Here we investigate the effects of horizontal radiative transfer (RT) in combination with non-local thermodynamic equilibrum (NLTE) on important diagnostic iron lines in a realistic atmosphere. Using a snapshot of a 3D radiation-hydrodynamic (HD) simulation and a multilevel iron atom, we computed widely used Fe i line profiles at three different levels of approximation of the RT (3D NLTE, 1D NLTE, LTE). By comparing the resulting line profiles and the circumstances of their formation, we gain new insight into the importance of horizontal RT. We find that the influence of horizontal RT is of the same order of magnitude as that of NLTE, although spatially more localized. Also, depending on the temperature of the surroundings, horizontal RT is found to either weaken or strengthen spectral lines. Line depths and equivalent width may differ by up to 20% from the corresponding LTE value if 3D RT is applied. Residual intensity contrasts in LTE are found to be larger than those in 3D NLTE by up to a factor of two. When compared to 1D NLTE, we find that horizontal RT weakens the contrast by up to 30% almost independently of the angle of line of sight. While the center-to-limb variation (CLV) of the 1D and 3D NLTE contrasts have a similar form, the LTE contrast CLV shows a different run. Determination of temperatures by 1D NLTE inversions of spatially resolved observations may produce errors of up to 200 K if one neglects 3D RT. We find a linear correlation between the intensity difference of 1D and 3D NLTE and a simple estimate of the temperature in the horizontal environment of the line formation region. This correlation could be used to coarsely correct inversions done in 1D NLTE for some of the effects of horizontal RT. Horizontal RT is less important if one considers spatially averaged line profiles because local line strengthening and weakening occur with similar frequency in our HD atmosphere. Thus, the iron abundance is underestimated by 0.012 dex if calculated using 1D NLTE RT. Since effects of horizontal RT are greatest for spatially resolved quantities, the use of 3D RT is particularly important for interpreting high spatial resolution observations.

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 thermodynamicequilibrium (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.

Abstract. Although the triplet polarization structure of the Na  D 2 and Ca  4227 Å lines in the second solar spectrum has been known for more than two decades, a clear and consistent explanation has been lacking. Here we show that the qualitative profile shape may be explained in terms of the anisotropy of the radiation field and partial frequency redistribution (PRD) effects. The complicated frequency and depth dependence of the anisotropy can be understood in terms of simple arguments that involve the source function gradient and boundary effects. We show in particular that the triplet peak structure of the polarization profile of Na  D 2 has basically the same origin as for the Ca  4227 Å line. Hyperfine structure and lower-level atomic polarization only modify the core polarization without altering the overall qualitative features. For our calculations we adopt a numerical method that combines the advantages of both the classical formalism with integral source function and the density-matrix formalism. In a first step, a multi-level, PRD-capable MALI code, which solves the statistical equilibrium and the radiative transfer equation self-consistently, computes intensity, opacities and collision rates. Keeping these quantities fixed, we obtain the scattering polarization in a second step by solving the radiative transfer equation for the transitions of interest with the classical formalism, which assumes a two-level atomic model with unpolarized lower level. Quantum interferences and lower-level atomic polarization are included in terms of a wavelength dependent polarizability W 2 , which is independently obtained with the density-matrix formalism.