Areas of Polar Coronal Holes from 1996 Through 2010

Abstract

Polar coronal holes (PCHs) trace the magnetic variability of the Sun throughout the solar cycle. Their size and evolution have been studied as proxies for the global magnetic field. We present measurements of the PCH areas from 1996 through 2010, derived from an updated perimeter-tracing method and two synoptic-map methods. The perimeter-tracing method detects PCH boundaries along the solar limb, using full-disk images from the SOlar and Heliospheric Observatory/Extreme ultraviolet Imaging Telescope (SOHO/EIT). One synoptic-map method uses the line-of-sight magnetic field from the SOHO/Michelson Doppler Imager (MDI) to determine the unipolarity boundaries near the poles. The other method applies thresholding techniques to synoptic maps created from EUV image data from EIT. The results from all three methods suggest that the solar maxima and minima of the two hemispheres are out of phase. The maximum PCH area, averaged over the methods in each hemisphere, is approximately 6 % during both solar minima spanned by the data (between Solar Cycles 22/23 and 23/24). The northern PCH area began a declining trend in 2010, suggesting a downturn toward the maximum of Solar Cycle 24 in that hemisphere, while the southern hole remained large throughout 2010.

Appendix: Periodicity

PCH areas from both of the EIT image analyses have an annual periodicity in the area results, caused by the yearly variations in the B ₀-angle. Additional analysis was made in the PT algorithm in an effort to reduce these fluctuations in the area results. The strongest concern regarding the periodicity was that it appeared when using the PT method, which was designed to remove the effects of B ₀ from the data.

The fluctuations follow the annual variation of the B ₀-angle: the pole tilted toward Earth has the larger area. A change from a polar-cap area of 5 % to 2 % (see Figures 1 and 3) implies a change in the limiting latitude from 64^∘ to 74^∘. This represents almost all of the possible 14^∘ change in B ₀.

In an effort to understand the source of the periodicity, we first verified the orbital information of the SOHO spacecraft. Next, several simple explanations were investigated, but none were able to explain the variation. We also applied new filtering techniques to automate the removal of false detections from our area analysis, which we suspected were contributing to the periodicity. These filters improved the accuracy of our results, but were ultimately unsuccessful in removing the annual fluctuations.

The various investigations and filtering techniques are discussed here. We first discuss some geometric effects in the images in Section A.1 and then address a change in our working coordinate system in Section A.2. Section A.3 describes the role of the B ₀-angle in the longitudinal-coordinate calculations. Last, Section A.4 discusses the new false-detection filtering techniques that were applied to the PT analysis.

1.1 A.1 Investigation 1: Geometric Effects

1.1.1 A.1.1 The Wall Effect

As an equatorial coronal hole rotates into view on the limb, its leading edge is obscured by the coronal material along the LOS and then revealed as the coronal hole passes the central meridian (Timothy, Krieger, and Vaiana 1975). We have modified their consideration of this “wall effect” for polar latitudes, including the variation in the B ₀-angle, which causes an annual modulation in the measured area not seen in the equatorial case.

For polar latitudes, the wall effect can be quantified by assuming that the coronal material is a sharp edge, one scale height [H] higher than the actual solar radius [R], perpendicular to the surface of the Sun. As the solar B ₀-angle increases (decreases), the LOS angle through the coronal material also increases (decreases), and H subsequently obscured more (less) to the observer. The net effect is that an external observer views a higher latitude point than the actual boundary latitude of the PCH. Adding the B ₀ and wall effects, the relationship between the actual boundary latitude [θ] and the observed latitude [θ′] becomes

$$ \sin \bigl( \theta' + B_{0} \bigr) = {R\over{R + H}} \sin ( \theta+ B_{0} ), $$

(3)

yielding a calculated area of

$$ A = \bigl(1 - \sin\theta' \bigr)/2, $$

(4)

which is always smaller than the actual area of (1−sinθ)/2.

The observed periodicity cannot be produced by the wall effect described here, where the coronal material blocks some of the area, because the limb and central-meridian sampling show the same effect. Moreover, the wall effect decreases as the area increases, while the calculations show that the amplitude increases with the area.

1.1.2 A.1.2 Rotation Axis

An error in the assumed position of the rotation axis at the surface of the Sun could cause the observed fluctuations in both analyses. It might also affect the determination of the longitude near the limb more than the latitude. As shown by Beck and Giles (2005), the location of the Sun’s rotation axis is known well enough that this effect is too small to cause the observed fluctuations.

