Combining magneto-hydrostatic constraints with Stokes profiles inversions. III. Uncertainty in the inference of electric currents

Abstract

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. We study how accurately we can infer electric currents under different scenarios. 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, $\mathbf{B}$, from which the electric current density, $\mathbf{j}$, is derived by applying Ampere's law. 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 ($j_{\mathrm{x}}$, $j_{\mathrm{y}}$, $j_{\mathrm{z}}$) with an accuracy of $\sigma =0.90-1.00$ dex, whereas the modulus ($\Vert \mathbf{j}\Vert$) can only be determined with $\sigma =0.75$ 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 $\sigma =0.70-0.75$ dex for the individual components and $\sigma =0.5$ dex for the modulus. Moreover, in regions where the magnetic field is above 300 gauss, $\Vert \mathbf{j}\Vert$ can be inferred with an accuracy of $\sigma =0.3$ dex. In general, the $x$ and $y$ components of the electric current density are retrieved slightly better than the $z$ component.

arXiv commentaccepted for publication in Astronomy & Astrophysics (A&A): 12 pages, 8 figures, 5 tables

References in corpus (29)

• VFISV: Very Fast Inversion of the Stokes Vector for the Helioseismic and Magnetic Imager
• The origin, early evolution and predictability of solar eruptions
• An Open Source, Massively Parallel Code for Non-LTE Synthesis and Inversion of Spectral Lines and Zeeman-induced Stokes Profiles
• Numerical sunspot models: Robustness of photospheric velocity and magnetic field structure
• STiC -- A multi-atom non-LTE PRD inversion code for full-Stokes solar observations
• Inversion of the radiative transfer equation for polarized light
• Spatially coupled inversion of spectro-polarimetric image data I: Method and first results
• High-resolution observations of flare precursors in the low solar atmosphere
• An active region filament studied simultaneously in the chromosphere and photosphere: I - Magnetic structure
• Spectropolarimetric NLTE inversion code SNAPI
• Inferring the magnetic field vector in the quiet Sun. I. Photon noise and Selection Criteria
• Magnetohydrodynamics of the Weakly Ionized Solar Photosphere
• Are Electric Currents Heating the Magnetic Chromosphere?
• Three-dimensional structure of a sunspot light bridge
• Comparison of inversion codes for polarized line formation in MHD simulations. I. Milne-Eddington codes
• A geometrical height scale for sunspot penumbrae
• Deep probing of the photospheric sunspot penumbra: no evidence for magnetic field-free gaps
• Inferring the magnetic field vector in the quiet Sun. II. Interpreting results from the inversion of Stokes profiles
• FIRTEZ-dz: A Forward and Inverse solver of the polarized Radiative Transfer Equation under Zeeman regime in geometrical scale
• TIC: A Stokes inversion code for scattering polarization with partial frequency redistribution and arbitrary magnetic fields
• Combining magneto-hydrostatic constraints with Stokes profiles inversions
• Flux tubes as the origin of Net Circular Polarization in Sunspot Penumbrae
• The electrical current density vector in the inner penumbra of a Sunspot
• Active region chromospheric magnetic fields
• Heating of the solar chromosphere in a sunspot light bridge by electric currents
• Inferring the magnetic field vector in the quiet Sun. III. Disk variation of the Stokes profiles and isotropism of the magnetic field
• Combining magneto-hydrostatic constraints with Stokes profile inversions. II. Application to Hinode/SP observations
• Capabilities of bisector analysis of the Si I 10827 A line for estimating line-of-sight velocities in the quiet Sun
• Inference of electric currents in the solar photosphere

Cited by in corpus (2)

• Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D): I. Overview, Magnetohydrodynamic Modeling, and Stokes Profile Synthesis
• Inference of horizontal velocity fields from the induction equation in the solar atmosphere. I. Analytical and numerical solutions in 2D