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 t 2 , of nearly constant R ( t ) covering one or several local maxima. The magnitude of R ( t ) averaged over Δ 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 ) × 10 20 Mx hour − 1 for ARs with a maximum total unsigned flux of ( 0.5 – 3 ) × 10 22 Mx . 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 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 Δ 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.