Sparse reconstruction of electric fields from radial magnetic data

Yeates, A.R.

Abstract

Accurate estimates of the horizontal electric field on the Sun's visible surface are important not only for estimating the Poynting flux of magnetic energy into the corona but also for driving time-dependent magnetohydrodynamic models of the corona. In this paper, a method is developed for estimating the horizontal electric field from a sequence of radial-component magnetic field maps. This problem of inverting Faraday's law has no unique solution. Unfortunately, the simplest solution (a divergence-free electric field) is not realistically localized in regions of non-zero magnetic field, as would be expected from Ohm's law. Our new method generates instead a localized solution, using a basis pursuit algorithm to find a sparse solution for the electric field. The method is shown to perform well on test cases where the input magnetic maps are flux balanced, in both Cartesian and spherical geometries. However, we show that if the input maps have a significant imbalance of flux - usually arising from data assimilation - then it is not possible to find a localized, realistic, electric field solution. This is the main obstacle to driving coronal models from time sequences of solar surface magnetic maps.

Citation

Yeates, A. (2017). Sparse reconstruction of electric fields from radial magnetic data. Astrophysical Journal, 836(1), Article 131. https://doi.org/10.3847/1538-4357/aa5c84

• Journal Article Type: Article
• Acceptance Date: Jan 27, 2017
• Online Publication Date: Feb 14, 2017
• Publication Date: Feb 14, 2017
• Deposit Date: Jan 27, 2017
• Publicly Available Date: Jan 27, 2017
• Journal: Astrophysical Journal
• Print ISSN: 0004-637X
• Electronic ISSN: 1538-4357
• Publisher: American Astronomical Society
• Peer Reviewed: Peer Reviewed
• Volume: 836
• Issue: 1
• Article Number: 131
• DOI: https://doi.org/10.3847/1538-4357/aa5c84
• Related Public URLs: https://arxiv.org/abs/1701.06780