The X-ray coronae of solitary late-type stars

For solar cycles 20 and 21, the longitudinal distribution of the D, G, and H-type solar flares which are related to the final phases of active region evolution, have been analysed for the northern and the southern hemispheres separately. One active zone has been found for D, G, and H-type flares, and one more active zone has been found for the H-type flares of the northern hemisphere for cycle 20. Two active zones have been found for the D and H-type flares of the northern hemisphere for cycle 21. Southern-hemisphere flares are concentrated in two active zones for cycle 20. The active zone in the northern hemisphere, which rotates with a synodic period of about 26.73 days, produced 30% of the examined D-type flares during cycle 20 and persisted in the same position during the two solar cycles, 20 and 21. The active zone in the southern hemisphere rotated with a synodic period of about 27.99 days. Only the active zone producing D-type flares persisted in the same position during the two solar cycles.     

The distribution of sunspots over the Sun

The distribution of the sunspots for the period 1967–1987 (solar cycles 20 and 21) is presented here. We find that the ±11–20° latitude belt is most prolific for the occurrence of various spot types irrespective of magnetic-field ranges. Furthermore, longitudinally sunspots occur most prolifically at six or more places on the Sun. Spatially 7–9 zones are present in each hemisphere (north or south) of the Sun where about 50% sunspots occur and occupy only about 4% area of the Sun. During the above cycles at least 5 flare zones were regularly present in each hemisphere. The existing models cannot explain these active zones on the Sun. Thus, the present analysis emphasizes the need for a new magnetic models of the Sun.     

Multifractality as a Measure of Complexity in Solar Flare Activity

In this paper we use the notion of multifractality to describe the complexity in Hα flare activity during the solar cycles 21, 22, and 23. Both northern and southern hemisphere flare indices are analyzed. Multifractal behavior of the flare activity is characterized by calculating the singularity spectrum of the daily flare index time series in terms of the Hölder exponent. The broadness of the singularity spectrum gives a measure of the degree of multifractality or complexity in the flare index data. The broader the spectrum, the richer and more complex is the structure with a higher degree of multifractality. Using this broadness measure, complexity in the flare index data is compared between the northern and southern hemispheres in each of the three cycles, and among the three cycles in each of the two hemispheres. Other parameters of the singularity spectrum can also provide information about the fractal properties of the flare index data. For instance, an asymmetry to the left or right in the singularity spectrum indicates a dominance of high or low fractal exponents, respectively, reflecting a relative abundance of large or small fluctuations in the total energy emitted by the flares. Our results reveal that in the even (22nd) cycle the singularity spectra are very similar for the northern and southern hemispheres, whereas in the odd cycles (21st and 23rd) they differ significantly. In particular, we find that in cycle 21, the northern hemisphere flare index data have higher complexity than its southern counterpart, with an opposite pattern prevailing in cycle 23. Furthermore, small-scale fluctuations in the flare index time series are predominant in the northern hemisphere in the 21st cycle and are predominant in the southern hemisphere in the 23rd cycle. Based on these findings one might suggest that, from cycle to cycle, there exists a smooth switching between the northern and southern hemispheres in the multifractality of the flaring process. This new observational result may bring an insight into the mechanisms of the solar dynamo operation and may also be useful for forecasting solar cycles.     

A new pattern for the north–south asymmetry of sunspots

We study the solar cycle evolution during the last 8 solar cycles using a vectorial sunspot area called the LA (longitudinal asymmetry) parameter. This is a useful measure of solar activity in which the stochastic, longitudinally evenly distributed sunspot activity is reduced and which therefore emphasizes the more systematic, longitudinally asymmetric sunspot activity. Interesting differences are found between the LA parameter and the more conventional sunspot activity indices like the (scalar) sunspot area and the sunspot number. E.g., cycle 19 is not the highest cycle according to LA. We have calculated the separate LA parameters for the northern and southern hemisphere and found a systematic dipolar-type oscillation in the dominating hemisphere during high solar activity times which is reproduced from cycle to cycle. We have analyzed this oscillation during cycles 16–22 by a superposed epoch method using the date of magnetic reversal in the southern hemisphere as the zero epoch time. According to our analysis, the oscillation starts by an excess of the northern LA value in the ascending phase of the solar cycle which lasts for about 2.3 years. Soon after the maximum northern dominance, the southern hemisphere starts dominating, reaching its minimum some 1.2–1.7 years later. The period of southern dominance lasts for about 1.6 years and ends, on an average, slightly before the end of magnetic reversal.     

