Context. The relationship between the brightness and field strength of small-scale solar magnetic features is an important factor for solar irradiance variations and a constraint for simulations of solar magneto-convection. Aims. We wish to clarify the origin of the apparent discrepancy between observational results and radiative MHD simulations. Methods. Maps of (bolometric) brightness and magnetic field strength from the simulation of a plage region were convolved and rebinned to mimic observations obtained with telescopes with finite aperture. Results. Image smearing changes the monotonic relation between brightness and field strength obtained at the original resolution of the simulation into a profile with a maximum at intermediate field strength, which is in qualitative agreement with the observations. This result is mainly due to the smearing of strong magnetic fields at the bright edges of magnetic structures into the weakly magnetized adjacent areas. Conclusions. Observational and simulation results are qualitatively consistent with each other if the finite spatial resolution of the observations is taken into account.
Context. Variations of solar irradiance are mainly determined by the changing coverage of the visible solar disk with magnetic flux concentrations. The relationship between brightness and field strength is an important ingredient for models and reconstructions of irradiance variations. Aims. We assess the effect of limited observational resolution on the relationship between brightness and magnetic field by comparing comprehensive MHD simulations with observational results. Methods. Simulations of magnetoconvection representing the near-surface layers of a plage region were used to determine maps of the continuum brightness and Stokes profiles for the Fe line at 630.22 nm. After convolving with instrumental profiles, synthetic observations of the magnetic field were generated by applying a Stokes inversion code. We compare the resulting relation between brightness and apparent vertical magnetic field to the corresponding outcome derived from real observations of a plage region with the Hinode satellite. Results. Consideration of the image smearing effects due to the limited resolution of the observations transform the largely monotonic relation between brightness and field strength at the original resolution of the simulations into a profile with a maximum at intermediate field strength, which is in good agreement with the observations. Conclusions. Considering the effect of limited observational resolution renders the relation between brightness and magnetic field from comprehensive MHD simulations consistent with observational results. This is a necessary prerequisite for the utilization of simulations for models and reconstruction of solar irradiance variations.
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