INFERRING THE DEPTH EXTENT OF THE HORIZONTAL SUPERGRANULAR FLOW

The 2D horizontal velocity field determined from local correlation tracking of granulation and its divergence have remarkably different appearances. The 2D horizontal velocity shows the classical 32 Mm supergranular cellular outflow bounded by the chromospheric network, whereas the divergence is dominated by distinct long-lived sources and sinks of about 7 Mm size. The 2D horizontal velocity shows no obvious evidence for approximate to 7 Mm cells, and the divergence exhibits little power with the approximate to 32 Mm scale. However, by mass continuity for a steady 3D flow in a stratified atmosphere, the divergence of the 2D horizontal component is equal to the vertical velocity divided by a height scale. Thus the 3D steady solar flow field at the bottom of the photosphere has a vertical component consisting primarily of approximate to 7 Mm sources and sinks, which define the 2D cellular-like approximate to 32 Mm continuous horizontal outflows. Simultaneous Doppler vertical velocity measurements verify the mass-continuity relation, and give a height scale equal to the density scale height in the photosphere within observational error. The observational result is consistent with our theoretical expectation. Any height scale other than the density scale height would indicate a vertical velocity that e-folds on a scale comparable to or smaller than the density scale height, which we argue is unphysical near the top of the convection zone. The continuity relation indicates that vortex-free steady horizontal velocities seen at the solar surface, i.e., the horizontal supergranular flow, must diminish with depth due to the increasing density scale height. We estimate that the horizontal supergranular flow cannot extend much more than one e-fold increase in the density scale height below the visible solar surface, about 2.4 Mm. Therefore the convection below the solar surface should be characterized by the scale of the principal steady vertical velocity component, i.e., by vertical plumes having a dimension of approximate to 7 Mm - what we have called 'mesogranulation' - rather than closed approximate to 32 Mm cells as is widely believed.