Flaring Rates and the Evolution of Sunspot Group McIntosh Classifications

Abstract

Sunspot groups are the main source of solar flares, with the energy to power them being supplied by magnetic-field evolution (e.g. flux emergence or twisting/shearing). To date, few studies have investigated the statistical relation between sunspot-group evolution and flaring, with none considering evolution in the McIntosh classification scheme. Here we present a statistical analysis of sunspot groups from Solar Cycle 22, focusing on 24-hour changes in the three McIntosh classification components. Evolution-dependent $\ge \mathrm{C}1.0$, $\ge \mathrm{M}1.0$, and $\ge \mathrm{X}1.0$ flaring rates are calculated, leading to the following results: i) flaring rates become increasingly higher for greater degrees of upward evolution through the McIntosh classes, with the opposite found for downward evolution; ii) the highest flaring rates are found for upward evolution from larger, more complex, classes (e.g. Zurich D- and E-classes evolving upward to F-class produce $\ge \mathrm{C}1.0$ rates of $2.66\pm 0.28$ and $2.31 \pm 0.09$ flares per 24 hours, respectively); iii) increasingly complex classes give higher rates for all flare magnitudes, even when sunspot groups do not evolve over 24 hours. These results support the hypothesis that injection of magnetic energy by flux emergence (i.e. increasing in Zurich or compactness classes) leads to a higher frequency and magnitude of flaring.

Appendices

Appendix A: Zurich Class

Here we present accompanying tables and figures for the McIntosh Zurich class analysis. Evolution-dependent occurrence numbers and flaring rates of sunspot groups within $\pm75^{\circ}$ longitude are provided in Tables 4 and 5, respectively. These data correspond directly to that presented in Figures 2 and 3, respectively. In addition, evolution-dependent flaring rates for the east and west limb regions (i.e. $>75^{\circ}$ heliographic longitude) are displayed in Figures 4 and 5, respectively, for direct comparison to the “within $\pm75^{\circ}$ longitude” case presented in Figure 3.

Figure 4

Zurich evolution-dependent 24-hour flaring rates from groups at the east limb. Each column concerns different flaring levels: $\ge\mathrm{C}1.0$ (left); $\ge\mathrm{M}1.0$ (centre); $\ge\mathrm{X}1.0$ (right). As in Figure 2, each row shows evolution from a different starting class and histogram bars are coloured by evolution: no change (black); upward evolution (red); downward evolution (blue).

Figure 5

Zurich evolution-dependent 24-hour flaring rates from groups at the west limb. Each column concerns different flaring levels: $\ge\mathrm{C}1.0$ (left); $\ge\mathrm{M}1.0$ (centre); $\ge\mathrm{X}1.0$ (right). As in Figure 2, each row shows evolution from a different starting class and histogram bars are coloured by evolution: no change (black); upward evolution (red); downward evolution (blue).

Table 4 Evolution-dependent McIntosh modified Zurich class occurrence numbers of sunspot groups within $\pm75^{\circ}$ heliographic longitude.

Table 5 Evolution-dependent McIntosh modified Zurich class flaring rates of sunspot groups within $\pm75^{\circ}$ heliographic longitude.

Appendix B: Penumbral Class

Here we present equivalent tables and figures for the McIntosh penumbral class analysis. Frequency histograms of each penumbral class are shown in the left column of Figure 6, while overall evolution steps on a 24-hour timescale are given in the right column of Figure 6 as percentage occurrence. Evolution-dependent occurrence numbers are provided in Table 6 and graphically represented in Figure 7 (equivalent to the Zurich class Table 4 and Figure 2, respectively). Finally, flaring rates of sunspot groups within $\pm75^{\circ}$ longitude are provided in Table 7 and graphically represented in Figure 8 (equivalent to the Zurich class Table 5 and Figure 3, respectively).

Figure 6

Frequency histograms of each penumbral class in the McIntosh classification scheme (left column) and occurrence percentage histograms of their overall evolution steps on 24-hour timescales (right column). Each row presents data from different spatial locations on the Sun: full disk (panels a – b); within $\pm75^{\circ}$ heliographic longitude (panels c – d); east limb (panels e – f); west limb (panels g – h). Positive evolution steps correspond to moving downwards through penumbral classes in Table 2.

Figure 7

Penumbral class 24-hour evolution histograms. Each column concerns different locations on the Sun: within $\pm75^{\circ}$ longitude (left); east limb (centre); west limb (right). Each row presents evolution from a different starting class, while bars give the percentage of that starting class coloured by evolution: no change (black); upward evolution (red); downward evolution (blue).

Figure 8

Penumbral evolution-dependent 24-hour flaring rates from groups within $\pm75^{\circ}$ longitude. Each column concerns different flaring levels: $\ge\mathrm{C}1.0$ (left); ⩾ M1.0 (centre); $\ge\mathrm{X}1.0$ (right). As in Figure 7, each row shows evolution from a different starting class and histogram bars are coloured by evolution: no change (black); upward evolution (red); downward evolution (blue).

Table 6 Evolution-dependent McIntosh penumbral class occurrence numbers of sunspot groups within $\pm75^{\circ}$ heliographic longitude.

Table 7 Evolution-dependent McIntosh penumbral class flaring rates of sunspot groups within $\pm75^{\circ}$ heliographic longitude.

Appendix C: Compactness Class

Here we present equivalent tables and figures for the McIntosh compactness class analysis. Frequency histograms of each compactness class are shown in the left column of Figure 9, while overall evolution steps on a 24-hour timescale are given in the right column of Figure 9 as percentage occurrence. Evolution-dependent occurrence numbers are provided in Table 8 and graphically represented in Figure 10 (equivalent to the Zurich class Table 4 and Figure 2, respectively). Finally, flaring rates of sunspot groups within $\pm75^{\circ}$ longitude are provided in Table 9 and graphically represented in Figure 11 (equivalent to the Zurich class Table 5 and Figure 3, respectively).

Figure 9

Frequency histograms of each compactness class in the McIntosh classification scheme (left column) and occurrence percentage histograms of their overall evolution steps on 24-hour timescales (right column). Each row presents data from different spatial locations on the Sun: full disk (panels a – b); within $\pm75^{\circ}$ heliographic longitude (panels c – d); east limb (panels e – f); west limb (panels g – h). Positive evolution steps correspond to moving downwards through compactness classes in Table 3.

Figure 10

Compactness class 24-hour evolution histograms. Each column concerns different locations on the Sun: within $\pm75^{\circ}$ longitude (left); east limb (centre); west limb (right). Each row presents evolution from a different starting class, while bars give the percentage of that starting class coloured by evolution: no change (black); upward evolution (red); downward evolution (blue).

Figure 11

Compactness evolution-dependent 24-hour flaring rates from groups within $\pm75^{\circ}$ longitude. Each column concerns different flaring levels: $\ge\mathrm{C}1.0$ (left); $\ge\mathrm{M}1.0$ (centre); $\ge\mathrm{X}1.0$ (right). As in Figure 10, each row shows evolution from a different starting class and histogram bars are coloured by evolution: no change (black); upward evolution (red); downward evolution (blue).

Table 8 Evolution-dependent McIntosh compactness class occurrence numbers of sunspot groups within $\pm75^{\circ}$ heliographic longitude.

Table 9 Evolution-dependent McIntosh compactness class flaring rates of sunspot groups within $\pm75^{\circ}$ heliographic longitude.