A Comparison of Sparse and Non-sparse Techniques for Electric-Field Inversion from Normal-Component Magnetograms

Abstract

An important element of 3D data-driven simulations of solar magnetic fields is the determination of the horizontal electric field at the solar photosphere. This electric field is used to drive the 3D simulations and inject energy and helicity into the solar corona. One outstanding problem is the localisation of the horizontal electric field such that it is consistent with Ohm’s law. Yeates (Astrophys. J.836(1), 131, 2017) put forward a new “sparse” technique for computing the horizontal electric field from normal-component magnetograms that minimises the number of non-zero values. This aims to produce a better representation of Ohm’s law compared to previously used “non-sparse” techniques. To test this new approach we apply it to active region (AR) 10977, along with the previously developed non-sparse technique of Mackay, Green, and van Ballegooijen (Astrophys. J.729(2), 97, 2011). A detailed comparison of the two techniques with coronal observations is used to determine which is the most successful. Results show that the non-sparse technique of Mackay, Green, and van Ballegooijen (2011) produces the best representation for the formation and structure of the sigmoid above AR 10977. In contrast, the Yeates (2017) approach injects strong horizontal fields between spatially separated, evolving magnetic polarities. This injection produces highly twisted unphysical field lines with significantly higher magnetic energy and helicity. It is also demonstrated that the Yeates (2017) approach produces significantly different results that can be inconsistent with the observations depending on whether the horizontal electric field is solved directly or indirectly through the magnetic vector potential. In contrast, the Mackay, Green, and van Ballegooijen (2011) method produces consistent results using either approach. The sparse technique of Yeates (2017) has significant pitfalls when applied to spatially resolved solar data, where future studies need to investigate why these problems arise.

Automated Driving for Global Nonpotential Simulations of the Solar Corona

“…Thus we find that the local inductive E 0 ^is an improvement. Note that, although it does not concern us here, the sparse solution is also found to lead to significant spurious coronal currents when applied with higher-cadence sequences of observational magnetograms (Mackay & Yeates 2021). Since minimizing the L 1 norm is equivalent to finding the sparsest solution, we can compare the relative sparseness of the different E ⊥ by their L 1 norms, which for this example are 2256 V m −1 for the local inductive solution, 6115 V m −1 for the global inductive solution, and 1978 V m −1 for the global sparse solution.…”

Reconstruction of Photospheric Velocity Fields from Highly Corrupted Data

“…Reconstruction of flows where spatially coherent magnetic fields are not present has potential applications for data-driven models of the solar atmosphere (e.g., Hoeksema et al 2020). The subject of appropriate choices of boundary conditions for dynamical models in weak-field regions is an area of ongoing research (Mackay & Yeates 2021). Consequently, methods to inpaint flows in regions lacking strong, coherent magnetic fields are of interest.…”