A Simon–Weiss model for supergranule flows and their cross-correlations

Abstract

Supergranule revolution rate and lifetime can be measured by cross-correlating pairs of Doppler-velocity maps that have been filtered (by Hathaway's method) to remove other flows. As a conceptual framework for that analysis, this exploratory paper develops an idealized, phenomenological model of supergranule flows. Assumptions made about supergranule cells on the Sun's photosphere include: random location in space and time, and horizontal flows with circular symmetry and having a Simon–Weiss velocity function. Each supergranule is stable for a time, dies, and after a while, a daughter is born at a nearby position determined by a random walk. The effect on the cross-correlations of changing projection onto the line-of-sight as the Sun rotates is analyzed. The total cross-correlation for strips of constant latitude depends on two generic, slowly-varying projection functions. Effects of differential rotation and time-evolution are also considered. GONG observations of June 1994 show systematic variations in the width and shape of correlation peaks with latitude; our model suggests that projection effects alone can account for these without invoking any intrinsic variations of the supergranules.