The Astrophysical Journal, 669:636Y 641, 2007 November 1 # 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A.
LATITUDE DISTRIBUTION OF POLAR MAGNETIC FLUX IN THE CHROMOSPHERE NEAR SOLAR MINIMUM N.-E. Raouafi, J. W. Harvey, and C. J. Henney National Solar Observatory, 950 North Cherry Avenue, Tucson, A Z 85719;
[email protected] Received 2007 June 4; accepted 2007 July 2
ABSTRACT The distribution of magnetic flux elements as a function of latitude in the polar solar caps at a time close to solar cycle minimum is explored. High-sensitivity line-of-sight magnetograms acquired by the Synoptic Optical Long-term Investigations of the Sun (SOLIS) vector spectromagnetograph (VSM) in the chromospheric line Ca ii 854.2 nm are utilized. The area density distribution of the magnetic flux averaged over months is found to decrease close to the solar poles. This trend is more pronounced when considering only flux elements with relatively large size (larger than 5 00 ; 5 00 ). The flux density of the latter is relatively flat from the edge of the polar cap up to latitudes of 75 Y80 and decreases by more than 50% up to the solar pole. The density of smaller flux features is more uniformly distributed. Although the density decrease is still present, it is less pronounced. Hence, we believe there are two populations of flux elements in the polar caps. The small flux elements are probably produced uniformly across the polar area, in contrast to the large flux elements that are the product of magnetic fields of decaying active regions. The latter are concentrated by solar convection and carried up to high latitudes by differential rotation and meridional circulation. This result is important in studying meridional flows that transport the magnetic flux from lower to higher solar latitudes resulting, in particular, to the solar-cycle-related polar reversal. It is also of importance in studying polar structures contributing to the fast solar wind, such as polar plumes. Subject headingg s: line: formation — methods: statistical — polarization — Sun: activity — Sun: atmosphere — Sun: chromosphere — Sun: magnetic fields
1. INTRODUCTION
related pseudoperiodic magnetic polarity changes of the polar caps. The polar caps are prominent and almost permanently present from the minimum up to the maximum of the solar activity cycle, when they disappear briefly to reappear with the opposite magnetic polarity. This process is known as the polar magnetic reversal (Bilenko 2002). BB55 suggested that the poleward migration of trailing polarity flux from bipolar magnetic regions acts to annihilate and reverse the Sun’s polar fields over a sunspot cycle. Later on, Babcock (1961) speculated about meridional flows as the main transport process to explain the observed poleward motion of flux from the sunspot belts. Leighton (1964) considered only the effect of supergranular diffusion with relatively high diffusion rates (770Y1540 km 2 s1; see Wang et al. 1989) driven by the field gradient, together with the tilted Hale orientation of emerging bipolar regions (Hale et al. 1919), and found that this would lead to polar field reversal without the need for additional flux transport processes (i.e., meridional flows). More recent simulations show that supergranule motion alone is not sufficient and leads to other manifestations that are not observed ( DeVore et al. 1984). Wang et al. (1989) invoked the diffusion of the leading polarity of emerging bipolar regions near solar minimum across the solar equator and the surplus of the trailing polarity flux being carried toward the poles by means of meridional flows. Webb et al. (1984) found that the process of polarity reversal and redevelopment of polar holes is discontinuous, occurring in 2 or 3 longitude bands and that there is a persistent asymmetry in these processes between the two hemispheres; the polarity reversal in the two hemispheres is offset by 6 months to 1.5 yr (see also Makarov et al. 1983; Harvey & Recely 2002). Fox et al. (1998), analyzing the reversal of the solar polar magnetic field in cycles 21 and 22, suggested that the polar reversal originates from global processes rather than from local magnetic flux annihilation. Babcock (1961)’s suggestion that meridional circulation transports magnetic flux from the low-latitude active region belts
The solar polar caps that are magnetically unipolar-dominated (as observed in the photosphere by Babcock & Livingston 1958; Babcock 1959; Howard 1972; Timothy et al. 1975; Harvey et al. 1982; Varsik et al. 1999) are among the most prominent features at the minimum of solar magnetic activity. Higher up in the corona, the funneling magnetic lines offorce spread out and fill a significant portion of the heliosphere, resulting in the streaming fast solar wind (Schwenn et al. 1979) and plasma heating (Schatzman 1949; Osterbrock 1961), and the physical processes laying behind that are still far from being completely understood. Despite the great importance of the solar polar areas for numerous solar and astrophysical phenomena (e.g., cosmic rays; see Nagashima & Morishita 