Spectropolarimetric diagnostics of the lower solar atmosphere: A review of inversion techniques

The Sun, our host star, plays a fundamental role in astrophysics due to its vicinity. To understand the processes taking place in the outermost layers of the Sun, but also, indirectly, in its interior, we conduct high spectral and spatial resolution, high cadence observations of diagnostically important spectral lines. The intensity and the polarization of the electromagnetic radiation in the observed spectral lines are a result of the joint action of absorption, emission, and scattering processes, further altered by the Zeeman and Hanle effects. Spectropolarimetric inversions are the techniques devised for the inference of the physical parameters in the solar atmosphere through the interpretation of spectral line shapes and line polarization. This review aims to provide a pedagogical overview of the necessary radiative transfer formalism and cutting-edge techniques, and to help interested readers enter the field and use some of the concepts in their own research. The secondary aim is a critical assessment of the emerging directions for the development of spectropolarimetric inversions, namely, to discuss the friction between physical realism, numerical efficiency, and modeling of the instrumental effects.