VARIATION OF THE X-RAY BRIGHT POINT NUMBER OVER THE SOLAR ACTIVITY CYCLE H. Hara. and K. Nakakubo-Morimoto

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1 The Astrophysical Journal, 589: , 2003 June 1 # The American Astronomical Society. All rights reserved. Printed in U.S.A. VARIATION OF THE X-RAY BRIGHT POINT NUMBER OVER THE SOLAR ACTIVITY CYCLE H. Hara National Astronomical Observatory, , Osawa, Mitaka, Tokyo , Japan; hara@solar.mtk.nao.ac.jp and K. Nakakubo-Morimoto Suginami Science Center, , Shimizu, Suginami, Tokyo , Japan Received 2002 December 20; accepted 2003 February 11 ABSTRACT We have counted the number of X-ray bright points (XBPs) in the quiet-sun region from Yohkoh soft X-ray images during a period of Since we define XBPs as a small region that is less than with a significantly enhanced emission in soft X-ray intensity compared with the adjacent background corona, the number of XBPs in the whole Sun area is affected by the soft X-ray intensity of the background corona and the presence of the solar active regions. Under these conditions, the number of XBPs in the whole Sun area is anticorrelated with the sunspot number owing to the change of background X-ray intensity and the occultation by active regions during the 11 yr activity cycle. In order to estimate the real number variation with little artifact, we have calculated the number of XBPs in a unit area by limiting the X-ray intensity range of the background corona and by removing a bias effect of a selected intensity threshold for the XBP counting. The evaluated change of the XBP number density in the quiet Sun is less than a factor of 2 over the period in the present study, and there is no clear enhancement in XBP number near the solar minimum. We conclude that the number density of XBPs is nearly independent of the 11 yr solar activity cycle. Since an XBP found in the quiet Sun is believed to be an event that is produced through an interacting process of opposite-polarity magnetic fields in the quiet Sun, the low-amplitude variation of the XBP number density suggests that there is a mechanism to create solar magnetic fields, which are different from those associated with active regions, irrespective of the 11 yr solar activity cycle. Subject headings: Sun: activity Sun: corona Sun: magnetic fields Sun: X-rays, gamma rays 1. INTRODUCTION X-ray bright points (XBPs) were first observed with a sounding rocket X-ray telescope in 1969 by the AS&E group (Vaiana et al. 1970). They are small, compact regions of diameter and are found all over the latitude almost uniformly (Golub et al. 1974). Some XBPs have also been found as He i dark points (Harvey 1985; Golub et al. 1989) and microwave bright points (Kundu, Schmahl, & Fu 1988; Habbal & Harvey 1988) of a similar size. Magnetic bipolar regions are observed on the photosphere beneath XBPs. Although the magnetic bipolar structures were first understood as a direct emergence of short-lived small magnetic bipoles such as ephemeral regions (Golub et al. 1977), during the course of extensive studies and because of highcadence observations afterward, they are believed to be produced as a chance encounter of opposite magnetic polarities in the corona through the magnetic reconnection process (Harvey 1985, 1996; Webb et al. 1993). Importance of the physical process is also confirmed in the recent studies (Pres & Philips 1999; Brown et al. 2001). Since a statistical interaction of the magnetic field is associated with the production of XBPs, the variation of the XBP number on the Sun will be a measure of the magnetic activity of its origin. Davis, Golub, & Krieger (1977) first noticed that the number of XBPs is increased near the sunspot minimum. Golub, Davis, & Krieger (1979) and Davis (1983) insisted on the anticorrelation of XBPs with the sunspot in number, showing that the number at the sunspot minimum became a factor of 3 larger than that at the sunspot maximum during the period (Golub et al. 1979), or an order of 1062 magnitude larger during the period of (Davis 1983). These results are based on the synoptic X-ray data that were obtained during the Skylab mission and independent sounding rocket flights. Schüssler (1980) and Yoshimura (1983) have tried to explain the anticorrelation of XBP number in their own dynamo models, which demonstrate the cyclic behavior of the 11 yr magnetic activity of the Sun, under a hypothesis that all magnetic fields on the Sun are created by a single mechanism. We have reported our preliminary study on the number variation of XBPs during the solar cycle in Nakakubo & Hara (2000) based upon the analysis of Yohkoh soft X-ray synoptic data. We defined an XBP as a small X-ray enhanced region adjacent to the nearby X-ray background intensity. Therefore, the variation of the X-ray background intensity affects the number of XBPs in our counting method. Although the number of XBPs that we showed is anticorrelated with the sunspot number with a very small amplitude, we did not instantly believe that it is a real variation because the number of XBPs at the low X-ray intensity increases near the solar minimum where the X-ray background intensity is significantly decreased (Hara 1997). Sattarov et al. (2002) have counted the number of XBPs from Yohkoh soft X-ray data in a manual procedure and the number of small-scale photospheric bipoles of similar size from Kitt Peak magnetograms in an automatic procedure for the period of The number of XBPs in Sattarov et al. (2002) is also anticorrelated with the sunspot cycle with a larger amplitude than that in our preliminary study. On the other hand, the number of small-scale photospheric magnetic bipoles is approximately the same in the duration of

2 X-RAY BRIGHT POINT NUMBER OVER SOLAR ACTIVITY CYCLE 1063 their data. Since they consider a fraction of such small-scale photospheric bipoles to be associated with XBPs, they anticipate that the number of XBPs is nearly constant over the solar cycle and that the anticorrelation is derived because of bias effects by the presence of active regions and the change of background corona during the solar cycle. In this paper we further investigate the variation of XBPs during a nearly single 11 yr solar activity cycle by considering the various effects of instrument origin on the XBP number. We estimate the number density of XBPs to represent the variation of XBPs by simplifying the effect of occultation owing to bright area like active regions, although the detection of XBP is made for whole Sun regions. In the calibration of the X-ray data, we consider the effects of dark noise and noise from visible stray light, those of which are changing with time over a long period of observations. A component showing anticorrelation with the sunspot number is not found during the course of this study. 