Intensity contrast from MHD simulations and HINODE observations

Context. Changes in the solar surface area, which is covered by small-scale magnetic elements, are thought to cause long-term changes in the solar spectral irradiance, which are important for determining the impact on Earth's climate. Aims. To study the effect of small-scale magnetic elements on the total and spectral irradiance, we derive their contrasts from 3-D MHD simulations of the solar atmosphere. These calculations are necessary because measurements of small-scale flux tube contrasts are confined to a few wavelengths and affected by scattered light and instrument defocus, even for space observations. Methods. To test the contrast calculations, we compare rms contrasts from simulations with those obtained with the broad-band filter imager mounted on the Solar Optical Telescope (SOT) onboard the Hinode satellite and also analyse centre-to-limb variations (CLV). The 3-D MHD simulations include the interaction between convection and magnetic flux tubes. They are performed by assuming non-grey radiative transfer and using the MURaM code. The simulations have an average vertical magnetic field of 0 G, 50 G, and 200 G. Emergent intensities are calculated with the spectral synthesis code ATLAS9 and are convolved with a theoretical point-spread function to account for the properties of the observations' optical system. Results. We find reasonable agreement between simulated and observed intensity distributions in the visible continuum bands. Agreement is poorer for the CN and G-bands. The analysis of the simulations uncovers a potentially more realistic centre-to-limb behaviour than calculations based on 1-D model atmospheres. Conclusions. We conclude that starting from 3-D MHD simulations represents a powerful approach to obtaining intensity contrasts for a wide wavelength coverage and different positions across on the solar disk. This also paves the way for future calculations of facular and network contrast as a function of magnetic fluxes.