Phase Relationship Between Sunspot Number, Flare Index and Solar Radio Flux

To understand better the variation of solar activity indicators originated at different layers of the solar atmosphere with respect to sunspot cycles, we carried out a study of phase relationship between sunspot number, flare index and solar radio flux at 2800 MHz from January 1966 to May 2008 by using cross-correlation analysis. The main results are as follows: (1) The flare index and sunspot number have synchronous phase for cycles 21 and 22 in the northern hemisphere and for cycle 20 in the southern hemisphere. (2) The flare index has a noticeable time lead with respect to sunspot number for cycles 20 and 23 in the northern hemisphere and for cycles 22 and 23 in the southern hemisphere. (3) For the entire Sun, the flare index has a noticeable time lead for cycles 20 and 23, a time lag for cycle 21, and no time lag or time lead for cycle 22 with respect to sunspot number. (4) The solar radio flux has a time lag for cycles 22 and 23 and no time lag or time lead for cycles 20 and 21 with respect to sunspot number. (5) For the four cycles, the sunspot number and flare index in the northern hemisphere are all leading to the ones in the southern hemisphere. These results may be instructive to the physical processes of flare energy storage and dissipation.     

Comments on the course of solar activity during the declining phase of solar cycle 20 (1970–74)

In the declining phase of solar cycle 20 (1970–74) three pulses of activity occurred and resulted in two well defined ‘stillstands’ in the smoothed means of sunspot, 2800 MHz, and calcium plage data. Marked diminutions in spot and 2800 MHz flux took place in 1970 and 1971, respectively, and were accompanied by concomitant decreases in flare-occurrence. Studies of the latitude distribution of spots and flares show the extent of the dominance of the northern hemisphere in cycle 20 and the marked phase shift between northern and southern hemispheres. In the years studied, the longitudes of centers of activity clustered in identifiable zones or hemispheres for relatively long intervals of time. From mid-1973 to mid-1974 the Sun had a relatively inactive hemisphere centered on ～0° longitude. The relationship of certain well defined ‘coronal holes’ to this inactive hemisphere of the chromosphere is noted. The first two spot groups of the new cycle formed in November 1974 and January 1975 in the longitude zone associated with relatively high levels of old cycle activity, a repetition of the pattern observed in 1963–64.     

Solar-cycle Time Delay of Rotating Sunspots

As shown by statistical results, in the 23rd solar activity cycle the variation of the latitudes of rotating sunspots with time exhibits a butterfly pattern. We have studied the variations with phase for the mean square errors among the 4 fitting curves of the 2 wings of the butterfly diagram of sunspots and the 2 wings of the butterfly diagram of rotating sunspots in the 23rd solar activity cycle. The results show that a systematic time delay exists not only between the northern and southern hemispheres of the butterfly diagram of sunspots, but also between the northern and southern hemispheres of the butterfly diagram of rotating sunspots, even between the butterfly diagrams of the sunspots and rotating sunspots in the same hemisphere. This means that the 23rd-cycle sunspot activities in the northern and southern hemispheres happened not simultaneously, that a systematic time delay or advance (phase difference) exists between the northern and southern hemispheres, that the southern hemisphere lags behind the northern hemisphere, that a phase difference exists between the butterfly diagram of rotating sunspots and the butterfly diagram of sunspots in the 23rd cycle, and that the butterfly diagram of rotating sunspots lags behind that of sunspots. The observed delay is a little less than the theoretical value predicted by the dynamo model.     

