The role of slow magnetostrophic waves in dipole formation in rapidly rotating dynamos

<p>It is known that the columnar structures in rapidly rotating convection are affected by the magnetic field in ways that enhance their helicity. This may explain the dominance of the axial dipole in rotating dynamos. Dynamo simulations starting from a small seed magnetic field have shown that the growth of the field is accompanied by the excitation of convection in the energy-containing length scales. Here, this process is studied by examining axial wave motions in the growth phase of the dynamo for a wide range of thermal forcing. In the early stages of evolution where the field is weak, fast inertial waves weakly modified by the magnetic field are abundantly present. As the field strength(measured by the ratio of the Alfven wave to the inertial wave frequency) exceeds a threshold value, slow magnetostrophic waves are spontaneously generated. The excitation of the slow waves coincides with the generation of helicity through columnar motion, and is followed by the formation of the axial dipole from a chaotic, multipolar state. In strongly driven convection, the slow wave frequency is attenuated, causing weakening of the axial dipole intensity. Kinematic dynamo simulations at the same parameters, where only fast inertial waves are present, fail to produce the axial dipole field. The dipole field in planetary dynamos may thus be supported by the helicity from slow magnetostrophic waves.</p>

Simple stochastic model for geomagnetic excursions and reversals reproduces the temporal asymmetry of the axial dipole moment

We present a simple model for the axial dipole moment (ADM) of the geomagnetic field based on a stochastic differential equation for two coupled particles in a biquadratic potential, subjected to Gaussian random perturbations. This model generates aperiodic reversals and excursions separated by stable polarity periods. The model reproduces the temporal asymmetry of geomagnetic reversals, with slower decaying rates before the reversal and faster growing rates after it. This temporal asymmetry is possible because our model is out of equilibrium. The existence of a thermal imbalance between the two particles sets a preferential sense for the energy flux and renders the process irreversible.

Quantitative estimates of average geomagnetic axial dipole dominance in deep geological time

A defining characteristic of the recent geomagnetic field is its dominant axial dipole which provides its navigational utility and dictates the shape of the magnetosphere. Going back through time, much less is known about the degree of axial dipole dominance. Here we use a substantial and diverse set of 3D numerical dynamo simulations and recent observation-based field models to derive a power law relationship between the angular dispersion of virtual geomagnetic poles at the equator and the median axial dipole dominance measured at Earth’s surface. Applying this relation to published estimates of equatorial angular dispersion implies that geomagnetic axial dipole dominance averaged over 107–109 years has remained moderately high and stable through large parts of geological time. This provides an observational constraint to future studies of the geodynamo and palaeomagnetosphere. It also provides some reassurance as to the reliability of palaeogeographical reconstructions provided by palaeomagnetism.

Can one use Earth’s magnetic axial dipole field intensity to predict reversals?

Summary We study predictions of reversals of Earth’s axial magnetic dipole field that are based solely on the dipole’s intensity. The prediction strategy is, roughly, that once the dipole intensity drops below a threshold, then the field will continue to decrease and a reversal (or a major excursion) will occur. We first present a rigorous definition of an intensity threshold-based prediction strategy and then describe a mathematical and numerical framework to investigate its validity and robustness in view of the data being limited. We apply threshold-based predictions to a hierarchy of numerical models, ranging from simple scalar models to 3D geodynamos. We find that the skill of threshold-based predictions varies across the model hierarchy. The differences in skill can be explained by differences in how reversals occur: if the field decreases towards a reversal slowly (in a sense made precise in this paper), the skill is high, and if the field decreases quickly, the skill is low. Such a property could be used as an additional criterion to identify which models qualify as Earth-like. Applying threshold-based predictions to Virtual Axial Dipole Moment (VADM) paleomagnetic reconstructions (PADM2M and Sint-2000) covering the last two million years, reveals a moderate skill of threshold-based predictions for Earth’s dynamo. Besides all of their limitations, threshold-based predictions suggests that no reversal is to be expected within the next 10 kyr. Most importantly, however, we show that considering an intensity threshold for identifying upcoming reversals is intrinsically limited by the dynamic behavior of Earth’s magnetic field.

A full sequence of the Matuyama–Brunhes geomagnetic reversal in the Chiba composite section, Central Japan

