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.
Highlights
One of the major goals of solar physics is to understand how magnetic energy and magnetic helicity are injected into the solar corona through plasma motions occurring at the solar photosphere
This approach to study the long-term quasi-static evolution of the magnetic field is supported by the fact that photospheric boundary motions on the Sun are very slow compared to the coronal Alfvén speed (Mackay, Green, and van Ballegooijen, 2011)
While the results described have focused on the L1-norm simulation that solves for A since this simulation produces the correct forward-S shaped flux rope, similar distributions of the electric field and reconnection of field lines produce the incorrect inverse-S shaped structure for the L1-norm simulation that solves for E
Summary
One of the major goals of solar physics is to understand how magnetic energy and magnetic helicity are injected into the solar corona through plasma motions occurring at the solar photosphere. The simplest data-driven models use only a time series of normal-component magnetograms to determine the horizontal electric field; this process has been successfully applied in a number of studies (Mikicet al., 1999; Amari et al, 2003; Mackay, Green, and van Ballegooijen, 2011; Cheung and DeRosa, 2012; Gibb et al, 2014; Yardley, Mackay, and Green, 2018) While these studies have had significant success in reproducing coronal features above active regions, complete agreement between the observations and models has not been found. While the use of vector magnetic fields, Doppler velocities, and local correlation tracking is the most comprehensive approach, a number of studies have continued to use only normal-component magnetograms to specify the horizontal electric field, even though this approach is unlikely to capture all of the boundary driving Developing and testing such techniques is still useful for a number of reasons: (i) It allows data-driven techniques to be applied to pre-SDO observations (SDO, Solar Dynamic Observatory).
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