Is there a non-monotonic relation between photospheric brightness and magnetic field strength in solar plage regions?

Abstract

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.