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Register a new userTracking of magnetic flux concentrations over a five-day observation and an insight into surface magnetic flux transport
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Y. Iida
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The solar dynamo problem is the question of how the cyclic variation in the solar magnetic field is maintained. One of the important processes is the transport of magnetic flux by surface convection. To reveal this process, the dependence of the squared displacement of magnetic flux concentrations upon the elapsed time is investigated in this paper via a feature-recognition technique and a continual five-day magnetogram. This represents the longest time scale over which a satellite observation has ever been performed for this problem. The dependence is found to follow a power-law and differ significantly from that of diffusion transport. Furthermore there is a change in the behavior at a spatial scale of 10^{3.8} km. A super-diffusion behavior with an index of 1.4 is found on smaller scales, while changing to a sub-diffusion behavior with an index of 0.6 on larger ones. I interpret this difference in the transport regime as coming from the network-flow pattern.
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(abridged) Context: The mechanisms that cause the formation of sunspots are still unclear. Aims: We study the self-organisation of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection. Methods: We perform simulations of magnetoconvection in Cartesian domains that are $8.5$-$24$ Mm deep and $34$-$96$ Mm wide. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow. Results: We find that super-equipartition magnetic flux concentrations are formed near the surface with domain depths of $12.5$ and $24$ Mm. The size of the concentrations increases as the box size increases and the largest structures ($20$ Mm horizontally) are obtained in the 24 Mm deep models. The field strength in the concentrations is in the range of $3$-$5$ kG. The concentrations grow approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in the majority of the domain, which is unfavourable for the negative effective magnetic pressure instability (NEMPI). Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern. Conclusions: The linear growth of large-scale flux concentrations implies that their dominant formation process is tangling of the large-scale field rather than an instability. One plausible mechanism explaining both the linear growth and the concentrate on of the flux in the regions of converging flow pattern is flux expulsion. Possible reasons for the absence of NEMPI are that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign and that there may not be sufficient scale separation.
The choice of free parameters in surface flux transport (SFT) models describing the evolution of the large-scale poloidal magnetic field of the Sun is critical for the correct reproduction of the polar magnetic flux built up during a solar cycle, which in turn is known to be a good predictor of the amplitude of the upcoming cycle. For an informed choice of parameters it is important to understand the effect and interplay of the various parameters and to optimize the models for the polar magnetic field. Here we present the results of a large-scale systematic study of the parameter space in an SFT model where the source term representing the net effect of tilted flux emergence was chosen to represent a typical, average solar cycle as described by observations. Comparing the results with observational constraints on the spatiotemporal variation of the polar magnetic field, as seen in magnetograms for the last four solar cycles, we mark allowed and excluded regions in the 3D parameter space defined by the flow amplitude u0, the magnetic diffusivity eta and the decay time scale tau, for three different assumed meridional flow profiles. Without a significant decay term in the SFT equation (i.e., for tau >10 yr) the global dipole moment reverses too late in the cycle for all flow profiles and parameters, providing independent supporting evidence for the need of a decay term, even in the case of identical cycles. An allowed domain is found to exist for tau values in the 5-10 yr range for all flow profiles considered. Generally higher values of eta (500-800 km^2/s) are preferred though some solutions with lower eta are still allowed.
Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding the growth rate of this large-scale instability, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached. This results in magnetic spots that are reminiscent of sunspots. Here we want to find out under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. We use a combination of MFS, DNS, and implicit large-eddy simulations to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. We confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using turbulence simulations, we find that magnetic flux concentrations occur for different values of the Mach number between 0.1 and 0.7. DNS and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated.
Deep learning has drawn a lot of interest in recent years due to its effectiveness in processing big and complex observational data gathered from diverse instruments. Here we propose a new deep learning method, called SolarUnet, to identify and track solar magnetic flux elements or features in observed vector magnetograms based on the Southwest Automatic Magnetic Identification Suite (SWAMIS). Our method consists of a data pre-processing component that prepares training data from the SWAMIS tool, a deep learning model implemented as a U-shaped convolutional neural network for fast and accurate image segmentation, and a post-processing component that prepares tracking results. SolarUnet is applied to data from the 1.6 meter Goode Solar Telescope at the Big Bear Solar Observatory. When compared to the widely used SWAMIS tool, SolarUnet is faster while agreeing mostly with SWAMIS on feature size and flux distributions, and complementing SWAMIS in tracking long-lifetime features. Thus, the proposed physics-guided deep learning-based tool can be considered as an alternative method for solar magnetic tracking.
The motions of small-scale magnetic flux elements in the solar photosphere can provide some measure of the Lagrangian properties of the convective flow. Measurements of these motions have been critical in estimating the turbulent diffusion coefficient in flux-transport dynamo models and in determining the Alfven wave excitation spectrum for coronal heating models. We examine the motions of internetwork flux elements in a 24 hour long Hinode/NFI magnetogram sequence with 90 second cadence, and study both the scaling of their mean squared displacement and the shape of their displacement probability distribution as a function of time. We find that the mean squared displacement scales super-diffusively with a slope of about 1.48. Super-diffusive scaling has been observed in other studies for temporal increments as small as 5 seconds, increments over which ballistic scaling would be expected. Using high-cadence MURaM simulations, we show that the observed super-diffusive scaling at short temporal increments is a consequence of random changes in the barycenter positions due to flux evolution. We also find that for long temporal increments, beyond granular lifetimes, the observed displacement distribution deviates from that expected for a diffusive process, evolving from Rayleigh to Gaussian. This change in the distribution can be modeled analytically by accounting for supergranular advection along with motions due to granulation. These results complicate the interpretation of magnetic element motions as strictly advective or diffusive on short and long timescales and suggest that measurements of magnetic element motions must be used with caution in turbulent diffusion or wave excitation models. We propose that passive trace motions in measured photospheric flows may yield more robust transport statistics.
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