1980a, 1980b), the polar caps are not sufficiently studied, because of observational and modeling challenges. This is due to the weakness of the polar magnetic fields (Grigor’ev 1988; Bogart et al. 1992; Varsik et al. 1999, 2002) and the solar geometry close to the limb, which makes their measurement difficult from the ecliptic plane (see Bilenko 2002), but mainly it is due to instrumental limitations in matters of sensitivity and accuracy. In order to get significant measurements of the polar magnetic field, instruments with high polarimetric sensitivity and resolution are needed to compensate for the weakness of the field, projection effects, and other difficulties. In addition, the solar poles are only partially observable from the ecliptic plane due to small values of B0 . Babcock & Babcock (1955, hereafter BB55) were the first to study solar large-scale magnetic fields, in particular the polar solar caps. It is widely believed that the large-scale solar magnetic field (and its variations resulting in the solar cycle) is the product of various physical mechanisms (i.e., differential rotation, meridional flows, supergranular diffusion) acting on decaying solar active regions (Leighton 1964; DeVore & Sheeley 1987; Sheeley et al. 1987; Bilenko 2002). BB55 also studied the solar-cycle636
LATITUDE DISTRIBUTION OF POLAR MAGNETIC FLUX poleward to the high latitudes of the Sun was observationally confirmed as the main flux transport process first by Howard (1974) and then by numerous other studies (Duvall 1979; Cameron & Hopkins 1998; Snodgrass & Dailey 1996; Durrant et al. 2004). The flow magnitude is estimated to range from 10 m s1 to few times 10 m s1 from Doppler measurements (Duvall 1979; LaBonte & Howard 1982; Ulrich et al. 1988) and from magnetic tracers (Howard & LaBonte 1981; Topka et al. 1982; Wang et al. 1989). It is noteworthy that meridional flows are only traceable up to midsolar latitudes, because of the limitations of helioseismic measurements beyond this limit. However, it is of capital importance to obtain additional constraints on these flows up to high latitudes close to the solar poles. This would be of great use for models dealing with flux transport and the solar dynamo. Svalgaard et al. (1978) and Wang & Sheeley (1988) studied the distribution of the polar magnetic flux using Wilcox Solar Observatory measurements during the 1970s and 1980s, respectively. They obtained colatitude distributions of the form cos n , where n ¼ 8. In addition, from the observed sizes of polar coronal holes around sunspot minimum, Nash et al. (1988) and Sheeley et al. (1989) inferred values of the flux concentration index n in the range 6Y8. Raouafi et al. (2006a, 2006b, 2007) studied the plasma dynamic properties in the coronal polar plumes by means of forward modeling. They found that modeled spectroscopic emissions from polar coronal plumes rooted close to the solar poles do not match the observed coronal spectra by the Ultraviolet Coronagraph Spectrometer ( UVCS; Kohl et al. 1995) on board the Solar and Heliospheric Observatory (SOHO; Domingo et al. 1995). They speculated that polar plumes would preferentially be based within the polar holes about 10 away from the solar poles. It is well known from previous studies that polar plumes are the product of magnetic reconnection of a relatively large unipolar flux element with an emerging opposite polarity. Thus, the study of the polar magnetic flux distribution would yield insights and clues about the distribution of the coronal structures, such as polar plumes. In the present paper, we confirm Raouafi et al.’s results through the study of the polar flux distribution as a function of latitude and suggest the probable effects on solar phenomena that are at the origin of such a distribution. Saito (1958) used eclipse observations and found a similar distribution of the socalled polar rays. The paper is organized as follows. A brief overview of the SOLIS VSM observations and an analysis of the data are given in x 2. Results and discussion are given in x 3. Conclusions and perspective are given in x 4. 2. OBSERVATIONS AND DATA ANALYSIS The Synoptic Optical Long-term Investigations of the Sun (SOLIS) project is one of the most recent facilities dedicated for studying solar magnetic fields. SOLIS is designed to help understand the origin of the solar cycle (complementing helioseismic studies) through the study of different aspects of the Sun’s magnetic activity at different scales (e.g., solar cycle, dynamo, turbulent magnetic fields, irradiance changes, differential rotation). One of the main goals of SOLIS is to develop methods and techniques for solar activity forecast (e.g., flares, coronal mass ejections). The vector spectromagnetograph ( VSM ) produces high-sensitivity magnetograms using photospheric and chromospheric spectral lines characterized by their suitable Zeeman-induced polarization for measuring the magnetic field, in addition to a chromospheric line that serves as a proxy for coronal structure ensuring observational continuity at different heights in the solar atmosphere.