2. DATA We use soft X-ray full-disk images obtained with the Yohkoh Soft X-Ray Telescope (SXT; Tsuneta et al. 1991) covering the period between 1993 January and 2000 December. We select images taken with the AlMg filter of 4>9 pixel sampling. For this study we make a composite image consisting of images of three different exposures of 30, 5.3, and 0.17 s to do a deep survey of XBPs and to correct a saturated area in images taken with 30 and 5.3 s owing to bright active regions. The three images used for a single composite image are obtained within 30 minutes. There are data gaps in some periods in which images with 30 s exposures were not taken. We do not use data with other shorter exposures alone for this period because of uniform quality of data as a function of time. After the alignment of three images following dark and stray light corrections of each image, the saturated bright active-region area is replaced with unsaturated images with shorter exposures to make the composite image. For the present study we prepare 96, 126, 113, 176, 63, 90, 125, and 108 composite images for each year starting from 1993 to Images of the different shortest exposures, 0.04 and 0.08 s, are used for five composite images. It does not practically affect the results, however. The unit of soft X-ray intensity I in a single image pixel of the composite image is DN pixel 1 s 1, in which DN is equivalent to 365 ev in X-ray photon energy and pixel is the size of image pixel of 4:9 4:9 arcsec 2. We define DN pixel 1 s 1 as soft X-ray intensity unit (SXU) here. The use of images taken with a constant exposure guarantees that no calibration in XBP number between images of different exposures is required. 3. XBP DETECTION We develop a method that is capable of finding and counting XBPs from Yohkoh SXT composite images. The algorithm of this procedure is summarized as follows: 1. We remove bright/dark spikes occupying a singleimage pixel from the composite data with a twodimensional median filter. These spikes are caused by a bad pixel and a cosmic-ray hit. The area applying the median filter is pixels. Because of this process obvious local spikes are removed. This process is important to estimate the background intensity of X-ray corona (hereafter background corona) in the next process. 2. We make image data of the X-ray background intensity (I back ) from composite data (I signal ) by a spatial running mean of the composite data over an area of pixels centered at a pixel of interest. In order to estimate the X-ray intensity of enhanced X-ray regions (I diff ), subtraction of I back from I sig is done: I diff ¼ I sig I back : Since the running mean background intensity on the solar disk near the limb is strongly affected by the X-ray intensity above the limb where the line-of-sight length is large, we limit the search area of XBPs to be within a circle with radius of R from the center of X-ray Sun, where R is the radius of the Sun. 3. We calculate the noise level (DI back ) of the X-ray background data I back from the X-ray photon statistical noise DI ph, dark noise DI dark, noise of visible stray light data DI stray, the readout noise DI read, the uncertainty introduced by the compression DI compress, and the digitization DI digit,as DI back ¼ ðdi ph Þ 2 þðdi dark Þ 2 þðdi stray Þ 2 þðdi read Þ 2 þðdi comp Þ 2 þðdi digit Þ 2 1=2 : The replacement of saturated area is correctly taken into account to calculate the photon noise DI ph. The characteristic of each noise is described in Appendix A. 4. For estimating the significance of local X-ray enhancement (I diff ) we calculate the following index : ¼ I diff : ð3þ DI back We define XBP candidates as regions in which the index showing deviation from the mean exceeds 3. In this process extremely small and large bright areas cannot be rejected. We add some restriction for shape and size. 5. We regard a group of spatially neighbor pixels of XBP candidates as a single XBP. We define the number of pixels in a group as size of XBP (S XBP ). Selection rules of XBP in shape for this study are as follows: a) The ratio of horizontal width (W h ) to vertical width (W v ) of XBP, W h =W v, shall be in a range of b) S XBP shall occupy more than 40% of the product of its horizontal and vertical widths (W h W v ). c) S XBP shall be in the following range: 3 S XBP 144ð¼ 12 2 Þ The local X-ray enhancement that satisfies the criteria described above are regarded as XBPs in this paper. Small enhanced regions and thin structures are removed by the second rule. Figure 1 shows two examples of detected XBPs with the method described above. The timing of two selected data is the declining phase of the 11 yr solar cycle for 1993 September 1 image and the minimum phase for 1996 June 1 image. Although some active region loops are selected as XBPs, this can be removed by considering the background X-ray intensity as shown later. The outer circles of middle and right panels show the radius of R from the center in which the XBP detection is made, and the inner circle indicates the radius of 0.5 R inside which the XBP density is estimated later. The dark area shows the region whose ð1þ ð2þ

3 1064 HARA & NAKAKUBO-MORIMOTO Vol. 589 Fig. 1. Yohkoh X-ray images on 1993 September 1 and 1996 June 1 (left), detected XBP candidates that meet the intensity threshold of 3 of the background fluctuation (center), and detected XBP after the pattern recognition (right). Inner and outer circles indicate the radius of 0.5 and R, respectively. X-ray intensity is larger than 10 SXU and is regarded as the area of active regions. The change of X-ray intensity across an XBP is indicated by a thick solid line in Figure 2, together with the background intensity by a thin dotted line. Through the procedure for XBP detection we make a simple database to include the image parameters and information of recognized XBPs. We analyze the database in detail for this study. Since the active region area is not removed in the database, small solar active region loops can be included in it, although XBPs in active regions can be excluded by using recorded information of X-ray background intensity around XBPs in the database. In this study XBPs are defined by a small soft X-ray enhanced region that is significantly higher than the fluctuation of the X-ray background intensity as stated before. Since the X-ray background intensity changes with the solar cycle (Hara 1997), there is a selection effect, and it should be taken into account in estimating the variation of XBP number on the solar disk. Fig. 2. (a) Examples of detected XBPs in Fig. 1. (b) X-ray intensity of the XBP I (solid line) and its background intensity I back (dotted line) across the horizontal line in the figure of the plot.

