Context. Despite their importance, routine and direct measurements of electric currents, j, in the solar atmosphere have generally not been possible.
Aims: We aim at demonstrating the capabilities of a newly developed method for determining electric currents in the solar photosphere.
Methods: We employ three-dimensional radiative magneto-hydrodynamic (MHD) simulations to produce synthetic Stokes profiles in several spectral lines with a spatial resolution similar to what the newly operational 4-meter Daniel K. Inouye Solar Telescope solar telescope should achieve. We apply a newly developed inversion method of the polarized radiative transfer equation with magneto-hydrostatic (MHS) constraints to infer the magnetic field vector in the three-dimensional Cartesian domain, B(x, y, z), from the synthetic Stokes profiles. We then apply Ampere's law to determine the electric currents, j, from the inferred magnetic field, B(x, y, z), and compare the results with the electric currents present in the original MHD simulation.
Results: We show that the method employed here is able to attain reasonable reliability (close to 50% of the cases are within a factor of two, and this increases to 60%-70% for pixels with B ≥ 300 G) in the inference of electric currents for low atmospheric heights (optical depths at 500 nm τ5∈[1, 0.1]) regardless of whether a small or large number of spectral lines are inverted. Above these photospheric layers, the method's accuracy strongly deteriorates as magnetic fields become weaker and as the MHS approximation becomes less accurate. We also find that the inferred electric currents have a floor value that is related to low-magnetized plasma, where the uncertainty in the magnetic field inference prevents a sufficiently accurate determination of the spatial derivatives.
Conclusions: We present a method that allows the inference of the three components of the electric current vector at deep atmospheric layers (photospheric layers) from spectropolarimetric observations.