Archaeomagnetic results from Cambodia in Southeast Asia: Evidence for possible low-latitude flux expulsion

Extensive spatial and temporal distribution of high-quality data are essential for understanding regional and global behaviors of the geomagnetic field. We carried out chronological and archaeomagnetic studies at the Angkor-era iron-smelting site of Tonle Bak in Cambodia in Southeast Asia, an area with no data available to date. We recovered high-fidelity full-vector geomagnetic information from the 11th to 14th century for this region, which fill gaps in the global distribution of data and will significantly improve the global models. These results reveal a sharp directional change of the geomagnetic field between 1200 and 1300 CE, accompanied by an intensity dip between 1100 and 1300 CE. The fast geomagnetic variation recorded by our data provides evidence for the possible existence of low-latitude flux expulsion. Related discussions in this paper will inspire a new focus on detailed geomagnetic research in low-latitude areas around the equator, and exploration of related dynamic processes.

Imprint of magnetic flux expulsion at the core–mantle boundary on geomagnetic field intensity variations

SUMMARY During the last decade, rapid or extreme geomagnetic field intensity variations associated with rates greater than the maximum currently observed have been inferred from archeomagnetic data in the Near-East and in Western Europe. The most extreme events, termed geomagnetic spikes, are defined as intensity peaks occurring over a short time (a few decades), and are characterized by high variation rates, up to several μT yr–1. Magnetic flux expulsion from the Earth’s outer core has been suggested as one possible explanation for these peaks but has not yet been examined in detail. In this study, we develop a 2-D kinematic model for magnetic flux expulsion whose key control parameter is the magnetic Reynolds number Rm, the ratio of magnetic diffusion time to advection time. This model enables the tracking of magnetic field lines which are distorted and folded by a fixed flow pattern. Two processes govern the magnetic evolution of the system. The first is the expulsion of magnetic flux from closed streamlines, whereby flux gradually concentrates near the boundaries of the domain, which leads to an increase of the magnetic energy of the system. If the upper boundary separates the conducting fluid from an insulating medium, a second process then takes place, that of diffusion through this interface, which we can quantify by monitoring the evolution of the vertical component of magnetic induction along this boundary. It is the conjunction of these two processes that defines our model of magnetic flux expulsion through the core–mantle boundary. We analyse several configurations with varying flow patterns and magnetic boundary conditions. We first focus on flux expulsion from a single eddy. Since this specific configuration has been widely studied, we use it to benchmark our implementation against analytic solutions and previously published numerical results. We next turn our attention to a configuration which involves two counter-rotating eddies producing an upwelling at the centre of the domain, and comprises an upper boundary with an insulating medium. We find that the characteristic rise time and maximum instantaneous variation rate of the vertical component of the magnetic field that escapes the domain scale like $\sim R_m^{0.15}$ and $\sim R_m^{0.45}$, respectively. Extrapolation of these scaling laws to the Earth’s régime is compared with various purported archeointensity highs reported in the Near-East and in Western Europe. According to our numerical experiments magnetic flux expulsion is unlikely to produce geomagnetic spikes, while intensity peaks of longer duration (one century and more) and smaller variation rates appear to be compatible with this process.

Flux expulsion with dynamics

In the process of flux expulsion, a magnetic field is expelled from a region of closed streamlines on a $TR_{m}^{1/3}$ time scale, for magnetic Reynolds number $R_{m}\gg 1$ ($T$ being the turnover time of the flow). This classic result applies in the kinematic regime where the flow field is specified independently of the magnetic field. A weak magnetic ‘core’ is left at the centre of a closed region of streamlines, and this decays exponentially on the $TR_{m}^{1/2}$ time scale. The present paper extends these results to the dynamical regime, where there is competition between the process of flux expulsion and the Lorentz force, which suppresses the differential rotation. This competition is studied using a quasi-linear model in which the flow is constrained to be axisymmetric. The magnetic Prandtl number $R_{m}/R_{e}$ is taken to be small, with $R_{m}$ large, and a range of initial field strengths $b_{0}$ is considered. Two scaling laws are proposed and confirmed numerically. For initial magnetic fields below the threshold $b_{core}=O(UR_{m}^{-1/3})$, flux expulsion operates despite the Lorentz force, cutting through field lines to result in the formation of a central core of magnetic field. Here $U$ is a velocity scale of the flow and magnetic fields are measured in Alfvén units. For larger initial fields the Lorentz force is dominant and the flow creates Alfvén waves that propagate away. The second threshold is $b_{dynam}=O(UR_{m}^{-3/4})$, below which the field follows the kinematic evolution and decays rapidly. Between these two thresholds the magnetic field is strong enough to suppress differential rotation, leaving a magnetically controlled core spinning in solid body motion, which then decays slowly on a time scale of order $TR_{m}$.

The galactic dynamo and superbubbles

In previous galactic dynamo theories of the origin of the magnetic field in our galaxy, the subject of flux-freezing has been omitted. As a consequence, the equation of mass flow has generally also been omitted, particularly in the halo where the galactic gravitational field will operate on the mass flow. In this paper, it has been shown that this neglect could have serious consequences for the results obtained from those galactic dynamo simulations that include the halo. A modification of these dynamo theories is proposed which involves the expulsion of very small pieces of the magnetic field lines, rather than the wholesale expulsion of the complete magnetic lines encapsulated in the previous theories. This expulsion is accomplished by a spike instability that arises from superbubbles when they break out of the galactic disc and their shells fragment. This leads to a cut in the lines of force that still remain in the disc. Subsequently, normal disc turbulence rotates the cut lines and thus dissipates their mean flux, removing them from a role in the dynamo theory. This new process takes a length of time comparable to, but slightly longer than, the previous growth time of the disc dynamo, but avoids the previous difficulties associated with flux freezing and flux expulsion.