4 No. 2, 2003 X-RAY BRIGHT POINT NUMBER OVER SOLAR ACTIVITY CYCLE VARIATION OF XBP NUMBER 4.1. Temporal Variation of Detected XBP Number We examine the temporal variation of detected XBP numbers across a good fraction of the solar cycle. The result is shown in Figure 3a. The shaded area indicates a period of no data for the 30 s exposure image. Each dot shows the XBP number in a single composite image within R from 1993 January onward with the counting method described in the previous section. Correction for obscuration by bright active regions is not made in this figure, although we show a figure in which this effect is corrected by showing the density of XBPs later. There are periods of data gap in 1997 and 1998 because of no images of 30 s exposures in these periods. The solid line shows the sunspot number from Solar-Geophysical Data reports. The number of XBPs shown in this figure is not exactly consistent with that in Nakakubo & Hara (2000). This is because DI dark that we used in the preliminary study is somewhat underestimated for the recent data and because DI stray is added in this study. In order to see the difference of XBP variation that appeared in the bright and dark area in the so-called quiet-sun regions outside active regions, we show Figures 3b and 3c in which thick solid lines indicate the XBP number of 10 days running mean and thin solid lines show the sunspot number. The X-ray background intensity for the dark (bright) area is I back < 10 0:8 (10 0:8 I back < 10 1:6 ) SXU. Figure 3d shows the fractional area in an X-ray image that is occupied by a region having a background intensity range: thin for the bright area and thick for the dark area. We notice the following: 1. Although the number of all XBPs that we have detected here increases at the solar minimum as shown in Figure 3a, the increase is small when we add up all small X-ray enhancements. 2. The fluctuation of XBP number in a short period of less than a month originates the occultation of the solar disk by active regions. 3. The variation of XBP number detected in the dark area is anticorrelated with the sunspot number (Fig. 3b), and it shows a similar variation of the fractional area of mixed magnetic polarity regions on the photosphere (Giovanelli 1982). On the other hand, the variation in bright area is correlated to the sunspot number (Fig. 3c). These are partially explained by the change of occupied area on the Sun in the 11 yr solar activity cycle as shown in Figure 3d. In order to mention the variation of the XBP number, both the area and the background intensity for XBP counting should carefully be considered. The reasons are (1) the former directly affects the total number of XBPs on the Sun; (2) there is a bias effect in a way of counting XBPs from the nearly whole Sun area because the actual area on the Sun in a single image pixel is different; and (3) the latter determines Fig. 3. (a) Number of XBPs in an X-ray composite image, detected within R, and its 10 days running mean average are indicated in dots and thick solid line. A bias owing to the background level and area covered by active regions are not corrected. The monthly averaged sunspot number is also shown in thin solid lines. Hatched areas indicate periods of no data for XBP detection because there are no 30 s exposure observations. (b) Number of detected XBP in an area whose background X-ray intensity is in I back < 10 0:8 SXU and (c) in10 0:8 I back < 10 1:6 SXU are shown in thick lines together with the monthly averaged sunspot numbers. (d ) Fractional areas occupied by dark (I back < 10 0:8 SXU) and bright (10 0:8 I back < 10 1:6 SXU) are indicated in thick and thin solid lines.

5 1066 HARA & NAKAKUBO-MORIMOTO Vol. 589 Fig. 4. Yearly averaged histograms of the background X-ray intensity within 0.5 R. The dotted histogram in each plot is the histogram in 1996 for reference. the lowest intensity level of XBPs under a condition in which the background intensity is changing during the solar activity cycle in phase (Hara 1997). In Nakakubo & Hara (2000) these effects were not considered as described. In order to remove these effects we estimate the number density of XBPs detected at the central area of the solar disk and in a limited X-ray background intensity in the next section Variation of Number Density of XBPs We estimate a variation of the number density of XBPs in the quiet-sun region here. The estimation is made in the following process: 1. We only count XBPs in a limited area where the pixel size is considered as almost the same. The selected region for the XBP counting is within a circle of 0.5 R (see the inner circle in the right panels of Fig. 1). The difference of pixel size within this limited area is about 15% at most. 2. We count the number of XBPs in a limited background intensity range (I b1 I back < I b2 ) within the limited area described above. Figure 4 shows the yearly mean intensity histograms of X-ray background per image within the XBP counting area (0.5 R ). Since the peak of the intensity histograms changes by more than an order of magnitude, a selection of the intensity range for XBP counting needs to be carefully made. We select the upper threshold I b2 to be a conservative number of 10 0:8 SXU for the quiet-sun region. 3. The maximum X-ray intensity per a single pixel area in an XBP (Max I XBP ) that is found in 0.5 R is plotted as a function of its background intensity I back in Figure 5. The solid line shows 3 confidence level for each background intensity. This line is determined by conditions at the end of the period of the data that are analyzed in the present study to cancel a long-term variation of the background uncertainty (see Appendix A). Since the uncertainty increases with time, some XBPs, which are detectable at the time of observations, may not appear in Figure 5. Fig. 5. Maximum X-ray intensity of XBP, detected within 0.5 R, is plotted as a function of its background X-ray intensity. Each solid line shows the 3 level of the background noise that is estimated in eq. (2).

