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 del(perpendicular to) 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. del(perpendicular to) B-z has been calculated using two approaches, modern and classical. In each case the parameters describing the quantity del(perpendicular to) B-z in the AR are determined. For the modern approach, this includes the average of del(perpendicular to) B-z over the AR, <del(perpendicular to) B-z> and the average value of del(perpendicular to) B-z in the neighborhood of the point with its maximum value, <max del(perpendicular to) B-z>; for the classical approach, the maximum value of del(perpendicular to) B-z between pairs of spots in the AR, <max del(perpendicular to) 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 del(perpendicular to) B-z is small (for the overwhelming majority of studied regions it lies within a range of 0.08-0.12 G<middle dot>km(-1)) and differs little for regions with low and high flare activity. 2. The numerical values of the parameter max(del(perpendicular to) 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(del(perpendicular to) 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 (del(perpendicular to) 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.