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Fig. 1.—Typical chromospheric (Ca ii 854.2 nm) LOS magnetogram from SOLIS recorded on 2006 September 21st. Note the good visibility of magnetic flux elements everywhere on the solar disk, in particular in the high-latitude polar caps.
It is difficult to infer the distribution of magnetic flux near the poles using photospheric spectral lines. The radial component of the photospheric field does not produce a large line-of-sight (LOS) signal, and the transverse field measurements are not sufficiently sensitive without very high spatial resolution. In an effort to avoid this problem, we use chromospheric (Ca ii 854.2 nm) LOS magnetograms from SOLIS VSM to study the latitude distribution of the unsigned magnetic flux in the polar regions. The use of the unsigned magnetograms is justified by the fact that the polar caps are dominated by one polarity each. The opposite polarity in these areas contributes little to the total flux and is represented by relatively small diffuse flux elements. The Ca ii 854.2 nm magnetograms have an advantage with respect to the photospheric ones close to the solar limb because of the canopy structure of the magnetic field in the chromosphere, which provides a better signal in the LOS field close to the limb. It is noteworthy that the photospheric LOS magnetograms from the same instrument are of equally good quality but near the limb the flux signal is mixed with a ubiquitous dynamic horizontal field ( Harvey et al. 2007) that is not as strong in the chromosphere. Figure 1 illustrates a typical LOS magnetogram in the Ca ii 854.2 nm line recorded on 2006 September 21. Note the visibility of the magnetic elements demonstrating the capability of the SOLIS VSM instrument to sense the magnetic field everywhere on the solar disk. It is noteworthy that the high signal-to-noise ratio in the polar regions up to the polar limb makes SOLIS a suitable instrument to study polar fields in the absence of out-of-ecliptic measurements. In order to normalize the visibility of the magnetic features close to the limb (which varies across the disk due to our changing view angle of the canopy structure), we apply a radial correction displayed in Figure 2. The radial correction is determined under the assumption that an average of a month or more worth of magnetograms properly corrected for varying visibility would show a relatively uniform distribution of quiet-Sun (far away from active regions) magnetic flux in the east-west direction. This empirical correction naturally enhances the flux elements observed near the
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Fig. 2.—Radial correction applied to the magnetogram to normalize the visibility of magnetic features near the solar limb.
limb. However, it also enhances the noise in the same regions. In order to avoid that, we impose a lower threshold on the initial magnetograms. We adopt the latter throughout this analysis. We set to zero all magnetic field measurements less than a threshold, which is in the present case is 5 G. This also helps make the determination of the flux elements’ boundaries easy. Magnetic flux elements are identified and located using simple closed-structure recognition methods. One of the advantages in using such methods is that one can set a lower limit on the size
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of the flux element. Features with sizes smaller than this size limit are not selected (see Figs. 3Y4). We can thus study the distribution offlux elements as a function of their sizes. An average location in terms of latitude is determined for every selected feature, and a histogram of the distribution of the selected elements as a function of latitude is built. In order to remove any effect of the surface area on the determined latitude flux distribution, we normalize every obtained histogram by the surface area distribution corresponding to each latitude bin. For any date, the solar geometry in terms of the polar axis tilt (B0 angle) is taken into account in computing the surface elements and the corresponding latitude map. This procedure is repeated for every magnetogram recorded in the time interval 2006 SeptemberYDecember. This period has been chosen because one of the solar poles is best seen and also the polar caps were well developed, in particular the northern one. Daily distribution histograms are noisy and are averaged for every month and for the whole period of time considered here. To test the efficiency of the radial correction we applied, we divide every magnetogram into three sectorial sections. The central section extends between 35 in central meridian distance and for all latitudes up to the solar pole, as shown by the darkgray area in the top panel of Figure 5. The signal-to-noise ratio in this central area is significantly better than in the sides areas (lightgray regions in the same figure) that form the second section. For a good radial correction the distribution of flux elements as a function of latitude in both section should show similar behavior. The bottom panel of Figure 5 displays the normalized distributions of the flux elements as a function of latitude. The two distributions clearly show similar variations. The radial correction we apply works reasonably well, although the signal near
Fig. 3.—Top: Unsigned magnetogram for the north polar region for 2006 October 27. Bottom: Flux elements selected by the method we use here to study the latitude flux distribution. The minimum size of flux element to be chosen in the present case is 5 ; 5 pixels2. Note that magnetic fields below 5 G were set to zero before the radial correction was performed.
