Open magnetic fields and the solar cycle

Models of open magnetic structures on the Sun are presented for periods near solar minimum (CR 1626–1634) and near solar maximum (CR 1668–1678). Together with previous models of open magnetic structures during the declining phase (CR 1601–1611) these calculations provide clues to the relations between open structures, coronal holes, and active regions at different times of the solar cycle. Near solar minimum the close relation between active regions and open structures does not exist. It is suggested that near solar minimum the systematic emergence of new flux with the proper polarity imbalance to maintain open magnetic structures may occur primarily at very small spatial scales. Near solar maximum the role of active regions in maintaining open structures and coronal holes is strong, with large active regions emerging in the proper location and orientation to maintain open structures longer than typical active region lifetimes. Although the use of He I 10830 Å spectroheliograms as a coronal hole indicator is shown to be subject to significant ambiguity, the agreement between calculated open structures and coronal holes determined from He I 10830 Å spectroheliograms is very good. The rotation properties of calculated open structures near solar maximum strongly suggest two classes of features: one that rotates differentially similar to sunspots and active regions and a separate class that rotates more rigidly, as was the case for single large coronal holes during Skylab.     

High-resolution observations of the polar magnetic fields of the sun

High-resolution magnetograms of the solar polar region were used for the study of the polar magnetic field. In contrast to low-resolution magnetograph observations which measure the polar magnetic field averaged over a large area, we focused our efforts on the properties of the small magnetic elements in the polar region. Evolution of the filling factor - the ratio of the area occupied by the magnetic elements to the total area - of these magnetic elements, as well as the average magnetic field strength, were studied during the maximum and declining phase of solar cycle 22, from early 1991 to mid-1993.We found that during the sunspot maximum period, the polar regions were occupied by about equal numbers of positive and negative magnetic elements, with equal average field strength. As the solar cycle progresses toward sunspot minimum, the magnetic field elements in the polar region become predominantly of one polarity. The average magnetic field of the dominant polarity elements also increases with the filling factor. In the meanwhile, both the filling factor and the average field strength of the non-dominant polarity elements decrease. The combined effects of the changing filling factors and average field strength produce the observed evolution of the integrated polar flux over the solar cycle.We compared the evolutionary histories of both filling factor and average field strength, for regions of high (70°–80°) and low (60°–70°) latitudes. For the south pole, we found no significant evidence of difference in the time of reversal. However, the low-latitude region of the north pole did reverse polarity much earlier than the high-latitude region. It later showed an oscillatory behavior. We suggest this may be caused by the poleward migration of flux from a large active region in 1989 with highly imbalanced flux.     

Does the Poleward Migration Rate of the Magnetic Fields Depend on the Strength of the Solar Cycle?

We present the pattern of the polar magnetic reversal for cycle 23 derived from H synoptic charts and have also included the reversals of the earlier cycles 18–22 for comparison. At the beginning of a new cycle (i.e., soon after the polar reversal) the zonal boundaries of unipolar magnetic regions of opposite polarities (seen as filament bands on the synoptic charts) appear close to and on either side of the equator continuing through the years of minimum indicating the onset of the cancellation of flux at these low latitudes. The cycle thus starts with cancellation of flux close to the equator and ends with the polar reversal or flux cancellation near the poles. The filament bands just below the polemost ones migrate and reach latitudes 35°–45° by the time of polar reversal and become the polemost, once the polar reversal has taken place. During the years of minimum that follow, these filament bands remain more or less stagnant at the latitudes 35°–45° except for occasional slow migration towards the equator. The migration to the poles starts at a low speed of 3 m s^–1 only when the spot activity has risen to a significant level and then it accelerates to 30 m s^–1 at the peak of the activity. It takes 3–4 years for the polemost bands to reach the poles moving at these high speeds. We quantify this possible cause and effect phenomenon by introducing the concept of the `strength of the solar cycle' and represent this by either of a set of three parameters. We show that the velocity of poleward migration is a linear function of the `strength of the solar cycle'.     

