Active Region Photospheric Magnetic Properties Derived from Line-of-Sight and Radial Fields

Abstract

The effect of using two representations of the normal-to-surface magnetic field to calculate photospheric measures that are related to the active region (AR) potential for flaring is presented. Several AR properties were computed using line-of-sight ($B_{\mathrm{los}}$) and spherical-radial ($B_{r}$) magnetograms from the Space-weather HMI Active Region Patch (SHARP) products of the Solar Dynamics Observatory, characterizing the presence and features of magnetic polarity inversion lines, fractality, and magnetic connectivity of the AR photospheric field. The data analyzed correspond to ${\approx\,}4{,}000$ AR observations, achieved by randomly selecting 25% of days between September 2012 and May 2016 for analysis at 6-hr cadence. Results from this statistical study include: i) the $B_{r}$ component results in a slight upwards shift of property values in a manner consistent with a field-strength underestimation by the $B_{\mathrm{los}}$ component; ii) using the $B_{r}$ component results in significantly lower inter-property correlation in one-third of the cases, implying more independent information as regards the state of the AR photospheric magnetic field; iii) flaring rates for each property vary between the field components in a manner consistent with the differences in property-value ranges resulting from the components; iv) flaring rates generally increase for higher values of properties, except the Fourier spectral power index that has flare rates peaking around a value of $5/3$. These findings indicate that there may be advantages in using $B_{r}$ rather than $B_{\mathrm{los}}$ in calculating flare-related AR magnetic properties, especially for regions located far from central meridian.

Appendix: Correlation Coefficients

Tables 2 and 3 each contain values of linear (Pearson) and nonlinear-rank (Spearman) correlation coefficients (CC) for all AR property-pair combinations for $B_{\mathrm{los}}$ and $B_{r}$, respectively. The coefficients are calculated separately for the three groups of SHARP longitudes with data points colour-coded in Figures 6 and 7: $|\phi| < 60^{\circ}$ (black); $60 \leqslant|\phi| < 75^{\circ}$ (blue); $|\phi| \geqslant 75^{\circ}$ (red). Figure 8 presents the errors for correlation coefficients contained in Tables 2 and 3. In both panels, plots of standard error versus CC value for linear (filled circles) and nonlinear (open circles) correlations in all three longitudinal-position groups (same colour code applies). The left panel corresponds to $B_{\mathrm{los}}$-calculated properties and the right panel corresponds to $B_{r}$-calculated properties. The standard error for a (linear/nonlinear) correlation coefficient is estimated as

$$ \mathrm{SE}_{r} = \sqrt{\frac{1-r^{2}}{n-2}}; $$

(5)

where $r$ can be the Pearson or the Spearman CC, and $n$ is the number of points used in their calculations. The dotted lines in the plots of Figure 8 mark ranges for expressing the standard errors in percentage of the CC value.

Figure 8

Error analysis for correlation coefficients displayed in Tables 2 and 3. The left and right panels correspond to property-pair (linear and nonlinear) correlations calculated from $B_{\mathrm{los}}$ and $B_{r}$, correspondingly. The colour code corresponds to Figure 6.