Association of Plages with Sunspots: A Multi-Wavelength Study Using Kodaikanal Ca ii K and Greenwich Sunspot Area Data

We generate the yearly averaged data from the daily plage observations and plot them (black solid line) in panel (a) of Figure 1 along with the sunspot area data (red solid line). Since we are interested in the association of the two structures, we plot the normalized values of the yearly averaged data. From the figure we readily see that the two time series show a good match with each other. Every feature, including the double peaks seen in the sunspot data, is also present in the plage area time series. To estimate this association quantitatively we plot the scatter diagram as shown in panel (b) of Figure 1. A correlation coefficient of 0.97 again confirms the close association of these two solar features, which have formed in two different layers in the solar atmosphere. However, we must emphasize that this high correlation in the yearly data does not imply the same for shorter timescales (months or days). This is because when a sunspot decays away, the remnant small magnetic field may still continue to show itself as a plage in the higher atmosphere. Also, small-scale magnetic fields, which survive for a few days or less, do not always develop as a sunspot.

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Now the hemispheric asymmetry in sunspot area is a well known phenomenon. We investigate the same from the plage area time series by computing the yearly data separately for the two hemispheres. Panels (c) and (d) in Figure 1 show the yearly averaged plage area data in the northern and southern hemispheres (plotted as red and green solid lines) respectively. The sunspot area data for the corresponding hemispheres are also plotted in the panels as black dotted lines. The hemispheric plage area series show a very good match with the sunspot area data. Similar to the sunspots, in this case too we find that the double peaks near the cycle maximum are not a persistent feature in both hemispheres. For example, the 16th cycle is double-peaked (see Figure 1(a)) but from Figures 1(c) and (d) we see that in this case only northern hemisphere shows a double-peak signature. In the case of the 19th cycle, no such double peak is seen in the overall case but both hemispheres have prominent double-peak signatures.

Next we compute the normalized asymmetry coefficient, defined as (A_pn − A_ps)/(A_pn + A_ps), as a measure of the hemispheric asymmetry in the plage area (A_pn and A_ps are the yearly averaged values of plage area in the northern and southern hemispheres). The evolution of this asymmetry coefficient is plotted in panel (a) of Figure 2. There are quite a few distinct features readily noticeable from the plot. During the minima of cycles 14, 15, and 16, we see that the northern hemisphere dominates whereas for the later cycles, i.e., cycles 17–19, the southern hemisphere dominates. This behavior is highlighted in the plot (Figure 2(a)) by using red arrows. It is also interesting to note that during the progression of a cycle the asymmetry coefficient changes its sign quite a few times, and this does not show any meaningful correlation with the cycle amplitude or any other property of that particular cycle. We also notice that on average the northern hemisphere dominates over the southern for the six cycles analyzed here. We revisit this dominance of the northern hemisphere in the following section.

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Since we are interested in the plage–sunspot association, we look for the same in the asymmetry coefficient also. In panel (b) in Figure 2 we plot a scatter diagram between the asymmetry coefficients obtained from hemispheric plage area and the same computed for sunspot area. We find a very good match between these two coefficients with a correlation value of 0.90. However, we also found some outliers, which probably have occurred during the cycle minima, when the asymmetry coefficient is prone to large departures.

3.2.1. Size Distribution

Individual values of plage area are considered for the analysis of the size distribution. In panel (a) of Figure 3 we show the plage area (size) distribution for the whole time period, i.e., from 1907 to 1965. The distribution pattern looks similar to an exponentially decaying function. We fit the histogram with a decaying exponential function of the form, $Y={A}_{0}{\exp }^{-(\tfrac{X}{B})}$, as shown by the red dashed line in Figure 3(a). From the fit we notice that the initial part of the histogram is fit well but the fitted function drops very rapidly in the wing and leaves a large deviation around that region.