1.2 A.2 Investigation 2: Coordinates

We suspected that the use of the Carrington coordinate system might contribute a rotational beating effect when applied to the slower-rotating polar regions. Heliographic Carrington coordinates rotate at the mean solar rotation rate, not taking into account the differential rotation of the Sun. The heliographic Stonyhurst coordinate system is fixed with respect to the observer, while the Sun rotates beneath (Thompson 2006). We converted the PT code to use Stonyhurst coordinates to prevent potential issues caused by rotational beating. No significant difference was detected between the Carrington coordinate system and Stonyhurst coordinate system results.

1.3 A.3 Investigation 3: Opening Angle

We also computed the PCH areas using a technique in which we found the polar position of boundary points in each image, then averaged those opening angles over each HR to determine the area. Rather than fitting the measured boundary as a polygon, this algorithm assumes the PCH is a spherical cap with the average opening angle. This approach is faster, but at the cost of a loss of accuracy in the shape of the PCH. Figure 9 shows that the annual variation from B ₀ was still dominant using this simplified method when using coordinates measured from the data, despite trying to enforce its removal automatically. This confirms that the remaining B ₀-variation is embedded in the images, but does not clarify how it is manifested in the results.

Figure 9

The areas for the northern (blue) and southern (red) PCHs, found using a simplified polar-cap calculation of the PCH boundary extent for each HR. The longitudinal coordinate inputs were found by the PT algorithm. The areas are calculated using the arithmetically averaged opening angles over each HR. This method assumes that each PCH is a polar cap.

We expected that the B ₀-angle variations would have the largest effect on our calculated latitudes, but instead found a strong annual fluctuation in our calculated longitudes, in phase with the B ₀-variation, even when using Stonyhurst coordinates. The longitudinal separation of detected points fluctuated between −180^∘ and +180^∘ in an annual periodic cycle. This anomaly most likely occurred because the PCH boundaries are detected at the polar limb and the uncertainty in longitude at the limb increases as the lines of longitude converge toward the poles. Therefore, as the measured limb points approached a latitude of ±90^∘, the uncertainty of the measured longitude increased.

However, examining near the polar limb also helped us to understand at least part of the problem. Spherical symmetry allows us to assume that the detected limb points have a constant longitudinal separation of 180^∘. We assigned the Harvey Longitude of the central meridian [H ₀] at the date and time of the data ±90^∘ to the longitudes of the eastern and western limbs, respectively. It should be noted that the H ₀-parameter induces the progression of longitude in time so that the PT fits to the boundary points can still be calculated. By forcing the longitudinal points to a constant 180^∘ difference between east and west limb points, we saw a reduction in the amplitude of the annual variation, but it also reduced the solar-cycle change in the areas, as seen in Figures 9 and 10. This confirms that the B ₀-fluctuation plays an important role in determining longitude in polar regions. However, while this correction decreased the periodic amplitude, the fluctuation was not entirely removed, and it remains a significant concern.

Figure 10

The polar-cap areas of Figure 9, calculated with the arithmetically averaged opening angles over each HR and with the longitudes of the data replaced by a fixed longitudinal difference. The areas have lost much of the solar cycle trend, but the prominent annual periodicity has been reduced. These areas vary in time the same as the amplitude peaks in Figure 9, suggesting that the actual PCH areas are near the upper limit of the variation.

Even so, an important insight was revealed by this investigation. Note that the northern and southern curves in Figure 10 appear to track the peaks (not the averages) of their corresponding curves in Figure 9. Therefore, we conclude that a running average cannot be used to smooth the data without underestimating the PCH areas. We must consider the peak area values to be the best estimates of the actual PCH areas.

1.4 A.4 Investigation 4: PT Filters

1.4.1 A.4.3 Detection Confidence

After detecting the PCH-boundary points of each wavelength, we determined the “confidence” of the detections using the ratio of the total number of PCH-pixels around the limb in either hemisphere with the total number of limb points above the limiting latitude. This detection-confidence (DC) factor is a measure of the likelihood that each detection confines a PCH. For example, if boundary points are detected close together on the limb, there must be very few potential PCH pixels in the image, and the probability that a PCH exists within the two boundary points is reduced (see Figure 11). A low DC factor would be associated with the boundary points in this case. The larger the DC factor, the more likely that a PCH is enclosed between the two boundary points in that hemisphere. This factor reveals nothing about the accuracy of the detections (whether the detected points are good representations of the PCH boundary points); however, the accuracy of our PT-detection technique has been verified by the results of our two synoptic methods.

