斜地层中多分量感应测井响应

利用数值模式匹配技术,研究并建立层状各向异性倾斜地层中多分量感应测井响应的快速数值模拟算法.首先将位于井轴上的三个相互正交磁偶极子转化成关于极角θ的三个谐变分量的叠加,以便将三个正交磁偶极子电磁场的正演问题完全简化成三个谐变分量电磁场的轴对称定解问题,并给出电磁场各个谐变分量在井轴上满足的边界条件,保证电磁场在井轴附近仍然可解.然后利用数值模式匹配技术建立电磁场各个谐变分量的正演过程,得到层状各向异性地层中磁流源并矢Green函数的半解析表达式,给出计算层状各向异性倾斜地层中多分量感应测井响应的具体方法,最后通过数值计算结果证明该算法的有效性并考察几种不同情况下多分量感应测井响应特征.