Plasma flows and sound-speed perturbations in the average supergranule

Supergranules create a peak in the spatial spectrum of photospheric velocity features. They have some properties of convection cells but their origin is still being debated in the literature. The time-distance helioseismology constitutes a method that is suitable for investigating the deep structure of supergranules. Our aim is to construct the model of the flows in the average supergranular cell using fully consistent time-distance inverse methodology. We used the Multi-Channel Subtractive Optimally Localised Averaging inversion method with regularisation of the cross-talk. We combined the difference and the mean travel-time averaging geometries. We applied this methodology to travel-time maps averaged over more than 10000 individual supergranular cells. These cells were detected automatically in travel-time maps computed for 64 quiet days around the disc centre. The ensemble averaging method allows us to significantly improve the signal-to-noise ratio and to obtain a clear picture of the flows in the average supergranule. We found near-surface divergent horizontal flows which quickly and monotonously weakened with depth; they became particularly weak at the depth of about 7 Mm, where they even apparently switched sign. To learn about the vertical component, we integrated the continuity equation from the surface. The derived estimates of the vertical flow depicted a sub-surface increase from about 5 m/s at the surface to about 35 m/s at the depth of about 3 Mm followed by a monotonous decrease to greater depths. The vertical flow remained positive (an upflow) and became indistinguishable from the background at the depth of about 15 Mm. We further detected a systematic flow in the longitudinal direction. The course of this systematic flow with depth agrees well with the model of the solar rotation in the sub-surface layers.