Accuracy of electric current inference assuming three-dimensional hydrostatic equilibrium
Abstract
The chromospheric and coronal heating problem is among the major open questions in solar physics. Some of the possible mechanisms that can explain the rise in temperature that is needed to reproduce the observations require the estimation of electric currents. Since these depend on the spatial derivatives of the magnetic field components, it is necessary to obtain the full magnetic field vector from observational data in a 3D geometrical grid. We developed a new method to obtain the 3D geometrical configuration of the atmosphere using the approximation of hydrostatic equilibrium in three dimensions to determine the gas pressure and density as a function of optical depth, column mass, or geometrical distance. This development has been designed as an extension for any inversion code that outputs a stratification of temperature and gas pressure or density to enable the estimation of electric current densities from observations. We investigated our approach using a snapshot from a sunspot MHD simulation. The difference between the solver output and the simulation, taken as the ground truth, is mostly between 30 and 45 %, showing a similar pattern over a large optical depth range. Additional tests also showed that the solver provides a unique solution, has a scarce sensitivity to the boundary condition and is only marginally impacted by the viewing angle. We conclude that the electric currents can be inferred at a reasonable accuracy with this approach using the simulation parameters as input. We also tested set-ups that aim at mimicking more realistic cases, where the code performed equally well. The results in this work show promise with respect to future applications to spectropolarimetric data, however, some additional challenges will need to be adressed when moving from the controlled input of the simulation to observational data.
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BibTeX
@misc{meissner2026accuracy,
title = {{Accuracy of electric current inference assuming three-dimensional hydrostatic equilibrium}},
author = {Aaron Meissner and Adur Pastor Yabar and Jaime de la Cruz Rodríguez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32547},
eprint = {2610.32547},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32547},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Accuracy of electric current inference assuming three-dimensional hydrostatic equilibrium
AU - Aaron Meissner
AU - Adur Pastor Yabar
AU - Jaime de la Cruz Rodríguez
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32547
UR - https://arxiv.org/abs/2610.32547
AB - The chromospheric and coronal heating problem is among the major open questions in solar physics. Some of the possible mechanisms that can explain the rise in temperature that is needed to reproduce the observations require the estimation of electric currents. Since these depend on the spatial derivatives of the magnetic field components, it is necessary to obtain the full magnetic field vector from observational data in a 3D geometrical grid. We developed a new method to obtain the 3D geometrical configuration of the atmosphere using the approximation of hydrostatic equilibrium in three dimensions to determine the gas pressure and density as a function of optical depth, column mass, or geometrical distance. This development has been designed as an extension for any inversion code that outputs a stratification of temperature and gas pressure or density to enable the estimation of electric current densities from observations. We investigated our approach using a snapshot from a sunspot MHD simulation. The difference between the solver output and the simulation, taken as the ground truth, is mostly between 30 and 45 %, showing a similar pattern over a large optical depth range. Additional tests also showed that the solver provides a unique solution, has a scarce sensitivity to the boundary condition and is only marginally impacted by the viewing angle. We conclude that the electric currents can be inferred at a reasonable accuracy with this approach using the simulation parameters as input. We also tested set-ups that aim at mimicking more realistic cases, where the code performed equally well. The results in this work show promise with respect to future applications to spectropolarimetric data, however, some additional challenges will need to be adressed when moving from the controlled input of the simulation to observational data.
ER -