The asymmetry of solar activity in the years 1959–1969

One of the most outstanding feature of solar activity in the decade 1959–1969 was a very strong asymmetry on the two hemispheres. On the northern hemisphere spots, faculae and prominences were more numerous and the white light corona was brighter than on the southern hemisphere. This happened as well in the main zone as in the polar zone. The green coronal line too was brighter on the northern hemisphere, but the intensity of the red line was asymmetric in the opposite sense. From this behaviour it follows that over the more active hemisphere the corona is denser and hotter. Between density N _e and temperature T holds the relation: N _e = 10^–10 T ³. The real asymmetry was strengthened by a phase difference of the two hemispheres. This phase shift is subject to a long period that contains 8 eleven-year cycles. The intensity of the individual cycles follows the same long period. With low maxima of solar activity the northern hemisphere precedes, with high maxima the southern hemisphere (Figure 3).Astronomische Mitteilungen der Eidgenössischen Sternwarte Zürich, No. 302.     

Solar-Cycle-Related Variations in the Solar Differential Rotation and Meridional Flow: A Comparison

We have analysed a large set of sunspot group data (1874 – 2004) and find that the meridional flow strongly varies with the phase of the solar cycle, and the variation is quite different in the northern and the southern hemispheres. We also find the existence of considerable cycle-to-cycle variation in the meridional velocity, and about a 11-year difference between the phases of the corresponding variations in the northern and the southern hemispheres. In addition, our analysis also indicates the following: (i) the existence of a considerable difference (about 180^°) between the phases of the solar-cycle variations in the latitude-gradient terms of the northern and the southern hemispheres’ rotations; (ii) the existence of correlation (good in the northern hemisphere and weak in the southern hemisphere) between the mean solar-cycle variations of meridional flow and the latitude-gradient term of solar rotation; (iii) in the northern hemisphere, the cycle-to-cycle variation of the mean meridional velocity leads that of the equatorial rotation rate by about 11 years, and the corresponding variations have approximately the same phase in the southern hemisphere; and (iv) the directions of the mean meridional velocity is largely toward the pole in the longer sunspot cycles and largely toward the equator in the shorter cycles.     

On the increase of solar activity in the southern hemisphere during solar cycle 21

The present paper investigates the north-south asymmetry for major flares (solar cycles 19 and 20), type II radio bursts (solar cycles 19,20 and 21), white light flares (solar cycle 19,20 and 21), and gamma ray bursts, hard X-ray bursts and coronal mass ejections (solar cycle 21). The results are compared with the found asymmetry in favour of the northern hemisphere during solar cycles 19 and 20 in favour of the southern hemisphere during solar cycle 21.     

Relative phase analyses of long-term hemispheric solar flare activity

Wavelet transform methods, including the continuous wavelet transform, cross-wavelet transform and wavelet coherence, have been proposed to investigate the phase synchrony of the monthly mean flare indices in the time interval 1966 January–2007 December in the solar northern and southern hemispheres, respectively. The Schwabe cycle is the only period of statistical significance, and its mean value is 10.7 yr for the monthly mean flare indices in the northern hemisphere but slightly smaller, 10.1 yr, in the southern hemisphere – this should lead to phase asynchrony between the two. Both the cross-wavelet transform and wavelet coherence analyses show asynchronous behaviour with strong phase mixing in the high-frequency components of hemispheric flare activity, and strong synchronous behaviour with coherent phase angles in the low-frequency components, corresponding to the period-scales around the Schwabe cycle. The northern flare activity should lead the southern for the low-frequency components.     

Structure of the maximum phase of solar cycles 21 and 22

A distinctive peak and gap structure in a number of solar indices was observed in the maximum phase of solar cycles 21 and 22. The effect became even more prominent after separating the northern and southern solar hemispheres. In cycle 21 the multi-peaked structures observed in the two solar hemispheres were not synchronous and their sum resulted in the rather shallow two-peaked solar maximum for the parameters taken over the whole solar disk. In cycle 22 there were only double peaks in each hemisphere which were rather synchronous. Examination of solar activity in the northern and southern hemispheres has shown that the structured maximum appears to be due to the superposition of two quasi-oscillating processes with characteristic time-scales of 11 years and of 1–3 years (quasi-biennial oscillations). The absolute amplitude of the quasi-biennial oscillations depends on the 11-year cycle phase and reaches its maximum at the maximum of the 11-year cycle. This explains the occurrence of a double- or triple-peak structure in the solar maximum phase.     

