A transverse component of the longitudinal magnetic field gradient in active regions with different levels of flare productivity: different approaches to calculating, dynamics and probable critical values
The study aims to analyze the value and dynamics of the transverse component of the longitudinal magnetic field gradient in active regions (ARs) with different levels of flare productivity. We used magnetographic data from the Helioseismic and Magnetic Imager (HMI) instrument aboard the Solar Dynamics Observatory (SDO) of the spatial distribution of the Bz component of the magnetic field vector at the solar photosphere level. Thirteen ARs were selected for analysis: 6 ARs with low activity and 7 ARs with high activity; two of them are regions with an additional increase of the magnetic flux. Monitoring of each of the ARs was carried out for 3-5 days within 30-35 heliographic degrees relative to the central meridian. Two approaches to calculating the longitudinal magnetic field gradient are considered: modern, requiring the magnetographic data of high spatial resolution, and classical. For each approach, the parameters characterizing the longitudinal magnetic field gradient in the AR were determined. For the modern approach, this is the average value of the transverse component of the longitudinal magnetic field gradient  over the AR; for the classical approach, this is the maximum value of the transverse component of the longitudinal magnetic field gradient for a set of the pairs of spots in the AR (max(∇⊥Bz)). The dynamics of the chosen parameters was compared with the level of AR flare productivity. It is shown that: (1) There are threshold values of the parameters that describe the longitudinal magnetic field gradient of the AR. For the quantity , the critical value is 0.08 G km-1, and for the parameter max(∇⊥Bz) it is 0.115 G km-1. (2) The first powerful flares of M or above roentren classes are observed in the AR 23-25 hours after the above parameters exceed the corresponding critical values