Long-Term Radio Scintillation Variations in the Circumsolar Plasma

Long-term scintillation measurements of the solar wind formation zone at solar elongations ranging from 1°–8° (Sun impact parameters: 4–30 R ) were recorded using the water maser source IRC-20431 at the wavelength =1.35 cm during its annual solar occultations in December 1981–1998. Dramatic changes in the spatial dependence of the scintillation index were recorded over the course of the 11-year solar cycle. Markedly diminished scattering, attributed to a pronounced heliolatitude effect, was observed at the closest solar approach distances in the years around solar activity minimum. From parallel investigations of the solar magnetic field structure it was determined that the field strength at the source of the solar wind streamlines is the governing factor for the solar wind acceleration process. Particularly apparent in the scintillation data during solar activity minimum is the increasing role of the polar coronal holes with their associated open magnetic field structure. The dependence of the solar scattering intensity on heliolatitude fades in the years of high solar activity as the level of scintillations increases at polar latitudes.     

The strength of the Sun's polar fields

The magnetic field strength within the polar caps of the Sun is an important parameter for both the solar activity cycle and for our understanding of the interplanetary magnetic field. Measurements of the line-of-sight component of the magnetic field generally yield 0.1 to 0.2 mT near times of sunspot minimum. In this paper we report measurements of the polar fields made at the Stanford Solar Observatory using the Fe i line 525.02 nm. We find that the average flux density poleward of 55° latitude is about 0.6 mT peaking to more than 1 mT at the pole and decreasing to 0.2 mT at the polar cap boundary. The total open flux through either polar cap thus becomes about 3 × 10¹⁴ Wb. We also show that observed magnetic field strengths vary as the line-of-sight component of nearly radial fields.     

Sector Structure, Rotation, and Cyclic Evolution of Large-Scale Solar Magnetic Fields

Auto-correlation analysis was performed using digitized synoptic charts of photospheric magnetic fields for the past three solar activity cycles (1965–1994). The obtained correlograms were used to study the rotation and the zonal-sector structure of large-scale solar magnetic fields all over the observable region of heliolatitudes in various phases of solar activity. It is shown that the large-scale system of solar magnetic fields is rather complex and comprises at least three different systems. One is a global rigidly rotating system. It determines the cyclic variation of magnetic fields and is probably responsible for the behavior of magnetic fields in the polar zones. Another is a rigidly rotating 4-sector structure in the central (equatorial and mid-latitude) zone. The third is a differentially rotating system that determines the behavior of the LSSMF structure elements with a size of 30–60° and less. This one is the most noticeable in the central zone and absent in the polar zones. Various cyclic and rotation parameters of the three field structures are discussed.     

The differential rotation of the corona as indicated by coronal holes

The rotation of the corona can be determined either directly by using Doppler methods or indirectly by using tracers, i.e., structures within the corona. In this study the rotational characteristics of the corona are determined using coronal holes as tracers, for the period 1978–1991. The coronal data used here are from an atlas of coronal holes mapped in Hei 10830 data. A comparison is made between our results and previous determinations of the coronal rotation rate, e.g., by Sime (1986), using white-light K-coronameter observations, by Timothy, Krieger, and Vaiana (1975), using soft X-ray observations, and by Shelke and Pande (1985) and Navarro-Peralta and Sanchez-Ibarra (1994), using Hei 10830 data. For the atlas of coronal holes used in this study the nature of the coronal hole distributions in number and latitude, in yearly averages, has been determined. These distributions show that at solar minimum the polar coronal holes dominate and the few non-polar holes are confined to a narrow band near the equator. At solar maximum, however, mid-latitude coronal holes dominate, with a large spread in latitudes. Given these distributions we consider the differential rotation data only as an average over a solar cycle. This removes spurious effects caused by having only a small number of coronal holes contributing to the results, or by having a narrow latitude band for the observations, thus limiting the results to that narrow latitude band. By considering these coronal holes as tracers of the differential rotation we show that the mid-latitude corona rotates more rigidly than the photosphere, but still exhibits significant differential rotation, with an equatorial rate of 13.30 ± 0.04° day^–1, and at 45° latitude a rate of 12.57 ± 0.13° day^–1. These results are comparable, within errors, to the Sime (1986) results which have an equatorial rate of approximately 13.2 ± 0.2° day^–1 and a rate of approximately 12.9 ± 0.3° day^–1 at 45° latitude.     

