The use of solar faculae in studies of the sunspot cycle

Comparison of the long-term variation of photospheric faculae areas with that of sunspots shows that studies of faculae provide both complementary and supplementary information on the behaviour of the solar cycle. Detailed studies of the development of sunspots with respect to faculae show that there is a high degree of order over much of a given cycle, but marked differences from cycle to cycle. Within a cycle the relationship between spot and faculae areas appears to be similar for the N and S solar hemispheres, and over the early stages of a cycle it is directly related to the magnitude of the maximum sunspot number subsequently attained in that cycle.This result may well have predictive applications, and formulae are given relating the peak sunspot number to simple parameters derived from this early developmental stage. Full application to the current cycle 21 is denied due to the cessation of the Greenwich daily photoheliographic measurements, but use of the cruder weekly data suggests a maximum smoothed sunspot number of 150 ± 22.The effects of the incompatibility of the spot and faculae data, in that faculae are unobservable over a large fraction of the solar disc and also do not always develop associated spots, have been examined in a detailed study of two cycles and shown not to vitiate the results.Now at NOAA, Environmental Data Service, NGSTDC, Boulder, Colo. 80302, U.S.A.     

Yearly comparisons of the martian polar caps: 1999-2003 Mars Orbiter Camera observations

The Mars Global Surveyor Mars Orbiter Camera wide-angle cameras were used to obtain images of the north and south seasonal and residual polar caps between 1999 and 2003. Wide-angle red camera images were used in assembling mosaics of the north and south polar recessions and regression rates were measured and compared. There are small variations in the north polar recession between 2000 and 2002, especially between LS=7° and LS=50°, however there is no evidence for the plateau in the recession curves that has been observed in some prior years. The south polar recession changes very little from year to year, and the 2001 dust storm had little if any effect on the average cap recession that year. Albedo values of the geographic north pole were measured using wide-angle red and blue camera images, and the residual south polar cap configuration was compared between the three years observed by MOC. The albedo of the geographic north pole generally varies between 0.5 and 0.6 as measured from MOC wide-angle red camera images. There were only minor variations near the edges of the residual south polar cap between the three years examined.     

Global solar cycle in the distribution of the green coronal emission period: 1940–1989

We have studied the latitude-time distribution of the green (5303 Å) coronal line emission for 1940–1989 from observations by Waldmeier (1957), Kislovodsk, Lomnický tít, Norikura, and Pic-du-Midi - Q.B.S.A. (1955–1987). We have compared these data with the distributions of the weak magnetic field (Stenflo, 1988), of polar faculae and sunspots, and have given our interpretation of the results. We have found that a new cycle of coronal activity commences after the polar field reversal in the form of two components in each hemisphere. We identify the first component with the polar faculae that appear at latitude 40° and migrate polewards. The second component representing sunspots shows up at 40° latitude 5–6 years after and drifts equatorward. Thus the global coronal activity cycle has a duration of 16–17 years and is described by two components that reflect the activity of polar faculae and sunspots.     

A new look at wolf sunspot numbers in the late 1700's

Long-term homogeneous observations of solar activity or many solar cycles are essential for investigating many problems in solar physics and climatology. The one key parameter used in most long-term studies is the Wolf sunspot number, which is susceptible to observer bias, particularly because it is highly sensitive to the observer's ability to see the smallest sunspots. In this paper we show how the Wolf sunspot number can be derived from the number of sunspot groups alone. We utilize this approach to obtain a Group Wolf number. This technique has advantages over the classical method of determining the Wolf number because corrections for observer differences are reduced and long-term self-consistent time series can be developed. The level of activity can be calculated to an accuracy of ± 5% using this method. Applying the technique to Christian Horrebow's observations of solar cycles 1, 2, and 3 (1761–1777), we find that the standard Wolf numbers are nearly homogeneous with sunspot numbers measured from 1875 to 1976 except the peak of solar cycle 2 is too low by 30%. This result suggests that further analyses of early sunspot observations could lead to significant improvements in the uniformity of the measurements of solar activity. Such improvements could have important impacts upon our understanding of long-term variations in solar activity, such as the Gleissberg cycle, or secular variations in the Earth's climate.     

