Transverse Gradients of Longitudinal Magnetic Field in Active Regions with Different Levels of Flare Productivity. I. Calculation Methods and Dynamics of Selected Parameters

This paper is a study of the dynamics of the parameters describing the transverse component of the gradient of the longitudinal magnetic field ∇_⊥ B_z in active regions (AR) with different levels of flare productivity. Data obtained by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) has been used to analyze 75 ARs in the 24-th cycle of solar activity. ∇_⊥ B_z has been calculated using two approaches, modern and classical. In each case the parameters describing the quantity ∇_⊥ B_z in the AR are determined. For the modern approach, this includes the average of ∇_⊥ B_z over the AR, <∇_⊥ B_z> and the average value of ∇_⊥ B_z in the neighborhood of the point with its maximum value, <max ∇_⊥ B_z>; for the classical approach, the maximum value of ∇_⊥ B_z between pairs of spots in the AR, <max ∇_⊥ B_z>. The dynamics of the chosen parameters are studied over the time of monitoring each of the regions of the analyzed sample. It is shown that: 1. the spread in values of ∇_⊥ B_z is small (for the overwhelming majority of studied regions it lies within a range of 0.08-0.12 G·km^-1) and differs little for regions with low and high flare activity. 2. The numerical values of the parameter max(∇_⊥ B_z) and its dynamics in the overwhelming majority of examined cases are greater in regions with a higher level of flare activity. 3. The numerical values of the parameter max(∇_⊥ B_z) and its dynamics are greater in regions with higher levels of flare activity. 4. In the AR NOAA 11283 a stable rise in the magnitude of max (∇_⊥ B_z)_sp was detected for approximately 19 h before the development of the first of a series of flares in high x-ray classes.