Unified theory of the interplanetary magnetic field

A simple model is used to present a unified picture of the polarity pattern of the interplanetary magnetic field observed during the solar cycle. Emphasis in this paper is on the field near solar maximum. The heliographic latitude dependence of the dominant polarity of the interplanetary magnetic field is explained in terms of weak poloidal (dipolar) field sources in the sun's photosphere. Unlike the Babcock theory, the author hypothesizes that the dipolar field exists at equatorial latitudes (0–20°), too, (as well as in polar regions) and that the major source of the interplanetary magnetic field observed near the ecliptic plane is the dipolar field from equatorial latitudes. The polarity of the interplanetary field data taken in 1968 and in the first half of 1969 near solar maximum may possibly be explained in terms of a depression of the dipolar field boundary in space. The effect on the solar wind of the greater activity in the northern hemisphere of the sun that existed in 1968 and in the first half of 1969 is believed responsible for this hypothesized depression, especially near solar maximum, of the plane separating the + and - dipolar polarity below the solar equatorial plane in space. Predictions are made concerning the interplanetary field to be observed near the ecliptic plane in each portion of the next solar cycle.     

Solar differential rotation determined by polar crown filaments

The rotation rates obtained by tracing 124 polar crown filaments are presented in comparison with previous results. Higher filament rotation rate in polar regions was detected and discussed in terms of the various phenomena such as: the projection effect due to the height of measured tracers, the connection of polar filaments with the magnetic field patterns which show an increase of the rotation rate at high latitudes, rigid rotation of polar filaments which form pivot points, and eventual change of the differential rotation law during the cycle. However, when the height correction for an average height of 1% of the solar radius is applied, the filament rotation rate in polar regions decreases. Then the rotation law becomes: () = 14.45 – 0.11 sin² – 3.69 sin⁴ (° day^–1, sidereal).     

The Evolution of the Sun's Open Magnetic Flux – II. Full Solar Cycle Simulations

In this paper the origin and evolution of the Sun's open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1–2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun's open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested.     

Some results of a statistical analysis of the S-component of solar radio emission

A statistical treatment of the mean daily solar radio flux between 9400 and 1000 MHz (cm-region) for two solar cycles leads to the following results: No differences have been found between the synodic rotation rates T _mon calculated for different single frequency time series as a whole (rigid rotation of emitting regions). From a piece-wise time series analysis it is concluded that T _mon averaged over all observed frequencies and over times belonging to related years of the two cycles shows a well-expressed dependence on cycle with a maximum of 28.8d following 2 y after the activity minimum and a minimum of 27d shortly after polar magnetic field reversal. Discrete spectral lines with periods smaller than T _mon point on the existence of elementary longitudinal regions of extension between 25° and 33°. The observed facts would support a relation between the sources of the large-scale magnetic field and the S-component.     

High-Resolution Studies of the Solar Polar Magnetic Fields

We present high-resolution studies of the solar polar magnetic fields near sunspot maximum in 1989 and towards sunspot minimum in 1995. We show that, in 1989, the polar latitudes were covered by several unipolar regions of both polarities. In 1995, however, after the polar field reversal was complete, each pole exhibited only one dominant polarity region.Each unipolar region contains magnetic knots of both polarities but the number count of the knots of the dominant polarity exceeds that of the opposite polarity by a ratio of order 4:1, and it is rare to find opposite polarity pairs, i.e., magnetic bipoles.These knots have lifetimes greater than 7 hours but less than 24 hours. We interpret the longitudinal displacement of the knots over a 7-hour period as a measure of the local rotation rate. This rotation rate is found to be generally consistent with Snodgrass' (1983) magnetic rotation law.In an attempt to obtain some insight into the operation of the solar dynamo, sketches of postulated subsurface field configurations corresponding to the observed surface fields at these two epochs of the solar cycle are presented.     

Magnetic field rotation at high solar latitudes

Measurements of the rotation rate of polar magnetic features during 1974–76 lead to a significantly slower rotation rate than that found earlier for polar faculae in 1951–54. Similarly, the rotation rate of these features is slower than the Doppler-determined rate at polar latitudes or the rotation rate of polar filaments. It is suggested that the strong latitude rotation gradient in the subsurface magnetic flux tubes which is implied by these results may presage a very active solar maximum for cycle 21.     