Long-term behavior of latitudinal cosmic-ray gradients

We have used neutron monitor data covering a wide range of energy over a period of 22 years (1966–1987), as well as sea-level multidirectional meson telescope data from Nagoya to examine the latitude effect of solar diurnal vectors and its dependence on the polarity of interplanetary magnetic field (IMF). By sorting the daily cosmic-ray data according to whether the IMF is toward (T) or away (A) from the Sun, the annual mean solar diurnal variations (amplitude and phase) for the T and A days were determined separately. Results showed a northward-pointing latitudinal gradient from neutron monitors of the most northerly latitudes, and a predominant southward gradient at high southerly latitudes. The resultant latitudinal cosmic-ray gradients are the sum of two gradients: a north-south symmetry gradient (occurring in minimum and maximum solar activity years), and a north-south asymmetry gradient (occurring during different phases of solar activity cycles). The difference vector (T - A) between the solar diurnal vector for two groups was calculated, which represents a good indicator for the resultant perpendicular gradient relative to the Earth. This difference vector shows a considerable change in phase for detectors located in the northern hemisphere of the Earth. On the other hand, there exists much less change in phase for detectors located in the southern hemisphere.     

North-south distribution of solar flares during cycle 23

In this paper, we investigate the spatial distribution of solar flares in the northern and southern hemispheres of the Sun that occurred during the period 1996 to 2003. This period of investigation includes the ascending phase, the maximum and part of the descending phase of solar cycle 23. It is revealed that the flare activity during this cycle is low compared to the previous solar cycle, indicating the violation of Gnevyshev-Ohl rule. The distribution of flares with respect to heliographic latitudes shows a significant asymmetry between northern and southern hemisphere which is maximum during the minimum phase of the solar cycle. The present study indicates that the activity dominates the northern hemisphere in general during the rising phase of the cycle (1997–2000). The dominance of northern hemisphere shifted towards the southern hemisphere after the solar maximum in 2000 and remained there in the successive years. Although the annual variations in the asymmetry time series during cycle 23 are quite different from cycle 22, they are comparable to cycle 21.     

Long-Term Variations in the Solar Differential Rotation

Using Greenwich data (1879–1976) and SOON/NOAA data (1977–2002) on sunspot groups we found the following results: (i) The Sun's mean (over all the concerned cycles during 1879–1975) equatorial rotation rate (A) is significantly larger (≈0.1%) in the odd-numbered sunspot cycles (ONSCs) than in the even-numbered sunspot cycles (ENSCs). The mean rotation is significantly (≈10%) more differential in the ONSCs than in the ENSCs. North–south difference in the mean equatorial rotation rate is larger in the ONSCs than in the ENSCs. North–south difference in the mean latitude gradient of the rotation is significant in the ENSCs and insignificant in the ONSCs. (ii) The known very large decrease in A from cycle 13 to cycle 14 is confirmed. The amount of this decrease in the mean A was about 0.017 μrad s⁻¹. Also, we find that A decreased from cycle 17 to cycle 18 by about 0.008 μrad s⁻¹ and from cycle 21 to cycle 22 by about 0.016 μrad s⁻¹. From cycle 13 to cycle 14 the decrease in A was more in the northern hemisphere than in the southern hemisphere, it is opposite in the later two epochs. The time gap between the consecutive drops in A is about 44 years, suggesting the existence of a `44-yr' cycle or `double Hale cycle' in A. The time gap between the two large drops, viz., from cycle 13 to cycle 14 and from cycle 21 to cycle 22, is about 90 years (Gleissberg cycle). We predict that the next drop (moderate) in A will be occurring from cycle 25 to cycle 26 and will be followed by a relatively large-amplitude `double Hale cycle' of sunspot activity. (iii) Existence of a 90-yr cycle is seen in the cycle-to-cycle variation of the latitude gradient (B). A weak 22-yr modulation in B seems to be superposed on the relatively strong 90-yr modulation. (iv) The coefficient A varies significantly only during ONSCs and the variation has maximum amplitude in the order of 0.01 μrad s<sup>−1</sup> around activity minima. (v) There exists a good anticorrelation between the mean variation of B during the ONSCs and that during the ENSCs, suggesting the existence of a `22-yr' periodicity in B. The maximum amplitude of the variation of B is of the order of 0.05 μrad s⁻¹ around the activity minima. (vi) It seems that the well-known Gnevyshev and Ohl rule of solar activity is applicable also to the cycle-to-cycle amplitude modulation of B from cycle 13 to cycle 20, but the cycles 12 (in the northern hemisphere, Greenwich data) and 21 (in both hemispheres, SOON/NOAA data) seem to violate this rule in B. And (vii) All the aforesaid statistically significant variations in A and B seem to be related to the approximate 179-yr cycle, 1811–1989, of variation in the Sun's motion about the center of mass of the solar system.     

