Empirical Scaling Relations for the Photospheric Magnetic Elements of the Flaring and Non-Flaring Active Regions

Here, we analyze magnetic elements of the solar active regions (ARs) observed in the line-of sight magnetograms (the 6173 angstrom FeI line) recorded with the Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI). The Yet Another Feature Tracking Algorithm (YAFTA) was employed to analyze the statistical properties of these features (e.g., filling factor, magnetic flux, and lifetime). Magnetic features were extracted from the areas of 180 '' x 180 '' inside the flaring AR (NOAA 12443) for November 3-5, 2015 and non-flaring AR (NOAA 12446) for November 4-6, 2015. The mean filling factor of polarities was found to be about 0.49 for the flaring AR, while this value was 0.08 for the non-flaring AR. Time series of the filling factors of the negative and positive polarities for the flaring AR showed anti-correlated behavior (with the Pearson value of -0.80 ). However, there was a strong positive correlation (with the Pearson value of 0.95) for the non-flaring AR. A power-law function was fitted to the frequency distributions of flux (F ), size (S), and lifetime (T ). Power exponents of the distributions of flux, size, and lifetime for the flaring AR were found to be -2.36 +/- 0.27 , -3.11 +/- 0.17, and -1.70 +/- 0.29, respectively, while for the non-flaring AR: -2.53 +/- 0.20 , -3.42 +/- 0.21, and -1.61 +/- 0.19, respectively. The code detected a magnetic element with the maximum flux of 23.54 x 10(20) Mx. The maximum size of detected patches was found to be about 300 Mm(2). The most long-lived patch in the flaring AR belonged to an element with a lifetime of 2208 min. We showed that S, F , and T for patches in the flaring AR follow empirical scaling relations: S proportional to F-0.66 +/- 0.01 , F proportional to T-0.48 +/- 0.04 , and S proportional to T-0.32 +/- 0.02 , respectively. For patches in the non-flaring AR, we obtained S proportional to F-0.64 +/- 0.02 , F proportional to T-0.37 +/- 0.06 , and S proportional to T-0.23 +/- 0.03 , respectively. The comparisons indicated that correlations between parameters of F and T , and also, S and T for the flaring AR, are larger than those of the non-flaring AR. The scaling law relation between the flux growth rate of positive polarities and their size indicates a strong correlation of more than 0.7 in both ARs.