The continuum intensity as a function of magnetic field: I. Active region and quiet Sun magnetic elements

Context. Small-scale magnetic fields are major contributors to the solar irradiance variations. Hence, the continuum intensity contrast of magnetic elements in the quiet Sun (QS) network and in active region (AR) plage is an essential quantity that needs to be measured reliably. Aims. By using Hinode/SP disk center data at a constant, high spatial resolution, we aim at updating results of earlier ground-based studies of contrast vs. magnetogram signal, and to look for systematic differences between AR plages and QS network. Methods. The field strength, filling factor and inclination of the field was retrieved by means of a Milne-Eddington inversion (VFISV code). As in earlier studies, we then performed a pixel-by-pixel study of 630.2 nm continuum contrast vs. apparent (i.e. averaged over a pixel) longitudinal magnetic field over large fields of view in ARs and in the QS. Results. The continuum contrast of magnetic elements reaches larger values in the QS (on average 3.7%) than in ARs (on average 1.3%). This could not be attributed to any systematic difference in the chosen contrast references, so that it mainly reflects an intrinsic brightness difference. The larger contrasts in the QS are in agreement with earlier, lower resolution results, although our values are larger due to our better spatial resolution. At Hinode's spatial resolution, moreover, the relationship between contrast and apparent longitudinal field strength exhibits a peak at around 700 G in both the QS and ARs, whereas earlier lower resolution studies only found a peak in the QS and a monotonic decrease in ARs. We attribute this discrepancy both to our careful removal of the pores and their close surroundings affected by the telescope diffraction, as well as to the enhanced spatial resolution and very low scattered light of the Hinode Solar Optical Telescope. We verified that the magnetic elements producing the peak in the contrast curve are rather vertical in the AR and in the QS, so that the larger contrasts in the QS cannot be explained by larger inclinations, as had been proposed earlier. The opposite polarities in ARs do not exhibit any noticeable difference in inclination either, although they reach different contrasts when the amount of flux is significantly unbalanced between the polarities. Conclusions. According to our inversions, the magnetic elements producing the peak of the contrast curves have similar properties (field strength, inclination, filling factor) in ARs and in the QS, so that the larger brightness of magnetic elements in the QS remains unexplained. Indirect evidence suggests that the contrast difference is not primarily due to any difference in average size of the magnetic elements. A possible explanation lies in the different efficiencies of convective energy transport in the QS and in ARs, which will be the topic of a second paper.