6 No. 2, 2003 X-RAY BRIGHT POINT NUMBER OVER SOLAR ACTIVITY CYCLE 1067 Fig. 6. (a) Regions for counting XBPs are indicated in hatched colors for the following plots of (b) and (c) in which the background ranges for estimation of the XBP density are 10 0:0 I back < 10 0:4 SXU and 10 0:0 I back < 10 0:8 SXU, respectively. For plots (e) and ( f ) a different higher threshold defined in plot (d ) is adopted. The XBP density is calculated in an area within 0.5 R. 4. We did not use composite images in which the counting area of XBPs is largely occupied by bright regions that are brighter than the upper threshold I b2. The rate of occupation is set to be smaller than 0.8, considering the XBP number density derived later. 5. The number density of XBPs is calculated by the ratio of total number of XBPs N XBP and total background area A XBP. For a higher statistical accuracy we calculate a mean XBP number density n XBP from multiple images obtained in some period of one month to several months, depending on the number of images: P j n XBP ¼ N XBPj P j A : ð4þ XBPj Figure 6b (6c) shows the number density of XBP whose background intensity is in a range of 10 0:0 I back < 10 0:4 (10 0:0 I back < 10 0:8 ) SXU. The period of no composite image is shown in the gray shaded area and the period in which there is no selected background is represented in the dark shaded area. The region of XBP counting is visually indicated in Figure 6a for Figures 6b and 6c. There is little change between Figures 6b and 6c during the plotted period, showing that the number density of XBPs in the quiet-sun region does not depend on the selection of background range. Since the uncertainty of background intensity in Figure 6a slightly increases as the background intensity, there is a small bias effect in which an XBP is easily detected at the lower intensity background level. In Figures 6e and 6f this bias effect is weakened by setting a constant threshold as a function of the background intensity as shown in Figure 6d. We conclude here that the variation of XBP number density is within only a factor of 2 and that the change of amplitude is much smaller than that in Davis (1983). Although the preliminary result on the variation of XBP number over the solar activity cycle in Nakakubo & Hara (2000) is apparently similar to the result in the present study, it is coincident because the preliminary study includes bright points in active regions and because it does not consider the variation of occultation due to bright regions Evaluation of Remaining Instrumental Bias Effect We have not cared for an effect of instrumental degradation over the period, although long-term changes of dark and stray visible light have already been considered. There is a change of spectral response of the instrument due to the prefilter failures. We estimate a variation of the CCD camera gain in Appendix B and show little change of the response to soft X-rays from solar flares in Appendix C. We have tried to evaluate the change of X-ray flux at each prefilter failure under an assumption that the X-ray flux of the quiet Sun does not vary before and after each prefilter failure and that newly added visible light flux can be estimated from the images that are obtained at the dusk of Yohkoh. Although a 10% 25% increase of X-ray flux with about 10% uncertainty in the same unit is found in our preliminary investigation, we do not use the result of the investigation to correct the bias effect until it is finalized. Instead, here we show a forward process to correct it. The soft X-ray response of SXT f ðt; tþ is a function of time t and the plasma temperature T. When a part of prefilter is broken at time t 1, f ðt; t 1 Þ is larger than the response at start of the observation f ðt; t 0 Þ at t 0. Since the photon statistics becomes higher when area of prefilter failure is

7 1068 HARA & NAKAKUBO-MORIMOTO Vol. 589 Fig. 7. Same as Fig. 4, but the change of the soft X-ray intensity owing to the SXT prefilter failures is simply corrected in a condition of T back ¼ 10 6:3 K, as described in the text. increasing, an XBP, which is not to be counted in the initial prefilter condition, may be counted by the change of spectral response due to the prefilter failure. We simply estimate this effect by assuming that the background coronal temperature for hunting XBP is constant over the solar cycle. This assumption will be adequate in first-order approximation because we limit the search region of XBP in X-ray intensity that is a weak function of the coronal temperature. When we analyze single composite data in the same way after dividing value of the X-ray data by the ratio of f ðt; tþ=f ðt; t 0 Þ, this effect is expected to be canceled. We use two spectral codes of Mewe (Mewe, Gronenschild, & van den Oord 1985; Mewe, Lemen, & van den Oord 1986) and CHIANTI (Dere et al. 1997) to estimate this ratio, and it little depends on the selection of spectral code and combination of atomic data like ionization equilibrium and abundance data. Figure 7 is the corrected background histogram, which is the same as Figure 4 for noncorrected case. Figure 8 shows the corrected XBP density as a black line together with that of Figure 6f as a gray line. It is shown that a trend of variation in the XBP number density after the correction becomes flatter than that before the correction, although there is still a short-term variation. power-law function of the maximum XBP intensity ^I XBP as dn XBP /ð^i XBP Þ ; ð5þ d ^I XBP the power index in 1994 (1996) is estimated to be 2:09 0:05 (1:90 0:04) in Figure 9a before the X-ray intensity correction and 2:02 0:07 (1:88 0:07) in Figure 9b after the correction. The range of this power-law fitting is :8 SXU < ^I XBP < 10 1:5 SXU, where 10 0:8 SXU is uncertainty at SXU. Although this may not directly be compared with the occurrence frequency of microflares (Shimizu 1995; Shimojo & Shibata 1999; Aschwanden et al. 2000), the power index shows a similar value, suggesting the same physical process of solar flaring events. As for the slight difference in the power index between 1994 and 1996, we think that it is within the error bar Number Distribution of XBPs We have only been looking at the XBP number density without considering the number distribution of XBPs as a function of the X-ray intensity. Figure 9 shows the yearly averaged differential number of XBPs as a function of the maximum X-ray intensity of XBPs for data of 1994 (1996) in gray (black) line. The correction of X-ray intensity for prefilter changes is (is not) applied for Figure 9a (9b). The background range of XBP counting for these plots is 10 0:0 I back < 10 0:8 in unit of SXU. The vertical dotted line indicates the 3 level of the statistical uncertainty at 10 0:8 SXU for reference. Thus, the shape of the distribution above this level is not affected by the background effect. At a glance these plots supplementary support that the variation of the number density of XBPs is small. When the differential number dn XBP =d^i XBP in Figures 9a and 9b is fitted by a Fig. 8. Variation of the XBP number density estimated in the background of SXU within 0.5 R after (before) correcting for the the SXT sensitivity change due to the SXT prefilter failures in black (gray) line. A condition of the coronal background temperature T back ¼ 10 6:3 Kis assumed over the period of analyzed data.

