The continuum intensity as a function of magnetic field: II. Local magnetic flux and convective flows

Context. To deepen our understanding of the role of small-scale magnetic fields in active regions (ARs) and in the quiet Sun (QS) on the solar irradiance, it is fundamental to investigate the physical processes underlying their continuum brightness. Previous results showed that magnetic elements in the QS reach larger continuum intensities than in ARs at disk center, but left this difference unexplained. Aims. We use Hinode/SP disk center data to study the influence of the local amount of magnetic flux on the vigour of the convective flows and the continuum intensity contrasts. Methods. The apparent (i.e. averaged over a pixel) longitudinal field strength and line-of-sight (LOS) plasma velocity were retrieved by means of Milne-Eddington inversions (VFISV code). We analyzed a series of boxes taken over AR plages and the QS, to determine how the continuum intensity contrast of magnetic elements, the amplitude of the vertical flows and the box-averaged contrast were affected by the mean longitudinal field strength in the box (which scales with the total unsigned flux in the box). Results. Both the continuum brightness of the magnetic elements and the dispersion of the LOS velocities anti-correlate with the mean longitudinal field strength. This can be attributed to the "magnetic patches" (here defined as areas where the longitudinal field strength is above 100 G) carrying most of the flux in the boxes. There the velocity amplitude and the spatial scale of convection are reduced. Due to this hampered convective transport, these patches appear darker than their surroundings. Consequently, the average brightness of a box decreases as the the patches occupy a larger fraction of it and the amount of embedded flux thereby increases. Conclusions. Our results suggest that as the magnetic flux increases locally (e.g. from weak network to strong plage), the heating of the magnetic elements is reduced by the intermediate of a more suppressed convective energy transport within the larger and stronger magnetic patches. This, together with the known presence of larger magnetic features, could explain the previously found lower contrasts of the brightest magnetic elements in ARs compared to the QS. The inhibition of convection also affects the average continuum brightness of a photospheric region, so that at disk center, an area of photosphere in strong network or plage appears darker than a purely quiet one. This is qualitatively consistent with the predictions of 3D MHD simulations.