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Fig. 4.—Same as Fig. 3, but for minimum size of flux element of 4 ; 2 pixels 2. Lots of the small elements are now selected, which is not the case in Fig. 3.
the limb is always of less quality than in the central part of the solar disk. 3. RESULTS AND DISCUSSION
Fig. 5.—Top: Sketch of the northern part of the solar disk divided into three sections to test the radial correction. Bottom: Normalized flux distribution as a function of latitude of the central section (solid curve) and lateral ones (dashed curve) of the top panel, respectively. The two distributions are relatively similar, showing that the radial correction is reasonable.
The monthly averaged surface-normalized density distributions of the unsigned polar flux elements as a function of latitude for 2006 September (solid line), October (dotted line), November (dashed line), and December (dot-dashed line) are shown in Figure 6. Only data for the north polar cap are presented. The thick long-dashed curve shows an average of the monthly histograms of September, October, and November. The December data are not taken into account in the average because of the relatively low counts, probably due to the solar geometry (B0 angle). These histograms are obtained by imposing a minimum square surface threshold on the features of 5 ; 5 pixels (5:65 00 ; 5:65 00 ) to select only relative large flux elements. Figure 3 shows an example of a real magnetogram (top) and the result of the flux element selection. It is clear that most of the small magnetic features are not selected and large ones are. The flux element selection is evenly distributed across the polar cap. The number of the nonselected apparent elements is relatively small. This shows the success of the method we use. The different curves in Figure 6 show a relatively flat distribution of the magnetic flux from the edge of the polar cap up to latitudes of about 75 Y80 . At higher latitudes the flux distributions tend to drop significantly to a minimum close to the solar pole (the right edge of the same figure). The peaks in the solid and dotted histograms correspond to features that observed close to the pole during the months of September and October. Although these features present, the corresponding distributions show the decreasing tendency mentioned previously. The zero values in the December histogram above latitude of 83 are due to the fact that the solar axis started tilting away from the observed
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Fig. 6.—Average histograms of the magnetic flux distribution for features larger than 5 ; 5 pixels (see Fig. 3) as a function of latitude for the north polar cap for 2006 September (solid line), October (dotted line), November (dashed line), and December (dot-dashed line). The thick dashed curve is the average of the four previous ones. Note that in section where the histogram values are zero are not included in the average.
line of sight and also the rarity of flux elements near the pole. The obtained density distributions as a function of latitude show higher uniform values out of the 10 range from the solar pole. This suggests that relatively large flux concentrations are preferentially distributed away from the pole. The latitude flux distributions with smaller lower limit on the area of the features are displayed on Figure 7. The minimum size adopted in this case is 4 ; 2 pixels (4:52 00 ; 2:26 00 ). These distributions are very similar to the ones obtained with greater area threshold, with a difference that the flux density drop is not as important closer to the pole. This suggests that small magnetic flux elements are distributed relatively uniformly, and the drop in their distribution is not as large as for the large structures. The latter are preferentially distributed with high density away from the solar pole. This might also suggest that there are two populations of flux elements within the polar caps. Large flux elements are denser toward the edge of the caps, and this is probably due to the low-latitude flux of decaying active regions that is concentrated by solar convection and carried to high latitudes by differential rotation and meridional circulation. Small flux elements are, on the other hand, produced locally by uniformly distributed flux emergence across the polar caps, as for the rest of the solar disk. Previous studies mentioned earlier have shown a cosine distribution of the flux with a maximum at the solar poles and gently decreases toward low latitudes. These results were obtained from low-resolution observations recorded in the 1970s and 1980s. If one assumes that magnetic field strength is independent of the latitude location of the flux elements, the former results are not in agreement with the findings of this work. Although we are not addressing the average field strength distribution, it is of great importance to revisit this topic taking into account the much better quality of the present measurements of the solar magnetic field. This will be the subject of a subsequent paper. The flux distribution as a function of latitude has an impact on numerous solar phenomena such the location of fine coronal polar structures. Raouafi et al. (2007) built different numerical models to study the plasma dynamics in polar plumes. In all these models, which cover almost all the possible cases for the outflow velocity and turbulence of the plasma, they found that polar plumes rooted close to the pole give spectral signatures that
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Fig. 7.—Same as Fig. 6, but for flux elements larger than 4 ; 2 pixels, corresponding to selected features shown in Fig. 4.