Cyclic variations of the polar coronal hole

The extension of the polar coronal holes has been studied for four cycles (1940–1978), using the observations of the corona line 530.3 nm. For about 7 years of each cycle, including sunspot minimum, the polar hole exists permanently and has a diameter of about 40° or even more. For about 3 years around sunspot maximum no polar hole does exist (Figure 5). The boundary of the hole is flanked at a distance of 10° by the polar zone of the corona and at one of 20° by that of the prominences. In the polar caps, so far they are occupied by the holes, polar photospheric faculae and the well-known plumes of the polar corona are found, and the polar crown of prominences, encircling the polar hole, is the belt where the reversal of the magnetic polarity takes place.     

East-west inclination of large-scale photospheric magnetic fields

Sixteen years of WSO magnetogram data have been studied to determine the solar cycle variation and latitude dependence of the east-west inclination of photospheric magnetic field lines. East-west inclination is here defined as the angle between a field line and its local radial vector, as projected onto the plane of the latitude and line of sight. Inclination is determined by a least-squares fit of observed magnetic fields to a simple projection model, and is found to depend on polarity and to change with the solar cycle. Leading and following polarities are tipped towards each by about 9° and have an overall net tilt in the direction of rotation (to the west) of 0.6°. New cycles are seen to begin at high latitudes and to grow through the lower latitudes over approximately 5 years, providing evidence for an extended cycle length of 16–18 years.     

Polar Coronal Holes During Cycles 22 and 23

The National Solar Observatory/Kitt Peak synoptic rotation maps of the magnetic field and of the equivalent width of the He i 1083 nm line are used to identify and measure polar coronal holes from September 1989 to the present. This period covers the entire lifetime of the northern and southern polar holes present during cycles 22 and 23 and includes the disappearance of the previous southern polar coronal hole in 1990 and and formation of the new northern polar hole in 2001. From this sample of polar hole observations, we found that polar coronal holes evolve from high-latitude (60° ) isolated holes. The isolated pre-polar holes form in the follower of the remnants of old active region fields just before the polar magnetic fields complete their reversal during the maximum phase of a cycle, and expand to cover the poles within 3 solar rotations after the reversal of the polar fields. During the initial 1.2–1.4 years, the polar holes are asymmetric about the pole and frequently have lobes extending into the active region latitudes. During this period, the area and magnetic flux of the polar holes increase rapidly. The surface areas, and in one case the net magnetic flux, reach an initial brief maximum within a few months. Following this initial phase, the areas (and in one case magnetic flux) decrease and then increase more slowly reaching their maxima during the cycle minimum. Over much of the lifetime of the measured polar holes, the area of the southern polar hole was smaller than the northern hole and had a significantly higher magnetic flux density. Both polar holes had essentially the same amount of magnetic flux at the time of cycle minimum. The decline in area and magnetic flux begins with the first new cycle regions with the holes disappearing about 1.1–1.8 years before the polar fields complete their reversal. The lifetime of the two polar coronal holes observed in their entirety during cycles 22 and 23 was 8.7 years for the northern polar hole and 8.3 years for the southern polar hole.     

The peculiarities of rotation of the solar polar regions

The sidereal rotation rate of the high-latitude solar regions is examined using long-lived photospheric polar faculae. The observations were carried out with the photoheliograph of Kislovodsk Mountain Station of the Pulkovo Observatory from 1982 to 1986. The following facts have been established: (a) There is a differential rotation of the polar faculae close to the maximum of solar activity, while the amount of latitude gradient of solar rotation decreases towards the sunspot minimum; (b) small differences of rotation in the northern and southern hemispheres of the Sun are observed; (c) some deviations of differential rotation curves constructed for each Carrington rotation from the mean curve of differential rotation are revealed. The total amplitude of the maximum positive and negative excesses is about 40–50 m s^–1. The positive surplus velocities of solar rotation (the amplitude of which is about 20–25 m s^–1) move in the form of a wave from heliographic latitudes 40° with a velocity of 1.6 m s^–1. The latitude width of this flow is B 15°. This wave of abnormally high velocity starts in the year of minimum solar activity and reaches the pole 11 years later. The picture is symmetrical relative to the equator.     

