Analysis of the Flux Growth Rate in Emerging Active Regions on the Sun

We studied the emergence process of 42 active regions (ARs) by analyzing the time derivative, R(t) , of the total unsigned flux. Line-of-sight magnetograms acquired by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) were used. A continuous piecewise linear fitting to the R(t) -profile was applied to detect an interval, Δ t₂, of nearly constant R(t) covering one or several local maxima. The magnitude of R(t) averaged over Δ t₂ was accepted as an estimate of the maximum value of the flux growth rate, R_MAX, which varies in a range of (0.5–5)×1020Mxhour−1 for ARs with a maximum total unsigned flux of (0.5–3)×1022Mx. The normalized flux growth rate, R_N, was defined under the assumption that the saturated total unsigned flux, F_MAX, equals unity. Out of 42 ARs in our initial list, 36 events were successfully fitted, and they form two subsets (with a small overlap of eight events): the ARs with a short (< 13 hours) interval Δ t₂ and a high (>0.024hour−1) normalized flux emergence rate, R_N, form the “rapid” emergence event subset. The second subset consists of “gradual” emergence events, and it is characterized by a long (> 13 hours) interval Δ t₂ and a low R_N (<0.024hour−1). In diagrams of R_MAX plotted versus F_MAX, the events from different subsets do not overlap, and each subset displays an individual power law. The power-law index derived from the entire ensemble of 36 events is 0.69 ± 0.10. The rapid emergence is consistent with a two-step emergence process of a single twisted flux tube. The gradual emergence is possibly related to a consecutive rising of several flux tubes emerging at nearly the same location in the photosphere.