Panel a: two-dimensional histogram of Δ ϕ, extracted from all plage locations. The white contours show a fitted 2D Gaussian on the 2D Δϕ histogram. The histogram reveals that shorter periods have positive phase difference, while longer periods move into the negative phase difference regime. With the help of a 2D Gaussian, the peak phase difference was estimated for each period. Panel b: distribution of phase difference at the period of 4.35 min. Panel c: phase difference as a function of period. A vertical dashed line in panel b indicates the position of peak phase difference. A dashed horizontal line in panel c indicates zero phase difference.