8 No. 2, 2003 X-RAY BRIGHT POINT NUMBER OVER SOLAR ACTIVITY CYCLE 1069 Fig. 9. Yearly averaged XBP number distributions in 1994 (1996) as a function of the maximum soft X-ray intensity in an XBP that is found in the background range of SXU. Panel (a) is the plot for no correction in terms of the SXT prefilter failures, and panel (b) is the plot after the correction. 5. DISCUSSION 5.1. Contribution of Ephemeral Regions to XBP Number Variation Ephemeral regions (ERs), which are small-scale emerging photospheric bipoles with no sunspot, are widely found in latitudes (Harvey, Harvey, & Martin 1975) like XBPs (Golub et al. 1974; Sattarov et al. 2002). These are regarded as small-scale, short-lived active regions (Wang 1988; Harvey 1993). Normal active regions are clearly observed in soft X-ray observations, and some ERs would have coronal counterparts that brighten in soft X-rays. Since the size of an ER, which is recognized in the photospheric magnetograms, is similar to that of XBPs in a snapshot X-ray image, we cannot discriminate a component of an ER from XBPs by its size in the present study. If the contribution is large, the evaluated XBP number variation in the quiet Sun over the solar cycle is affected by the occurrence frequency of ERs that varies with the sunspot cycle (Martin & Harvey 1979). From a single X-ray image and high-cadence Big Bear Solar Observatory magnetograms obtained simultaneously, Webb et al. (1993) have shown small contribution of emerging photospheric bipoles to XBPs and chance encounters of disappearing opposite magnetic polarities were mostly observed at the site of XBPs. It is also confirmed by Harvey (1996) from Yohkoh soft X-ray images and high-cadence Kitt Peak magnetograms. On the basis of these studies, we think that the contribution of the so-called ERs to the detected XBPs in the present study will be small, and the variation of the XBP number density estimated in this study would be the change of the number of magnetic interactions in the corona XBP Number Density in EUV Observations Zhang, Kundu, & White (2001) have reported that the number of XBPs seen in SXT images is smaller by about a factor of 3 4 than that seen in EUV Imaging Telescope (EIT) 195 Å images. The number density of XBPs in the EIT observation in a single image is 1.3 per km 2. The exposure duration of SXT images that they compared is 5.3 s and is shorter than that of SXT images which we use in this paper. When we compare our average number around the time of the data used in Zhang et al. (2001) with that in their result, we find there is still a factor of 2 difference between these two observations. Although there is a difference in the pixel size of image as spatial sampling interval between EIT and SXT for full-frame images, selected XBPs in Zhang et al. (2001) have enough size to be detected by our detection method. We speculate that the difference of XBP number between EUV and X-ray observations will be explained by the temperature response of the instruments because SXT has less sensitivity at million degrees, which is the most sensitive temperature in EIT 195 Å observations. In the transition region a higher number density of small-scale bright points including counterpart of coronal bright points, which we call XBPs here, is reported as network bright points in the Skylab EUV observations (Habbal, Dowdy, & Withbroe 1990) and ultraviolet brightening near the center of the network, implying that there are a higher number of events for smaller energy release that leads to a lower temperature, as normally expected Implication of the Observed Number Variation of XBP Using Yohkoh soft X-ray data of 8 yr, we show in the present study that the XBP number density in the quiet Sun does not change much during the 11 yr solar cycle. Figure 10 is shown to compare our result with works by Davis (1983) and Harvey (1985) by shifting our data to match the trend of sunspot numbers in different observing periods. The data of XBPs or He i dark points are normalized near the sunspot maximum for direct comparison of the change of their amplitudes. The increase of an order of magnitude in the XBP number density near the sunspot minimum, which was shown by Davis (1983), is not confirmed. Since XBP is associated with small-scale photospheric magnetic bipoles through a canceling process due to chance encounter of small-scale opposite magnetic polarities (Harvey 1985, 1996; Webb et al. 1993), the variation of the XBP number density over the solar cycle can be a measure of the quantity of the small-scale magnetic bipoles on the Sun. This variation is quite different from that of the magnetic bipoles such as sunspots, of which magnetic flux changes an order of magnitude during the 11 yr solar cycle. The presence of the nearly constant XBP number over the solar cycle suggests a different mechanism supplying magnetic fields from that producing the sunspots. We infer that the mechanism will be working in the entire Sun considering the wide distribution of XBPs in latitude (Golub et al. 1974; Sattarov et al. 2002), although we have not verified the variation of the XBP number density at