Are supergranule sizes anti-correlated with magnetic activity?

Context.The variation of supergranule cell sizes with the magnetic environment is still controversial. Aims.We study this relation in detail to understand the discrepancies observed between previous results. Methods.We determine the cell size using divergence of horizontal flows derived from local correlation tracking of intensity maps (MDI/SOHO). We study the variation of the cell size as a function of the magnetic field inside the cell. We also consider which component of the magnetic field most influences the cell size. Results.Our main conclusion is that there are no large cells when the magnetic field (in absolute value) averaged over the cell is large. This is mostly due to the magnetic field inside the cell (intranetwork fields), while strong network magnetic fields (at the cell boundary) are associated with larger cells. Further studies of the evolution of the cells and of the flux imbalance suggest that a high level of weak fields may prevent the formation of large cells. This is compatible with the expectation that strong magnetic fields should prevent large-scale flows. Conclusions.The relation between the local activity level determined by the average magnetic field inside the cells and the supergranule size is not linear. Furthermore, it strongly depends on the definition of the activity level (magnetic field inside the cell or magnetic network) and on the magnetic sensitivity of the data. This last point probably explains at least partially the conflicting results obtained up to now