# Analysis of the flux growth rate in emerging active regions on the Sun

## TL;DR

This study analyzes the flux growth rate in 42 emerging active regions on the Sun, identifying two distinct emergence behaviors and their relation to flux tube dynamics, using magnetogram data from SDO/HMI.

## Contribution

It introduces a method to classify active region emergence into rapid and gradual types based on flux growth rates and emergence durations, revealing different underlying physical processes.

## Key findings

- Rapid emergence involves a short, high flux growth rate with a two-step process.
- Gradual emergence features a longer duration and possibly multiple flux tubes rising sequentially.
- Power law relationships differ between the two emergence subsets.

## Abstract

We studied the emergence process of 42 active region (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, dt_2, of nearly-constant R(t) covering one or several local maxima. The averaged over dt_2 magnitude of R(t) was accepted as an estimate of the maximal value of the flux growth rate, R_MAX, which varies in a range of (0.5-5)x10^20 Mx hour^-1 for active regions with the maximal total unsigned flux of (0.5-3)x10^22 Mx. The normalized flux growth rate, R_N, was defined under an assumption that the saturated total unsigned flux, F_MAX, equals unity. Out of 42 ARs in our initial list, 36 event were successfully fitted and they form two subsets (with a small overlap of 8 events): the ARs with a short (<13 hours) interval dt_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 dt_2 and a low R_N (<0.024 hour^-1). In diagrams of R_MAX plotted versus F_MAX, the events from different subsets are not overlapped 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.