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To get a better fit, we consider the log-normal function next. This is inspired by the fact the sunspots are known to have a log-normal size distribution (Bogdan et al. 1988; Baumann & Solanki 2005; Mandal et al. 2017). Thus a log-normal function of the form

$$\begin{eqnarray*}&&y=\displaystyle \frac{1}{\sqrt{2\pi }\sigma x}\exp \left(-\displaystyle \frac{{[\mathrm{ln}(x)-\mu ]}^{2}}{2{\sigma }^{2}}\right)\end{eqnarray*}$$

is considered and fitted to the histogram as shown by the black dotted curve in Figure 3(a). In this case we notice that the full histogram along with the tail is fit very well. Thus the individual size distribution of the plages also follows the same "log-normal distribution" as we find for the sunspots. Here we must highlight the fact that the good match of the two functions (exponential and log-normal) at the core of the histogram (near to the origin, 1 arcmin²) is due to the use of a rigid cutoff of 1 arcmin² as the minimum detectable plage area. Thus the initial increment of the log-normal distribution has been suppressed and the function decays exponentially thereafter.

3.2.2. Latitudinal Distribution

Plages may be or may not be always associated with a sunspot for the reasons mentioned in Section 3.1. To investigate this, we divide the plages into four classes according to their individual sizes (A_p) and make use of the "butterfly diagram" for our further analysis. In different panels in Figure 4 we plot the time–latitude diagram for the individually detected plages with black circles whereas the green circles represent the locations of the sunspots. In the first size class (where A_p ≥ 1 arcmin²), we notice that there are a substantially large number of plages that do not have any sunspots associated with them. Also we notice that at the end of every cycle (or perhaps from the next cycle, due to the overlapping period) a large number of plages appear at high latitudes (≈60°), and this is much more prominent in the southern hemisphere.

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Now as we progressively go toward higher size thresholds (A_p ≥ 2 arcmin², A_p ≥ 3 arcmin², A_p ≥ 4 arcmin²) we see that the two butterfly diagrams (one for the sunspots and the other for the plages) show a progressively better match with each other. Thus, we conclude that the latitudinal locations of the plages with an area ≥4 arcmin² show a very good match with the sunspot latitudes.

A latitudinal match does not necessarily imply a one-to-one correspondence between the two. This is because these features can be at same latitudes but at different longitudes, implying that the two are not connected at all. To better establish the association of plage sizes with the sunspot locations, we plot the longitudinal scatter diagrams for every plage size range as shown in the side panels in Figure 4. We record the area-weighted average longitudes for both the plages and the sunspots during simultaneous observing days. A careful analysis reveals that the scatter plots between the plage and sunspot longitudes become progressively more linear as we consider greater plage areas. Thus, in combination with our previous results from analysis of the "butterfly diagram," we conclude that plages with area ≥4 arcmin² have a better one-to-one correspondence with the sunspot locations. We must again remind the reader that the decay of a sunspot does not necessarily mean the disappearance of the associated plage.

Various long-term and short-term properties of the sunspot cycle show a strong size dependence (Mandal & Banerjee 2016). Inspired by the findings of the dependence of plage size on the plage–sunspot association in the previous section, we look for different signatures in the cycle properties when the plages are considered according to their sizes. In panel (a) of Figure 5 we plot the "no thresholding" case, and in panels (b)–(d) we plot the yearly averaged variations in plage area for different size thresholds.

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For the smallest plages (1 arcmin² ≤ A_p < 2 arcmin²) we do not see much difference from the overall cycle characteristics (as found in panel 5(a)), except for the double-peak behavior for certain cycles. For example, the double peaks of cycle 16 and cycle 18 become less prominent or weaker. Also the overall strength of the cycle does not change much for the smallest plage size range, i.e., the 19th cycle is still the strongest during the analyzed time span. The scenario almost remains the same for the medium plage size range (panel (c)). As we move toward the biggest plages (panel (d)), we notice that the double peaks near the cycle maxima appear for almost every cycle. This is consistent with the behavior of the biggest sunspots found by Mandal & Banerjee (2016). Apart from that we also note an interesting behavior, i.e., the presence of a weaker peak near the cycle minimum. This is highlighted in the panel by red arrows. The separation of this peak from the cycle maximum seems to reduce as we move from cycle 14 to cycle 19. This trend, however, is not prominently visible for the 19th cycle because we see a double peak late after the cycle maximum.

Next, we investigate the "odd–even rule" or the "G-O rule," which states that each odd-numbered cycle is stronger than the preceding even-numbered one (Gnevyshev & Ohl 1948). This is well established for the data on sunspot area and sunspot numbers. From Figure 5 we notice that this rule is also valid for plage area time series for all the size ranges. Still, it should be mentioned here that the relative heights of the cycles change slightly when one considers different size ranges (panels (b)–(d) of Figure 5).