The Green Corona and Magnetic Fields

We present results of a study of the green corona (530.3 nm, Fexiv) and photospheric magnetic fields over the period 1976–1999 when both quantities were observed by ground-based observatories. By comparing both the limb green-line intensities and photospheric magnetograms we have found a relation between the strength of magnetic field and coronal intensities. This relation enables us to extend solar surface magnetic fields since 1976 back to 1939. From 1947 to 1992 the magnetic field strength grew at the cycle maxima by a factor of 1.5–2. On the other hand, both the green corona intensity and magnetic field strength in the present cycle are smaller compared to cycle 22, by a factor of 2. No relationship was found between the green corona intensities and magnetic field polarity as was previously supposed. Behavior for the green corona intensities is different between high-latitude and mid-latitude regions, and this break occurs at the heliographic latitude of ± 45°. Homogeneous coronal data set cannot be directly used to derive `the tilt angle', even though some similarities between the green coronal holes, poleward branches in the green corona and prominences and the tilt angle can be found.     

On the relationship between polar faculae and large-scale magnetic field

We investigate a latitude–time distribution of polar faculae observed at Ussuriysk Observatory in years 1966–1986. The distribution is compared with the longitude-averaged (zonal) magnetic field of the Sun calculated from the data obtained at Mount Wilson Observatory in the years 1966–1976, and at Kitt Peak National Observatory during the period from 1976 to 1985. We found that slow, poleward-directed migration of the polar faculae zones occurring during the course of the solar cycle is not a continuous process, but it contains several episodes of appearance and fast poleward drift of new zones of polar faculae. At the rising phase of the solar cycle, new zones of polar faculae appear at latitudes as low as 40°, but the ones observed during the declining phase of the solar cycle originate at higher latitudes of 50–55°. Such episodes of appearance and fast migration of the polar faculae zones are associated with the poleward-directed streams of magnetic field originated at low latitudes. Moreover, we found some evidence for existence of an additional component of the polar faculae activity that reveals an equatorward migration during the course of the solar cycle. We also investigated a relationship between the number of polar faculae, n, and absolute magnetic flux _z of the zonal mode of the solar magnetic field. We found that within the polar zones of the Sun, substantial correlation between temporal variations of n and _z takes place both on the time scale of the solar cycle and on a shorter time scale of 2–4 years. The relationship between the number of polar faculae and magnetic flux may be approximated by a linear dependence n=0.12_z (where _z is expressed in 10²¹ Mx), except for time interval 1977 through 1980 for which the factor of proportionality is found to have a systematically larger value of 0.20.     

Latitudinal Distribution of Polar Faculae

The distribution of polar faculae with respect to latitude is investigated, using data obtained at the Ussuriysk Observatory during the years 1963–1994. To correct the data for the effect of visibility, a visibility function of polar faculae is derived. Corrected surface density of polar faculae is calculated as a function of latitude and time. During most part of each solar cycle, polar faculae exhibit pronounced concentrations at high latitudes with maxima of the surface density located near the poles. Such concentrations of polar faculae (below referred to as `polar condensations') are formed after a lapse of 1–2 years from the polar magnetic field reversals, and then they persist for 7–9 years, until the high-latitude magnetic fields again start to reverse. During several years after the sunspot minima, the polar condensations co-exist with the new latitudinal belts of polar faculae which appear at middle latitudes and then migrate toward the poles. To describe the evolution of the polar condensations quantitatively, the polar faculae density n at latitudes above 60° has been approximated by means of the power law nn ₀ cos^m where is polar angle. The parameters n ₀ and m both are found to vary during the course of the solar cycle, reaching maximum values near or shortly after the minimum of sunspot activity. At the minimum phase of the solar cycle, on average, the surface density of polar faculae varies as cos¹⁴. In addition to the 11-yr variation, the latitude–time distribution of polar faculae exhibits short-term variations occurring on the time scale of 2–3 years.