Geological records of the Matuyama–Brunhes (M–B) geomagnetic reversal facilitate the development of an age model for sedimentary and volcanic sequences and help decipher the dynamics of the Earth’s magnetic field. However, the structure of the geomagnetic field during the M–B geomagnetic reversal remains controversial due to its complex field behavior. In this study, we conducted paleo- and rock-magnetic analyses of samples from the Chiba composite section (CbCS), a continuous and expanded marine succession in Central Japan, to reconstruct the full sequence of the M–B geomagnetic reversal. We define an average stratigraphic position of the M–B boundary and estimate its age based on three sections in the CbCS and a neighboring drill core, TB-2. The average stratigraphic position of the M–B boundary in the CbCS is established at 1.1 ± 0.3 m above a widespread volcanic ash bed (the Byk-E tephra). Assuming a chronological error associated with orbital tuning of 5 kyr and stratigraphic uncertainty of 0.4 kyr, the M–B boundary in CbCS is at 772.9 ± 5.4 ka (1σ). The virtual geomagnetic pole, which is calculated from the paleomagnetic directions, shows several short fluctuations between 783 and 763 ka, with concomitant decreases in geomagnetic field intensity index. After termination of the field instabilities, the field intensity recovered and became higher than before the M–B boundary, with a stable normal polarity direction. The paleomagnetic records in the CbCS exhibit a field asymmetry between the axial dipole decay and field recovery, providing a full sequence of the M–B reversal, suggesting that the non-axial dipole field dominated several times during periods ca. 20 kyr long across the M–B boundary, due to depletion in the main axial dipole component. Our results provide probably the most detailed sedimentary record of the M–B geomagnetic reversal and offer valuable information to further understand the mechanism and dynamics of geomagnetic reversals. Graphical abstract

How Good Is the Bipolar Approximation of Active Regions for Surface Flux Transport?

We investigate how representing active regions with bipolar magnetic regions (BMRs) affects the end-of-cycle polar field predicted by the surface flux transport model. Our study is based on a new database of BMRs derived from the SDO/HMI active region patch data between 2010 and 2020. An automated code is developed for fitting each active region patch with a BMR, matching both the magnetic flux and axial dipole moment of the region and removing repeat observations of the same region. By comparing the predicted evolution of each of the 1090 BMRs with the predicted evolution of their original active region patches, we show that the bipolar approximation leads to a 24% overestimate of the net axial dipole moment, given the same flow parameters. This is caused by neglecting the more complex multipolar and/or asymmetric magnetic structures of many of the real active regions, and may explain why previous flux transport models had to reduce BMR tilt angles to obtain realistic polar fields. Our BMR database and the Python code to extract it are freely available.

Axial dipole moments of solar active regions in cycles 21-24

<p>The axial dipole moments of emerging active regions control the evolution of the axial dipole moment of the whole photospheric magnetic field and the strength of polar fields. Hale's and Joy's laws of polarity and tilt orientation affect the sign of the axial dipole moment of an active region, determining the normal sign for each solar cycle. If both laws are valid (or both violated), the sign of the axial moment is normal. However, for some active regions, only one of the two laws is violated, and the signs of these axial dipole moments are the opposite of normal. The opposite-sign axial dipole moments can potentially have a significant effect on the evolution of the photospheric magnetic field, including the polar fields.</p><p>We determine the axial dipole moments of active regions identified from magnetographic observations and study how the axial dipole moments of normal and opposite signs are distributed in time and latitude in solar cycles 21-24.We use active regions identified from the synoptic maps of the photospheric magnetic field measured at the National Solar Observatory (NSO) Kitt Peak (KP) observatory, the Synoptic Optical Long term Investigations of the Sun (SOLIS) vector spectromagnetograph (VSM), and the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO).</p><p>We find that, typically, some 30% of active regions have opposite-sign axial dipole moments in every cycle, often making more than 20% of the total axial dipole moment. Most opposite-signed moments are small, but occasional large moments, which can affect the evolution of polar fields on their own, are observed. Active regions with such a large opposite-sign moment may include only a moderate amount of total magnetic flux. We find that in cycles 21-23 the northern hemisphere activates first and shows emergence of magnetic flux over a wider latitude range, while the southern hemisphere activates later, and emergence is concentrated to lower latitudes. We also note that cycle 24 differs from cycles 21-23 in many ways. Cycle 24 is the only cycle where the northern butterfly wing includes more active regions than the southern wing, and where axial dipole moment of normal sign emerges on average later than opposite-signed axial dipole moment. The total axial dipole moment and even the average axial moment of active regions is smaller in cycle 24 than in previous cycles.</p>

Field Intensity changes during the past 40 ka

<p>The period encompassing the past 40 ka is crucial to constrain the characteristic time of the axial dipole, which is computed so far from the historical period and still fails to be tested against long-term field changes. The past 7 kyr of geomagnetic history are primarily documented from archeological artefacts, yet the last 4 kyr remain relatively poorly constrained. Beyond this period, we are dealing with long-term changes of the dipole field that are relatively poorly documented by sedimentary records or by volcanic lava flows. Many measurements of absolute paleointensity do not incorporate directional information, while it is crucial to document the entire field vector and consequently can only be analyzed in terms of virtual axial dipole moments (VADM). In summary, no high resolution dataset covers the field changes which followed the Laschamp event and therefore we have poor knowledge of the pattern of fluctuations and the rate of the changes that were associated with the field recovery after the Laschamp. We have selected a set of marine sedimentary cores based on the quality of their oxygen isotope records. Their deposition rates are comprised between 10 and 20 cm/ka and therefore offer a great potential to constrain the filed intensity changes with a resolution of the order of 100 ka. during this period. We will present the results obtained from 7 marine core records and investigate their common and their discrepant features in order to identify the true paleointensity signal.</p><p> </p>