are not observed in the solar corona. They concluded that polar plumes would preferentially be rooted more than about 10 from the pole. There is also observational evidence that the base of polar plumes, in particular bright ones, are relatively large magnetic flux areas dominated by one polarity (Saito & Tanaka 1957a, 1957b; Harvey 1965; Newkirk & Harvey 1968; Lindblom 1990; Allen 1994). The latter and Raouafi et al.’s findings would agree well with the picture we are drawing here on the density distribution of magnetic flux on the polar caps. This is more evident in the case where we consider relatively large flux elements. Our results also impact other inaccurately determined and less known solar phenomena, such as meridional circulation. Meridional flows are known now to be one of the main factors causing the inversion of the magnetic polarity of the poles from one solar cycle to the next. Together with supergranular diffusion, meridional flows bring the magnetic flux of decaying active regions from low-to-high latitudes causing the well-known polar magnetic reversal. Due to the flow signal weakness in Doppler measurements (Zhao & Kosovichev 2004; Haber et al. 2002) it is not well understood how this phenomenon operates at high latitudes and in particular close to the poles. The density distribution of the unsigned magnetic flux at the polar regions reported here suggests that the mechanisms responsible for the flux transport greatly diminish before reaching the poles. Such results would be of great importance for models dealing with flux transport and the solar dynamo. 4. CONCLUSION We used chromospheric LOS magnetograms from SOLIS to study the unsigned magnetic flux distribution near the north pole close to the solar minimum of activity. The magnetic data is recorded during the time interval spanning from 2006 SeptemberY December. The north pole data was chosen for two reasons: (1) the north polar cap was well developed during this period of time, and (2) the north pole was better visible than the southern one. Completeness was almost daily except for a few days, due to unsuitable observational conditions. We developed a method of recognizing magnetic flux elements with a tunable threshold size. Once the magnetic features of interest were selected, we determined the average location of each of them in terms of latitude. The distribution of these features was then computed as function of latitude. The histograms were normalized with respect to the surface area corresponding to each bin, taking into account the different solar geometrical parameters for the each magnetogram. The normalized
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histograms were then averaged for each month and for the whole period, respectively. We found that the density distribution of the magnetic flux elements within the northern polar cap observed during 2006 SeptemberYDecember has a relatively strong dependence on latitude. The flux distribution normalized to the surface of the polar cap is relatively flat up to latitudes of about 75 Y80 , where it drops significantly up to the solar pole. This result was confirmed for the whole period of observations considered here. There is also a relative difference in the distributions of flux elements of different sizes. Large flux elements show a preferential high density at low latitudes. We believe that the mechanisms responsible for the flux transport from low latitudes toward the solar poles are less efficient close to the poles. This means that the meridional circulation responsible for the flux transport slows before reaching the poles. Such a result would have a significant impact on the
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theories and models dealing with flux transport. These results also put important constraints on solar phenomena that are inaccurately (if at all) determined by other means, such as helioseismic studies that become inefficient at high latitudes.
The authors are grateful for A. Norton and S. K. Solanki for helpful discussions. We would like to thank an anonymous referee for constructive comments on the manuscript. The National Solar Observatory ( NSO) is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. SOLIS data used here are produced cooperatively by NSF/NSO and NASA/ LWS. N. E. R.’s work is supported by NSO and NASA grant NNH05AA12I.
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