Figure 11

Illustration of why there is a higher detection-confidence (DC) factor for a PCH enclosed between two boundary points with a large opening angle (left) than there is if the detected points are close together (right). In both images, the polar region of the solar disk is shown in dark gray, with a black rim denoting the limb where there is a detected PCH and a white rim representing the limb-brightening outside the PCH. The light-gray regions outside of the limb represent the corona at some arbitrary scale height. The black dots on the limb depict detected boundary points of the PCH. The uncertainty of whether the detected points actually bound a PCH increases as the opening angle between the points decreases. Note that for wavelengths with smaller scale heights, such as 304 Å, chromospheric phenomena can also yield similar results in the detection uncertainty (e.g. bright spicules on the limb).

We investigated the evolution of the DC factor and noticed two distinct trends. First, the B ₀-fluctuations are embedded into the DC values because of the projection in the image. The DC factor is highest in either hemisphere when that pole is inclined toward Earth, as we expect from the projection effects. The B ₀ trend in the DC factor is lost within the detection noise during solar maximum. Second, the DC factor also distinguishes the solar-cycle trend in its magnitude. Outside of solar maximum, the DC factors range between a maximum of 1.0 to a minimum of about 0.4. During maximum, the DC factor frequently drops well below this range. We implemented a filter that weights the fit of the detected points according to their DC factor, disregarding any points with a DC factor below the 0.4 threshold. We then eliminated rotations with too few valid coordinate-point detections from consideration.

After fitting the polar plots of each filtered HR with trigonometric fits (Kirk et al. 2009), the polar fits were closed curves with improved goodness-of-fit and match the reality of the holes. The period of solar maximum was also made clear in the fitted polar plots as an unreasonably correlated distribution of the detected points. Figure 12 shows examples of the fitted polar plots for two HRs in Cycle 23, one during minimum, the other during maximum.

Figure 12

The northern (left) and southern (right) polar plots of the PT boundary points (+) for HR 1068 (May 1996) during solar minimum (top) and HR 1099 (March 1999) during solar maximum (bottom) of Solar Cycle 23. The solid line represents the curve of best fit from which we calculate the area of the PCH. The red asterisk ($\mathbf{\ast}$) is the center of the fitted curve. The detected points at minimum have a fairly uniform, circular distribution about the Pole. The best-fit line through the points is a smooth curve. During solar maximum, the detected points have a more correlated distribution, with linear features spread around the pole. These are false detections of filaments that the PT algorithm identifies as PCHs. The best-fit line is not a reasonable fit to the points. Such fits should be rejected as estimates of the PCH area.

1.4.2 A.4.4 Absorption

False detections due to absorption features, such as filaments, pass through the DC and boundary-forcing filters. These features appear in the polar plots of the data as smooth curves, and are particularly prevalent during the solar-maximum period (as seen in Figure 12). To remove absorption-feature detections, an absorption-feature filter was added to the algorithm, which takes advantage of the consistent curvature signature of most absorption feature data. The filter sets a lower-limit threshold on the latitudinal coordinate difference between consecutively detected points. This is effective because as a filament rotates across the limb of the solar disk, the detected latitude changes less with time than that of a PCH-boundary detection. Data with latitude differences that did not meet the threshold criteria were omitted from the fit. The data from each quadrant were treated separately.

After implementing this filter, we found that for the same solar maximum HR displayed in the bottom row of images in Figure 12, we constrain the fitted data to those shown in Figure 13, in which the “linear” false detections from absorption features are visibly reduced.

Figure 13

The northern (left) and southern (right) polar plots of the PT boundary points (+). The solid line represents the curve of best fit from which we calculate the area of the PCH. These plots show the distribution of points for HR 1099 (March 1999) during the solar maximum period of Cycle 23, after applying an absorption feature filter (compare with Figure 12). The red asterisk ($\mathbf{\ast}$) is the center of the fitted curve. The linear distribution of points is mainly removed and the area within the best-fit line is greatly reduced.