high-latitude regions. Magnetic field structures in the quiet Sun consist of three components: intranetwork, network, and ER. Webb et al. (1993) have reported that XBPs are associated with converging of opposite magnetic polarities, irrespective of their origin. Such magnetic canceling processes have been reported to be common on the solar photosphere (Livi, Wang, & Martin 1985; Zirin 1987; Martin 1988, 1990; Schrijver et al. 1997; Title 2000). The number of interactions changes with the number of magnetic elements when we consider a random motion of the elements as seen on the photosphere. Even if the number of three components changes differently through the solar activity cycle, the number of interactions between elements whose birth rate is the highest in the quiet Sun will dominate others. Intranetwork fields have the highest birth rate in the quiet Sun, and the number of the intranetwork fields is much larger than that of network fields as shown in Wang et al. (1995). However, we cannot directly connect the

9 1070 HARA & NAKAKUBO-MORIMOTO Vol. 589 Fig. 10. (a) Monthly averaged sunspot number in the period of is plotted together with that in , which is shifted to about 10 yr to show a similar variation at the rising phase of the sunspot cycle. (b) By shifting the same amount of time with the sunspot number, the variation of the XBP number density estimated within 0.5 R in the present study is compared to that of the XBP number from Davis (1983) and the variation of number density of He i dark points, found within 0.4 R, from Harvey (1985). Each is normalized near the sunspot maximum, showing an arrow for a direct comparison of the change of amplitude. intranetwork fields with XBPs, because the typical magnetic flux of intranetwork fields is Mx and converging magnetic fields of Mx are observed on the photosphere under XBPs (Golub, Krieger, & Vaiana 1976; Harvey 1996). Rather, the XBP related magnetic flux is a similar level of ERs, the number of which changes with amplitude of a factor of 2 nearly in phase with the solar cycle (Martin & Harvey 1979; Harvey 1985). Although Harvey (1993) concludes that ERs are in the small-scale end of a wide-size spectrum of bipolar active regions, a low-amplitude change of its number seems to indicate the presence of two components: an 11 yr cycle related component and a non cycle related component. If this assumption is correct, at least half of ERs reported so far originates from the non cycle related component. Our result of the nearly constant XBP number may show that the non cycle related component has a higher fraction. This may be supported by the result of Sattarov et al. (2002), in which the number of small-scale photospheric bipoles is independent of the solar cycle. Through a numerical simulation the generation of the quiet-sun magnetic field is recently proposed by a local dynamo action associated with the granular and supergranular flows (Cattaneo 1999). Since the timescale of the flow is much shorter than the solar cycle and a basic thermal structure of these convections does not change over the solar cycle, the number of magnetic bipoles generated by this mechanism will be constant during the 11 yr activity cycle. Our result may show this property via X-ray observations of magnetic interactions. We notice that there is a low-amplitude modulation of about 1 to 2 yr period in the variation of the XBP number density. Although this may be an important signature of magnetic fields associated with XBPs, we do not discuss it further in the present paper. 6. SUMMARY We count XBPs in an automatic manner from Yohkoh SXT data of the longest exposure and examine the variation of the XBP number in the quiet Sun over the 11 yr solar activity cycle. We find that the total number of XBPs in an image is strongly affected by the area of active regions on the Sun, and an order of magnitude variation in the XBP number is an apparent effect of this. We carefully select a conservative intensity range of the quiet-sun background corona in which we find XBPs and calculate the XBP number density from the total numbers of XBPs and the area in the intensity range for a region within 0.5 R where there is a small difference in the pixel size, resulting in almost uniform detection efficiency. We show that a variation of the XBP number density in the quiet Sun is roughly constant from 1993 to Although there is uncertainty about the change of the instrumental response owing to prefilter failures of SXT, we show that a small amplitude variation in the XBP number does not change even if we simply consider the effect of prefilter failure and the result is not consistent with that in Davis (1983). The nearly constant XBP number over the solar cycle suggests a different mechanism supplying quiet-sun magnetic fields from that producing the sunspots. We would like to thank T. Kosugi for his useful comments, and we also appreciate the Yohkoh SXT team for a long-term effort of calibration to remove visible-light component from the images after the first entrance-filter failure. Yohkoh is a spacecraft of the Institute of Space and Astronautical Science.

