Three-dimensional non-LTE radiative transfer effects in Fe I lines I. Flux sheet and flux tube geometries

In network and active region plages, the magnetic field is concentrated into structures often described as flux tubes (FTs) and sheets (FSs). Three-dimensional (3D) radiative transfer is important for energy transport in these concentrations. It is also expected to be important for diagnostic purposes but has rarely been applied for that purpose. Using true 3D, non-local thermodynamic-equilibrium (non-LTE or NLTE) radiative transfer (RT) in FT and FS models, we compute iron line profiles commonly used to diagnose the Sun's magnetic field by using and comparing the results with those obtained from LTE or one-dimensional (1D) NLTE calculations. Employing a multilevel iron atom, we study the influence of several basic parameters such as either FS or FT Wilson depression, wall thickness, radius/width, thermal stratification or magnetic field strength on Stokes I and the polarized Stokes parameters in the thin-tube approximation. The use of different levels of approximations of RT (3D NLTE, 1D NLTE, LTE) may lead to considerable differences in profile shapes, intensity contrasts, equivalent widths, and the determination of magnetic field strengths. In particular, LTE, which often provides a good approach in planar 1D atmospheres, is a poor approximation in our flux sheet model for some of the most important diagnostic Fe I lines (524.7 nm, 525.0 nm, 630.1 nm, and 630.2 nm). The observed effects depend on parameters such as the height of line formation, field strength, and internal temperature stratification. Differences between the profile shapes may lead to errors in the determination of magnetic fields on the order of 10% to 20%, while errors in the determined temperature can reach 300-400 K. The empirical FT models NET and PLA turn out to minimize the effects of 3D RT, so that results obtained with these models by applying LTE may also remain valid for 3D NLTE calculations. Finally, horizontal RT is found to only insignificantly smear out structures such as the optically thick walls of flux tubes and sheets, allowing features as narrow as 10 km to remain visible.