Abstract
Context. This paper forms the second part of our study of how neglecting non-local thermodynamic equilibrium (NLTE) conditions in the formation of Fe I 6301.5 Å and the 6302.5 Å lines affects the atmosphere that is obtained by inverting the Stokes profiles of these lines in LTE. The main cause of NLTE effects in these lines is the line opacity deficit that is due to the excess ionisation of Fe I atoms by ultraviolet (UV) photons in the Sun. Aims. In the first paper, these photospheric lines were assumed to have formed in 1D NLTE and the effects of horizontal radiation transfer (RT) were neglected. In the present paper, the iron lines are computed by solving the RT in 3D. We investigate the effect of horizontal RT on the inverted atmosphere and how it can enhance or reduce the errors that are due to neglecting 1D NLTE effects. Methods. The Stokes profiles of the iron lines were computed in LTE, 1D NLTE, and 3D NLTE. They were all inverted using an LTE inversion code. The atmosphere from the inversion of LTE profiles was taken as the reference model. The atmospheres from the inversion of 1D NLTE profiles (testmodel-1D) and 3D NLTE profiles (testmodel-3D) were compared with it. Differences between reference and testmodels were analysed and correspondingly attributed to NLTE and 3D effects. Results. The effects of horizontal RT are evident in regions surrounded by strong horizontal temperature gradients. That is, along the granule boundaries, regions surrounding magnetic elements, and its boundaries with intergranular lanes. In some regions, the 3D effects enhance the 1D NLTE effects, and in some, they weaken these effects. In the small region analysed in this paper, the errors due to neglecting the 3D effects are lower than 5% in temperature. In most of the pixels, the errors are lower than 20% in both velocity and magnetic field strength. These errors also persist when the Stokes profiles are spatially and spectrally degraded to the resolution of the Swedish Solar Telescope (SST) or Daniel K. Inouye Solar Telescope (DKIST). Conclusions. Neglecting horizontal RT introduces errors not only in the derived temperature, but also in other atmospheric parameters. The error sizes depend on the strength of the local horizontal temperature gradients. Compared to the 1D NLTE effect, the 3D effects are more localised in specific regions in the atmosphere and are weaker overall.
Highlights
The nature of the radiative transfer (RT) problem for any stellar atmosphere diagnostic is inherently multi-dimensional and coupled with the effects of non-local thermodynamic equilibrium
We investigate by how much the 3D effects strengthen or weaken the 1D non-local thermodynamic equilibrium (NLTE) effects and increase or decrease the errors in the inverted atmosphere
The Stokes profiles computed in LTE, 1D NLTE, and 3D NLTE were inverted in LTE using the SPINOR code (Solanki 1987; Frutiger et al 2000)
Summary
The nature of the radiative transfer (RT) problem for any stellar atmosphere diagnostic is inherently multi-dimensional and coupled with the effects of non-local thermodynamic equilibrium (non-LTE). In a series of papers, Holzreuter & Solanki (2012), Holzreuter & Solanki (2013), and Holzreuter & Solanki (2015) for the first time computed the photospheric iron lines at 5247 Å, 5250 Å, 6301.5 Å, and 6302.5 Å in 3D NLTE using different model atmospheres: a simple flux tube model, a 3D hydrodynamic (HD) simulation, and a 3D magnetohydrodynamic (MHD) simulation They presented a detailed comparison of the Stokes profiles computed in LTE, 1D NLTE, and 3D NLTE and highlighted the importance of accounting for the 3D NLTE effects in these lines. These effects were evident in Stokes profiles in granules, intergranular lanes, magnetic elements, their boundaries, basically in every region with strong vertical gradients in temperature, in the LOS velocity, or in the magnetic field In this second paper of this series, we account for the horizontal RT effects in the iron lines and investigate how they affect the inverted atmosphere. We investigate by how much the 3D effects strengthen or weaken the 1D NLTE effects and increase or decrease the errors in the inverted atmosphere
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