10 No. 2, 2003 X-RAY BRIGHT POINT NUMBER OVER SOLAR ACTIVITY CYCLE 1071 APPENDIX A ESTIMATION OF NOISE LEVEL OF THE BACKGROUND CORONA Six noise components are considered in estimating the noise level of the background corona in equation (2). Since the detection of the XBP is made by comparing this noise level with the X-ray intensity of XBPs, here we summarize how it is estimated in this study. DI ph is the statistical noise level originating from the X-ray photon detections. This is estimated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KðTÞI back DI ph ¼ ; ða1þ t exp where t exp is the exposure time and KðTÞ (DN photon 1 ) is a conversion factor as a function of the plasma temperature T (Hara 1996, p. 34, Fig. 2.7). In our study KðTÞ ¼2:3 DN photon 1 is used for a temperature at 3 million degrees by considering temperatures of XBPs reported in Nitta et al. (1992) and Hara et al. (1994). DI dark is the dark noise of CCD. This changes over a long period of time like an order of a year. For simplicity, pffiffiffi we estimate it by the standard deviation of differences between two dark images, and the standard deviation is divided by 2 and texp to estimate DI dark. In the Yohkoh analysis procedure the dark-frame data, which are obtained at the nearest neighbor in the time domain, are used for the dark calibration. The noise is a function of time. In equation (2) we use the dark noise of the worst case at the end of year 2000 to keep the condition the same for all data. Then the dark noise is 0.27 SXU. The stray light level also changes with time, and it leads to a variation of DI stray. Because of the entrance filter failure, the visible light is detected as stray light. This is corrected with images that were taken at the day-to-night transition of the spacecraft at which the visible stray light is only detected and X-ray is absorbed by the dense Earth s atmosphere. The noise owing to stray light at the end of year 2000 is expected to be 0.10 SXU in our estimate. The uncertainty introduced by the bit compression from 12 to 8 bits for SXT data depends on the digital value (see eqs. [3] and [4] in Tsuneta et al. 1991). Since the level of the background and stray light is changing with time over a timescale of a year, the uncertainty due to the SXT bit compression is changed even when the X-ray intensity is the same for a data set of long period. In this study we estimate this uncertainty at the end of the period for our data set. At the end of 2000, the compression errors for the X-ray signal (DI comp ) for I back ¼ 10 0:4 and SXU are 0.33 and 0.37 SXU, respectively. The number of readout electrons for SXT CCD is about 50 for the case of 1 1 binning, and the readout noise of 4 50 [electrons pixel 1 ]/100 [electrons DN 1 ] = 2.0 DN pixel 1 is introduced for the case of 2 2 binning. The resultant readout noise becomes DI read ¼ 2:0 DN pixel 1 /30 s ¼ 0:07 SXU. The uncertainty introduced by the digitization is 0.5 DN pixel 1, resulting in DI digit ¼ 0:5=30 s ¼ 0:02 SXU. When the X-ray background intensity is low, the dark and compression noises become dominant factors and the noise owing to the X-ray photon itself becomes dominant as the X-ray intensity increases. APPENDIX B VARIATION OF THE SXT CCD CAMERA GAIN The long-term variation of the SXT CCD camera gain, electrons per ADC unit, is simply checked from a small number of visible-light images with a diffuser filter for calibration. Combination of visible-light data of a lower 8 bit signal compression and the SXT square root compression in original 12 bit data are used for this purpose. The variance and mean value of local segments are estimated from the two lower 8 bit compression data and a single square root compression data. When the variance is plotted as a function of the mean value in linear scale, the data points are almost on the straight line with a moderate scatter. The SXT CCD gain is evaluated from the slope of this linear line with the least-squares fitting. Figure 11 shows the variation of CCD camera gain, and no systematic change is found. Thus, we regard the CCD camera gain as a constant value in the present study. The constant value is estimated to be 93:2 8:7 in this in-obit calibration. Although a higher accuracy of the camera gain is statistically achieved by using a number of data, it is beyond the scope of this paper. APPENDIX C VARIATION OF THE SXT CCD SENSITIVITY FOR X-RAYS The change of SXT sensitivity for X-rays is checked by comparing the SXT flux through the Be filter with the low channel flux of the GOES proportional counter during solar flares. Although the long-term SXT response for X-rays is changed due to the prefilter failures, the effect to the response is small in flare temperatures of log 10 T ¼ 7:0 7:3. There are 12 sectors in the prefilter area, and the filter failure has been reported seven times. When we assume that the whole area of each sector is fully opened, the change of flux in the flare temperature range is only 1.3% 1.7%. This percentage is calculated from the SXT effective area with/without the prefilter and model solar spectra. Although the absolute SXT response is relatively sensitive to the model spectrum, the ratio of SXT flux with some prefilter failures to the flux of no prefilter failure is insensitive to the model solar spectra as far as we check using the Mewe and CHIANTI codes (Mewe et al. 1985, 1986; Dere et al. 1997) with several combinations in the abundance and ionization equilibrium.

11 1072 HARA & NAKAKUBO-MORIMOTO Vol. 589 Fig. 11. Variation of the SXT CCD camera gain estimated from visible-light images with the diffuser filter. Error bars show 1 statistical uncertainties. The top panel in Figure 12 shows a temporal variation of a solar flare observed with the GOES-7 low channel. The flat flux before the flare originates from active regions. We subtract the flat level from the flare flux and overplot the flare flux observed with SXT through the Be filter by multiplying a factor to meet the level at the time of peak GOES flux in bottom panel of Figure 12, indicating a similar time variation. We search flares that occurred near the center of field of view, defined within 0.5 R, from the Yohkoh data for periods around 1992 and Figures 13a and 13b (13d and 13e) show a change of flux ratio between SXT and GOES flux at the time of peak GOES-7 (GOES-8) flux before (after) correcting the SXT effective area over Fig. 12. Top: Temporal profile of the GOES-7 low-channel soft X-ray flux (1 8 Å) during a solar flare. Bottom: Soft X-ray flux observed with SXT is overlaid in plus signs on the GOES flux that is subtracted from the flux level before the flare.

