The solar photospheric continuum brightness as a function of mean magnetic flux density. I. The role of the magnetic structure size distribution

Solar irradiance models indicate that irradiance variations are dominated by changes in the disk-coverage of magnetic structures, whose brightness is thought to be determined by their size and average magnetic flux density. Recent results suggest that the brightness of small-scale magnetic structures also depends on the mean magnetic flux of the extended region surrounding them due to reduced convective vigor. Low spatial resolution, however, may limit the ability to distinguish the role of magnetic structure size distributions from that of the mean magnetic flux. Using high-resolution 3D MHD simulations, we investigate the brightness of magnetic structures embedded in regions characterized by different mean magnetic flux. In agreement with previous results, we find reduced brightness with increasing mean magnetic flux when comparing the pixel-by-pixel continuum brightness versus magnetic field strength. Evaluating equivalently sized magnetic structures, however, we find no significant dependence of the magnetic structure brightness on the mean magnetic flux of the region in which they are embedded. Rather, we find that simulations with larger mean magnetic flux generate larger, and therefore darker, magnetic structures whose contributions result in an overall darkening of the region. The differences in magnetic structure size distributions alone can explain the reduced brightness of regions with larger mean magnetic flux. This implies that, for the range of mean magnetic flux of the simulations, convective suppression plays at most a secondary role in determining radiative output of magnetized regions. Quantifying the role of convective transport over a wider range of mean magnetic flux is the subject of the second paper in this series.