Bimodal distribution of area-weighted latitude of sunspots and solar North-South asymmetry

We study the latitudinal distribution of sunspots observed from 1874 to 2009 using the center-of-latitude (COL). We calculate COL by taking the area-weighted mean latitude of sunspots for each calendar month. We then form the latitudinal distribution of COL for the sunspots appearing in the northern and southern hemispheres separately, and in both hemispheres with unsigned and signed latitudes, respectively. We repeat the analysis with subsets which are divided based on the criterion of which hemisphere is dominant for a given solar cycle. Our primary findings are as follows: (1) COL is not monotonically decreasing with time in each cycle. Small humps can be seen (or short plateaus) around every solar maxima. (2) The distribution of COL resulting from each hemisphere is bimodal, which can well be represented by the double Gaussian function. (3) As far as the primary component of the double Gaussian function is concerned, for a given data subset, the distributions due to the sunspots appearing in two different hemispheres are alike. Regardless of which hemisphere is magnetically dominant, the primary component of the double Gaussian function seems relatively unchanged. (4) When the northern (southern) hemisphere is dominant the width of the secondary component of the double Gaussian function in the northern (southern) hemisphere case is about twice as wide as that in the southern (northern) hemisphere. (5) For the distribution of the COL averaged with signed latitude, whose distribution is basically described by a single Gaussian function, it is shifted to the positive (negative) side when the northern (southern) hemisphere is dominant. Finally, we conclude by briefly discussing the implications of these findings on the variations in the solar activity.     

Periodicities in the longitude distribution of sunspots

It is well known to the observer of sunspots that the spots seem not to be randomly distributed on the solar surface but rather occur at an increased rate at distances of 180° of each other on the same hemisphere while northern and southern hemispheres are independent. The following investigation - based on observational data of rotations No. 1457–1568 (1962–1970) shows four main results:

1. Northern and southern hemisphere behave independently.
2. Each hemisphere can be divided in longitude into sections of 45° so that successive sections alternatively show higher and lower spot occurrence. In other words: maximum spot occurrence is found in intervals of about 90° and 180°.
3. Second-order peaks can be found in intervals of 30° and multiples of it. The spot maxima explained above coincide with some of these second-order peaks.
4. Areas of minimal spot occurrence can be traced over a long period of time. These areas can be understood as the center of long-living magnetic areas along the borders of which we find the so-called ‘streets of prominences’ with its spots. This theory of Stanek (1971) explains the occurrence of prominences. Because of the steep magnetic gradient along these streets the theory is expected to hold true even for spots. This leads to a better understanding of the pattern already known and now being generalized to ‘streets of activity’.

