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Context. The amount of magnetic flux passing through the solar surface is an important parameter determining solar activity and the heliospheric magnetic field. It is usually determined from line-of-sight magnetograms. Aims. We aim to test the reliability of determining the line-of-sight magnetic field from 3D MHD (magnetohydrodynamic) simulations of unipolar regions. In contrast to earlier similar studies, we consider the full solar disk, by considering the full centre-to-limb variation, as well as regions with different averaged field strengths. Methods. We synthesised Stokes profiles from MURaM MHD simulations of unipolar regions with varying mean vertical magnetic flux densities, ranging from quiet Sun to active region plage. We did this for a comprehensive range of heliocentric angles: from μ = 1 to μ = 0.15, and for two commonly used photospheric spectral lines: Fe I 6173.3 and Fe I 5250.2 Å. The synthesised profiles were spatially foreshortened and binned to different spatial resolutions characteristic of space-based magnetographs currently in operation. The line-of-sight magnetic field was derived with a Milne-Eddington Inversion as well as with other commonly used methods. Results. The inferred spatially averaged ⟨ B LOS ⟩ is always lower than that present in the MHD simulations, with the exception of μ ≈ 1 and sufficiently high spatial resolution. It is also generally inconsistent with a linear dependence on μ . Above μ = 0.5 the spatial resolution greatly impacts the retrieved line-of-sight magnetic field. For μ ≤ 0.5 the retrieved B LOS is nearly independent of resolution, but is always lower than expected from the simulation. These trends persist regardless of the mean vertical magnetic field in the MHD simulations and are independent of the B LOS retrieval method. For μ ≤ 0.5, a larger ⟨ B LOS ⟩ is inferred for the 5250.2 Å spectral line than 6173.3 Å, but the converse is true at higher μ . Conclusions. The obtained results show that with high spatial resolution observations, for instance those achieved with SO/PHI-HRT (High Resolution Telescope of the Polarimetric and Helioseismic Imager on Solar Orbiter) at close perihelion, the magnetic flux can be reliably retrieved at high μ values, whereas in lower resolution observations, as well as at lower μ , a significant fraction of the magnetic flux is missed. The results found here raise some doubts of the reliability of determining the radial field by dividing the line-of-sight field by μ and are of considerable importance for deducing the total magnetic flux of the Sun. They may also contribute to the resolution of the open flux problem.
Sinjan et al. (Fri,) studied this question.