12 No. 2, 2003 X-RAY BRIGHT POINT NUMBER OVER SOLAR ACTIVITY CYCLE 1073 Fig. 13. X-ray flux ratio of SXT Be filter observations to the low channel (1 8 Å) GOES X-ray flux that is subtracted from its flux prior to the flare. The ratio at the peak of the GOES flux is used, and the flares observed near the disk center (within 0.5 R ) are selected. (a) Flux ratio of SXT/GOES-7 and (b)of SXT/GOES-8 as a function of time. The data points are fitted by a linear function of time, and the result of the least squares method is shown in solid lines. (c) Histograms of the SXT/GOES flux ratio clearly show an increase of the SXT response between the and periods. (d f ) Cases of the vignette correction for panels (a c). the field of view, and Figure 13c (13f ) is a histogram of flares as a function of the flux ratio before (after) the correction. We call the correction vignette correction here. The change of SXT flux from the beginning of Yohkoh observation before the filter failure to its end is 26% 28% when we assume that the GOES flux level is the same between GOES-7 and GOES-8. There are flares that are observed with both GOES-7 and GOES-8, and the flux ratio of GOES-7/GOES-8 is Thus, we conclude that the change of SXT flux for X-rays over the mission is 12% 14% at most. Since an expected change is 10% 12%, which is estimated from the SXT effective area and model spectra under an assumption that the whole of the prefilter in a single sector is lost in each filter failure, the change of SXT flux is mostly explained by a change of its effective area originating from the change of prefilter condition. Thus, we regard the rest of the components in the SXT sensitivity, which are the mirror reflectance and CCD efficiency, to be constant in the present study for simplicity. However, this argument is not applicable at the CCD portion near the east and west limbs, where drops of sensitivity about the 10% level are observed in the visible-light images through the diffuser filter. Aschwanden, M. J., Nightingale, R. W., Tarbell, T. D., & Wolfson, C. J. 2000, ApJ, 535, 1027 Brown, D. S., Parnell, C. E., Deluca, E. E., Golub, L., & McMullen, R. A. 2001, Sol. Phys., 201, 305 Cattaneo, F. 1999, ApJ, 515, L39 Davis, J. M. 1983, Sol. Phys., 88, 337 Davis, J. M., Golub, L., & Krieger, A. S. 1977, ApJ, 214, L141 Dere, K. P., Landi, E., Mason, H. E., Monsignori Fossi, B., & Young, P. R. 1997, A&AS, 125, 149 Giovanelli, R. G. 1982, Sol. Phys., 77, 27 Golub, L., Davis, J. M., & Krieger, A. S. 1979, ApJ, 229, L145 Golub, L., Harvey, K. L., Herant, M., & Webb, D. F. 1989, Sol. Phys., 124, 211 Golub, L., Krieger, A. S., Harvey, J. W., & Vaiana, G. S. 1977, Sol. Phys., 53, 111 Golub, L., Krieger, A. S., Silk, J. K., Timothy, A. F., & Vaiana, G. S. 1974, ApJ, 189, L93 Golub, L., Krieger, A. S., & Vaiana, G. S. 1976, Sol. Phys., 50, 311 Habbal, S. R., Dowdy, J. F., & Withbroe, G., L. 1990, ApJ, 352, 333 Habbal, S. R., & Harvey, K. L. 1988, ApJ, 326, 988 Hara, H. 1996, Ph.D. thesis, Univ. Tokyo. 1997, Adv. Space Res., 20, 2279 Hara, H., Tsuneta, S., Acton, L. W., Bruner, M. E., Lemen, J. R., & Ogawara, Y. 1994, PASJ, 46, 493 REFERENCES Harvey, K. L. 1985, Australian J. Phys., 38, , Ph.D. thesis, Univ. Utrecht. 1996, in ASP Conf. Ser. 111, Magnetic Reconnection in the Solar Atmosphere, ed. R. D. Bentley & J. T. Mariska (San Francisco: ASP), 9 Harvey, K. L., Harvey, J. W., & Martin, S. F. 1975, Sol. Phys., 40, 87 Kundu, M., Schmahl, E. J., & Fu, Q.-J. 1988, ApJ, 325, 905 Livi, S. H. B., Wang, J., & Martin, S. F. 1985, Australian J. Phys., 38, 855 Martin, S. F. 1988, Sol. Phys., 117, , in IAU Symp. 138, Solar Photosphere: Structure, Convection, and Magnetic Fields, ed. J. O. Stenflo (Dordrecht: Kluwer), 129 Martin, S. F., & Harvey, K. L. 1979, Sol. Phys., 64, 93 Mewe, R., Gronenschild, E. H. B. M., & van den Oord, G. H. J. 1985, A&AS, 62, 197 Mewe, R., Lemen, J. R., & van den Oord, G. H. J. 1986, A&AS, 65, 511 Nakakubo, K., & Hara, H. 2000, Adv. Space Res., 25, 1905 Nitta, N., Bastian, T. S., Aschwanden, M. J., Harvey, K. L., & Strong, K. T. 1992, PASJ, 44, L167 Pres, P., & Phillips, K. J. H. 1999, ApJ, 510, L73 Sattarov, I., Pevtsov, A. A., Hojaev, A. S., & Sherdonov, C. T. 2002, ApJ, 564, 1042 Schrijver, C. J., Title, A., Van Ballegooijen, A. A., Hagenaar, H. J., & Shine, R. A. 1997, ApJ, 487, 424 Schüssler, M. 1980, Nature, 288, 150

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