Combining magneto-hydrostatic constraints with Stokes profiles inversions

III. Uncertainty in the inference of electric currents

¹ Leibniz-Institut für Sonnenphysik, Schöneckstr. 6, 79104 Freiburg, Germany
e-mail: borrero@leibniz-kis.de
² Institute for Solar Physics, Department of Astronomy, Stockholm University, AlbaNova University Centre, 10691 Stockholm, Sweden

Received: 8 August 2022
Accepted: 29 October 2022

Abstract

Context. Electric currents play an important role in the energy balance of the plasma in the solar atmosphere. They are also indicative of non-potential magnetic fields and magnetic reconnection. Unfortunately, the direct measuring of electric currents has traditionally been riddled with inaccuracies.

Aims. We study how accurately we can infer electric currents under different scenarios.

Methods. We carry out increasingly complex inversions of the radiative transfer equation for polarized light applied to Stokes profiles synthesized from radiative three-dimensional magnetohydrodynamic (MHD) simulations. The inversion yields the magnetic field vector, B, from which the electric current density, j, is derived by applying Ampere’s law.

Results. We find that the retrieval of the electric current density is only slightly affected by photon noise or spectral resolution. However, the retrieval steadily improves as the Stokes inversion becomes increasingly elaborated. In the least complex case (a Milne-Eddington-like inversion applied to a single spectral region), it is possible to determine the individual components of the electric current density (j_x, j_y, j_z) with an accuracy of σ = 0.90 − 1.00 dex, whereas the modulus (∥j∥) can only be determined with σ = 0.75 dex. In the most complicated case (with multiple spectral regions, a large number of nodes, Tikhonov vertical regularization, and magnetohydrostatic equilibrium), these numbers improve to σ = 0.70 − 0.75 dex for the individual components and σ = 0.5 dex for the modulus. Moreover, in regions where the magnetic field is above 300 gauss, ∥j∥ can be inferred with an accuracy of σ = 0.3 dex. In general, the x and y components of the electric current density are retrieved slightly better than the z component. In addition, the modulus of the electric current density is the best retrieved parameter of all, and thus it can potentially be used to detect regions of enhanced Joule heating.

Conclusions. The fact that the accuracy does not worsen with decreasing spectral resolution or increasing photon noise, and instead increases as the Stokes inversion complexity grows, suggests that the main source of errors in the determination of electric currents is the lack of realism in the inversion model employed to determine variations in the magnetic field along the line of sight at scales smaller than the photon mean-free path, along with the intrinsic limitations of the model due to radiative transfer effects.