     

The Temperature of the Low Corona During Solar Cycles 21–23

Observations of the forbidden coronal lines Fe xiv 530.3 nm and Fe x 637.4 nm obtained at the National Solar Observatory at Sacramento Peak are used to determine the variation of coronal temperature at latitudes above 30^∘ during solar activity cycles 21–23. Features of the long-term variation of emission in the two lines are also discussed. Temperatures at latitudes below 30^∘ are not studied because the technique used to determine the coronal temperature is not applicable in active regions. The polar temperature varies cyclically from approximately 1.3 to 1.7 MK. The temperatures are similar in both hemispheres. The temperature near solar minimum decreases strongly from mid-latitudes to the poles. The temperature of the corona above 80^∘ latitude generally follows the sunspot cycle, with minima in 1985 and 1995–1996 (cf. 1986 and 1996 for the smoothed sunspot number, Rz) and maxima in 1989 and 2000 (cf. 1989 and 2000 for Rz). The temperature of the corona above 30^∘ latitude at solar maximum is nearly uniform, i.e., there is little latitude dependence. If the maximum temperatures of cycles 22 and 23 are aligned in time (superposed epochs), the average annual N + S temperature (average of the northern and southern hemisphere) in cycle 23 is hotter than that in cycle 22 at all times both above 80^∘ latitude and above 30^∘ latitude. The difference in the average annual N + S maximum temperature between cycles 23 and 22 was 56 kK near the poles and 64 kK for all latitudes above 30^∘. Cycle 23 was also hotter at mid-latitudes than cycle 22 by 60 kK. The last 3 years of cycle 21 were hotter than the last 3 years of cycle 22. The difference in average annual N + S temperatures at the end of cycles 21 and 22 was 32 kK near the poles and 23 kK for all latitudes above 30^∘. Cycle 21 was also hotter at mid-latitudes than cycle 22 by at least 90 kK. Thus, there does not seem to be a solar-cycle trend in the low-coronal temperature outside of active regions.     

Spherical asymmetry in thermospheric magnetic storms

During moderate magnetic storms, changes in the neutral composition suggest that energy is deposited in the auroral zones. This results in thermal expansion (enhancement in N₂, Ar) and consequent redistribution of the lighter species O and He such that their densities decrease at high latitudes and increase at low latitudes. From measurements obtained by the ESRO 4 gas analyzer during a major storm in late February 1973 (K_p = 7⁺) these typical high latitude characteristics were observed in the southern hemisphere and at certain longitudes to extend toward mid and low latitudes as far as ?20° invariant latitude. Further examination of these data for latitudes across the equator up to +20° latitude, however, shows evidence for an enhancement zone in He and O which is clearly displaced into the northern hemisphere thus suggesting a pronounced spherical asymmetry. Ground based observations on the state of the ionosphere between ±50° latitude confirm this asymmetry and suggest that the center of this enhancement zone occurs at about +15° invariant latitude. Adopting a suitable energy distribution in both hemispheres the magnetic storm response in the neutral composition is simulated with a circulation model. From this analysis it is concluded that for some longitudes a difference of a factor of two or more between the heating rates of the northern and southern hemispheres is required to match the ESRO-4 data.     

On the use of ‘first spotless day’ as a predictor for sunspot minimum

Defining the first spotless day of a sunspot cycle as the first day without spots relative to sunspot maximum during the decline of the solar cycle, one finds that the timing of that occurrence can be used as a predictor for the occurrence of solar minimum of the following cycle. For cycle 22, the first spotless day occurred in April 1994, based on the International sunspot number index, although other indices (Boulder and American) indicated the first spotless day to have occurred earlier (September 1993). For cycles 9–14, sunspot minimum followed the first spotless day by about 72 months, having a range of 62–82 months; for cycles 15–21, sunspot minimum followed the first spotless day by about 35 months, having a range of 27–40 months. Similarly, the timing of first spotless day relative to sunspot minimum and maximum for the same cycle reveals that it followed minimum (maximum) by about 69 (18) months during cycles 9–14 and by about 90 (44) months during cycles 15–21. Accepting April 1994 as the month of first spotless day occurrence for cycle 22, one finds that it occurred 91 months into the cycle and 57 months following sunspot maximum. Such values indicate that its behavior more closely matches that found for cycles 15–21 rather than for cycles 9–14. Therefore, one infers that sunspot minimum for cycle 23 will occur in about 2–3 years, or about April 1996 to April 1997. Accepting the earlier date of first spotless day occurrence indicates that sunspot minimum for cycle 23 could come several months earlier, perhaps late 1995.The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.