Population of Bright Plume Threads in Solar Polar Coronal Holes

Abstract

Coronal holes are well accepted to be source regions of the fast solar wind. As one of the common structures in coronal holes, coronal plumes might contribute to the origin of the nascent solar wind. To estimate the contribution of coronal plumes to the nascent solar wind, we make the first attempt to estimate their populations in the solar polar coronal holes. By comparing the observations viewed from two different angles taken by the twin satellites of STEREO and the results of Monte Carlo simulations, we estimate about 16 – 27 plumes rooted in an area of $4\times 10^{4}~\text{arcsec}^{2}$ of the polar coronal holes near the solar minimum, which occupy about 2 – 3.4% of the area. Based on these values, the contribution of coronal plumes to the nascent solar wind has also been discussed. A further investigation indicates that a more precise number of coronal plumes can be worked out with observations from three or more viewing angles.

Appendix: A Test to The Method

In order to test the method as described in Section 2, we apply it on a set of artificial data based on that 10 plumes (each has a size of a pixel) root in an area of $40~\text{pixels}\times 40~\text{pixels}$. In Figure 9, we show the IVCs at a set of viewing angles. We can see that in this case the local peaks in the IVCs are sparse, and this is similar to those determined from observations (as shown in Figure 3). In Figure 10, we show the histograms of the distributions of the correlation coefficients derived from the Monte Carlo simulations of these artificial data. We can see that the distributions based on two viewing angles (black curves in Figure 10) show clear dominant peaks near the right number. The numbers of plumes indicated by these dominant peaks are from 10 to 12, except the case based on $0^{\circ}$ and $30^{ \circ }$. Although the histogram of the case of $0^{\circ }$ and $30^{ \circ }$ has dominant peak at the guessed plume number of 18, the distribution around the plume number of 10 still appears to be larger than the rest in general. Therefore, one can have a good estimation of the number of plumes based on the histograms of the number of hits based on two viewing angles within an error of about 20%. If we increase the correlation coefficient threshold to $3\sigma$, we can see that very few (even none) hits can be obtained (see the red curves in Figure 10). It appears that one cannot get a better estimation of the plume number based on this threshold than that from $2\sigma$.

Figure 9

The intensity variation curves of the artificial data with 10 plumes in a region of $40~\text{pixels}\times 40~\text{pixels}$ viewed at $0^{\circ }$ (a), $30^{\circ }$ (b), $60^{\circ }$ (c), $90^{\circ }$ (d), $120^{\circ }$ (e) and $150^{\circ }$ (f).

Figure 10

Histograms of number of hits at various guessed number of plumes given in the Monte Carlo simulation based on the artificial data with 10 plumes (see Figure 9). Black curves are obtained from two viewing angles and a correlation coefficient threshold of $2\sigma$ (a: $0^{\circ }$ & $30^{\circ }$; b: $0^{\circ }$ & $60^{ \circ }$; c: $0^{\circ }$ & $90^{\circ }$; d: $0^{\circ }$ & $120^{ \circ }$; e: $0^{\circ }$ & $150^{\circ }$; f: $60^{\circ }$ & $120^{ \circ }$). Red curves are based on two viewing angles as same as those used in the black curves but with a correlation coefficient threshold of $3\sigma$. (Red curves are not shown in panel b because none has satisfied the threshold.) Orange curves are obtained from three viewing angles and a correlation coefficient threshold of $2\sigma$ (a: $0^{\circ }$, $30^{ \circ }$ & $60^{\circ }$; b: $0^{\circ }$, $60^{\circ }$ & $90^{ \circ }$; c: $0^{\circ }$, $30^{\circ }$ & $90^{\circ }$; d: $0^{ \circ }$, $30^{\circ }$ & $120^{\circ }$; e: $0^{\circ }$, $30^{ \circ }$ & $150^{\circ }$; f: $0^{\circ }$, $60^{\circ }$ & $120^{ \circ }$).

While we include additional data from a third viewing angle, we found that the histograms of the number of hits using a threshold of $2\sigma$ distribute at a few isolated numbers including one really close to the correct one (see the orange curves in Figure 10). Although this does not work out the exact answer, it gives a much better chance if one has to give a guess. If we are increasing the threshold further, the data from three viewing angles can derive a unique number that is very close to the answer at some point. However, we fail to find a universal threshold for all, and that seems to be different from case to case.