Inference of electric currents in the solar photosphere

Abstract

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.

The European Solar Telescope

“…Most theoretical studies of photospheric and chromospheric plasma dynamics use MHD models (Priest 1982) as the primary tool for successfully understanding the complex structure and dynamical processes of these solar atmospheric layers (among many references, Khomenko & Collados 2006;Cheung et al 2008;Rempel et al 2009;Cheung et al 2010;Carlsson et al 2016;Threlfall et al 2016). Yet, the solar photosphere and chromosphere are only partially ionised with an ionisation fraction below 10 −3 in the photosphere as described in Vernazza et al (1981), see also Ballester et al (2018) for a review on this topic and, for example, Pastor Yabar et al (2021). Therefore, a suitable alternative to the MHD approach is a multi-fluid approach where the plasma species are considered separate fluids interacting by collisions (see, Khomenko et al 2014, and references within).…”

Prospects and challenges of numerical modeling of the Sun at millimeter wavelengths

“…The model typically includes the stratification of temperature, line-of-sight velocity, microturbulence, and the three components of the magnetic field as a function of column-mass or continuum optical-depth at a reference wavelength. Inversion techniques have been applied systematically to study photospheric datasets with different levels of complexity (Ruiz Cobo and del Toro Iniesta, 1992;van Noort, 2012;Ruiz Cobo and Asensio Ramos, 2013;Scharmer et al, 2013;Pastor Yabar et al, 2021) under the assumption of LTE.…”

Combining magneto-hydrostatic constraints with Stokes profiles inversions

“…In Borrero et al (2021) we present a novel Stokes inversion code that also employs MHS equilibrium and solves most of those shortcomings. The resulting method was subsequently employed to determine electric currents in the solar photosphere and compared to results from magnetohydrodynamic (MHD) simulations (Pastor Yabar et al 2021), thereby allowing us to study, for the first time, the accuracy in the inference of j. However, a missing piece of the puzzle is whether this accuracy actually improves results that employ MHS instead of HE and, if so, by how much.…”