Thermal evolution of the Earth's core during its formation taking into account heat release from the short-lived radioisotopes 26Al and 60Fe

Research subject. Based on the two-stage mechanism of the Earth's heterogeneous accumulation, previously proposed by V.N. Anfilogov and Yu.V. Khachay, the thermal evolution of the core during its formation was studied. Account is taken of both the heat release from 26Al, the content of which was established with a fairly reliable accuracy, and that from 60Fe.Materials and methods. The methods of mathematical modelling were used. Calculations were carried out for three estimates of the fractional content of the radioisotope 60Fe to stable 56Fe at the time of CAI formation (Ca-Al-In- clusions, calcium- and aluminium-rich inclusions found in carbonaceous chondrites) based on the results of various authors.Results. As a result of numerical experiments, variants of the temperature and melting temperature distributions at different stages of the core formation for different 60Fe/56Fe ratios were obtained.Conclusions. The results show that the central region of the forming core can remain melted even by the end of its accumulation. As a consequence, in this region for this time, the conditions for free thermal convection and, accordingly, for the implementation of the MHD dynamo mechanism remain.

Joint action of Hall and ambipolar effects in 3D magneto-convection simulations of the quiet Sun

The partial ionization of the solar plasma causes several nonideal effects such as the ambipolar diffusion, the Hall effect, and the Biermann battery effect. Here we report on the first three-dimensional realistic simulations of solar local dynamo where all three effects were taken into account. The simulations started with a snapshot of already saturated battery-seeded dynamo, where two new series were developed: one with solely ambipolar diffusion and another one also taking into account the Hall term in the generalized Ohm’s law. The simulations were then run for about 4 h of solar time to reach the stationary regime and improve the statistics. In parallel, a purely MHD dynamo simulation was also run for the same amount of time. The simulations are compared in a statistical way. We consider the average properties of simulation dynamics, the generation and dissipation of compressible and incompressible waves, and the magnetic Poynting flux. The results show that, with the inclusion of the ambipolar diffusion, the amplitudes of the incompressible perturbations related to Alfvén waves are reduced, and the Poynting flux is absorbed, with a frequency dependence. The Hall effect causes the opposite action: significant excess of incompressible perturbations is generated and an excess of the Poynting flux is observed in the chromospheric layers. The model with ambipolar diffusion shows, on average, sharper current sheets and slightly more abundant fast magneto-acoustic shocks in the chromosphere. The model with the Hall effect has higher temperatures at the lower chromosphere and stronger and more vertical magnetic field concentrations all over the chromosphere. The study of high-frequency waves reveals that significant power of incompressible perturbations is associated with areas with intense and more vertical magnetic fields and larger temperatures. This behavior explains the large Poynting fluxes in the simulations with the Hall effect and provides confirmation as to the role of Alfvén waves in chromospheric heating in internetwork regions, under the action of both Hall and ambipolar effects. We find a positive correlation between the magnitude of the ambipolar heating and the temperature increase at the same location after a characteristic time of 102 s.

Fluctuation dynamo in a weakly collisional plasma

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

A candidate secular variation model for IGRF-13 based on MHD dynamo simulation and 4DEnVar data assimilation

We have submitted a secular variation (SV) candidate model for the thirteenth generation of International Geomagnetic Reference Field model (IGRF-13) using a data assimilation scheme and a magnetohydrodynamic (MHD) dynamo simulation code. This is the first contribution to the IGRF community from research groups in Japan. A geomagnetic field model derived from magnetic observatory hourly means, and CHAMP and Swarm-A satellite data, has been used as input data to the assimilation scheme. We adopt an ensemble-based assimilation scheme, called four-dimensional ensemble-based variational method (4DEnVar), which linearizes outputs of MHD dynamo simulation with respect to the deviation from a dynamo state vector at an initial condition. The data vector for the assimilation consists of the poloidal scalar potential of the geomagnetic field at the core surface and flow velocity field slightly below the core surface. Dimensionless time of numerical geodynamo is adjusted to the actual time by comparison of secular variation time scales. For SV prediction, we first generate an ensemble of dynamo simulation results from a free dynamo run. We then assimilate the ensemble to the data with a 10-year assimilation window through iterations, and finally forecast future SV by the weighted sum of the future extension parts of the ensemble members. Hindcast of the method for the assimilation window from 2004.50 to 2014.25 confirms that the linear approximation holds for 10-year assimilation window with our iterative ensemble renewal method. We demonstrate that the forecast performance of our data assimilation and forecast scheme is comparable with that of IGRF-12 by comparing data misfits 4.5 years after the release epoch. For estimation of our IGRF-13SV candidate model, we set assimilation window from 2009.50 to 2019.50. We generate our final SV candidate model by linear fitting for the weighted sum of the ensemble MHD dynamo simulation members from 2019.50 to 2025.00. We derive errors of our SV candidate model by one standard deviation of SV histograms based on all the ensemble members.

On magnetostrophic mean-field solutions of the geodynamo equations. Part 2

A dynamo driven by motions unaffected by viscous forces is termed ‘magnetostrophic’, but cannot be found through today’s numerical simulations, which require substantial viscosity to stabilize solutions of the full magnetohydrodynamic (MHD) dynamo equations. By using an alternative numerical technique, proposed by Taylor (Proc. R. Soc. Lond. A, vol. 274, 1963, pp. 274–283), we recently obtained the first magnetostrophic dynamo solutions ever derived (Wu & Roberts, Geophys. Astrophys. Fluid Dyn., vol. 109, 2014, pp. 84–110). These were axisymmetric and of mean-field type. In an earlier paper (Roberts & Wu, Geophys. Astrophys. Fluid Dyn., vol. 108, 2014, pp. 696–715), we proposed an extension of Taylor’s method. Here we explore its numerical implications, comparing them to the consequences of Taylor’s original proposal. One of the differences between the two approaches is that our modification retains torsional waves but Taylor’s theory does not. A more important difference is that our extension of Taylor’s method is, for reasons presented here, the most general possible that does not suffer from the limitations imposed by viscosity on today’s numerical simulations.