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, Delta t(2), of nearly constant R(t) covering one or several local maxima. The magnitude of R(t) averaged over Delta t(2) 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) x 10(20) Mx hour(-1) for ARs with a maximum total unsigned flux of (0.5-3) x 10(22) Mx. The normalized flux growth rate, RN, 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 Delta t(2) and a high (> 0.024 hour(-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 Delta t(2) and a low R-N (< 0.024 hour(-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.