On the continuum intensity distribution of the solar photosphere

Context. For many years, there seemed to be significant differences between the continuum intensity distributions derived from observations and simulations of the solar photosphere. Aims. In order to settle the discussion on these apparent discrepancies, we present a detailed comparison between simulations and seeing-free observations that takes into account the crucial influence of instrumental image degradation. Methods. We use a set of images of quiet Sun granulation taken in the blue, green and red continuum bands of the Broadband Filter Imager of the Solar Optical Telescope (SOT) onboard Hinode. The images are deconvolved with point spread functions (PSF) that account for non-ideal contributions due to instrumental stray-light and imperfections. In addition, synthetic intensity images are degraded with the corresponding PSFs. The results are compared with respect to spatial power spectra, intensity histograms, and the centre-to-limb variation of the intensity contrast. Results. The intensity distribution of SOT granulation images is broadest for the blue continuum at disc-centre and narrows towards the limb and for longer wavelengths. The distributions are relatively symmetric close to the limb but exhibit a growing asymmetry towards disc-centre. The intensity contrast, which is connected to the width of the distribution, is found to be (12.8 ± 0.5)%, (8.3 ± 0.4)%, and (6.2 ± 0.2)% at disc-centre for blue, green, and red continuum, respectively. Removing the influence of the PSF unveils much broader intensity distributions with a secondary component that is otherwise only visible as an asymmetry between the darker and brighter than average part of the distribution. The contrast values increase to (26.7 ± 1.3)%, (19.4 ± 1.4)%, and (16.6 ± 0.7)% for blue, green, and red continuum, respectively. The power spectral density of the images exhibits a pronounced peak at spatial scales characteristic for the granulation pattern and a steep decrease towards smaller scales. The observational findings like the absolute values and centre-to-limb variation of the intensity contrast, intensity histograms, and power spectral density are well matched with corresponding synthetic observables from three-dimensional radiation (magneto-)hydrodynamic simulations. Conclusions. We conclude that the intensity contrast of the solar continuum intensity is higher than usually derived from ground-based observations and is well reproduced by modern radiation (magneto-)hydrodynamic models. Properly accounting for image degradation effects is of crucial importance for comparisons between observations and numerical models.