Photospheric Magnetic Field: Relationship Between North–South Asymmetry and Flux Imbalance

Photospheric magnetic fields were studied using the Kitt Peak synoptic maps for 1976?–?2003. Only strong magnetic fields (B>100 G) of the equatorial region were taken into account. The north–south asymmetry of the magnetic fluxes was considered as well as the imbalance between positive and negative fluxes. The north–south asymmetry displays a regular alternation of the dominant hemisphere during the solar cycle: the northern hemisphere dominated in the ascending phase, the southern one in the descending phase during Solar Cycles 21?–?23. The sign of the imbalance did not change during the 11 years from one polar-field reversal to the next and always coincided with the sign of the Sun’s polar magnetic field in the northern hemisphere. The dominant sign of leading sunspots in one of the hemispheres determines the sign of the magnetic-flux imbalance. The sign of the north–south asymmetry of the magnetic fluxes and the sign of the imbalance of the positive and the negative fluxes are related to the quarter of the 22-year magnetic cycle where the magnetic configuration of the Sun remains constant (from the minimum where the sunspot sign changes according to Hale’s law to the magnetic-field reversal and from the reversal to the minimum). The sign of the north–south asymmetry for the time interval considered was determined by the phase of the 11-year cycle (before or after the reversal); the sign of the imbalance of the positive and the negative fluxes depends on both the phase of the 11-year cycle and on the parity of the solar cycle. The results obtained demonstrate the connection of the magnetic fields in active regions with the Sun’s polar magnetic field in the northern hemisphere.     

Comparison of the Variations of CMEs and ICMEs with those of other Solar and Interplanetary Parameters During Solar Cycle 23

This paper examines the variations of coronal mass ejections (CMEs) and interplanetary CMEs (ICMEs) during solar cycle 23 and compares these with those of several other indices. During cycle 23, solar and interplanetary parameters had an increase from 1996 (sunspot minimum) to ∼2000, but the interval 1998–2002 had short-term fluctuations. Sunspot numbers had peaks in 1998, 1999, 2000 (largest), 2001 (second largest), and 2002. Other solar indices had matching peaks, but the peak in 2000 was larger than the peak in 2001 only for a few indices, and smaller or equal for other solar indices. The solar open magnetic flux had very different characteristics for different solar latitudes. The high solar latitudes (45^∘–90^∘) in both N and S hemispheres had flux evolutions anti-parallel to sunspot activity. Fluxes in low solar latitudes (0^∘–45^∘) evolved roughly parallel to sunspot activity, but the finer structures (peaks etc. during sunspot maximum years) did not match with sunspot peaks. Also, the low latitude fluxes had considerable N–S asymmetry. For CMEs and ICMEs, there were increases similar to sunspots during 1996–2000, and during 2000–2002, there was good matching of peaks. But the peaks in 2000 and 2001 for CMEs and ICMEs had similar sizes, in contrast to the 2000 peak being greater than the 2001 peak for sunspots. Whereas ICMEs started decreasing from 2001 onwards, CMEs continued to remain high in 2002, probably due to extra contribution from high-latitude prominences, which had no equivalent interplanetary ICMEs or shocks. Cosmic ray intensity had features matching with those of sunspots during 2000–2001, with the 2000 peak (on a reverse scale, actually a cosmic ray decrease or trough) larger than the 2001 peak. However, cosmic ray decreases started with a delay and ended with a delay with respect to sunspot activity.     

Correlation Between the Sunspot Number,the Total Solar Irradiance,and the Terrestrial Insolation

Our study deals with the correlations between the solar activity on the one hand and the solar irradiance above the Earth’s atmosphere and at ground level on the other. We analyzed the combined ACRIM I+II time series of the total solar irradiance (TSI), the Mauna Loa time series of terrestrial insolation data, and data of terrestrial cosmic ray fluxes. We find that the correlation between the TSI and the sunspot number is strongly non-linear. We interpret this as the net balance between brightening by faculae and darkening by sunspots where faculae dominate at low activity and sunspots dominate at high activity. Such a behavior is hitherto known from stellar analogs of the Sun in a statistical manner. We perform the same analysis for the Mauna Loa data of terrestrial insolation. Here we find that the linear relation between sunspot number and insolation shows more than 1% rise in insolation by sunspot number variations which is much stronger than for the TSI. Our conclusion is that the Earth atmosphere acts as an amplifier between space and ground, and that the amplification is probably controlled by solar activity. We suspect the cosmic rays intensity as the link between solar activity and atmospheric transparency. A Fourier analysis of the time series of insolation shows three dominant peaks: 10.5, 20.4, and 14.0 years. As a matter of fact, the cosmic rays data show the same pattern of significant peaks: 10.7, 22.4, and 14.9 years. This analogy supports our idea that the cosmic rays variation has influence on the transparency of the Earth atmosphere.     

Polar coronal holes and the sunspot cycle. A new method to predict sunspot numbers

Twenty years ago, Ohl (1966, 1968) found a correlation between geomagnetic activity around the minimum of the solar cycle and the Wolf sunspot number in the maximum of the following solar cycle. In this paper we shall show that such a relation means indeed a relation between the polar coronal holes area around the minimum of the solar cycle and the sunspot number in the maximum of the next. In fact, a very high positive correlation exists between the temporal evolution of the size of polar coronal holes and the Wolf sunspot number 6.3. years later.     

The Minimum Activity Epoch as a Precursor of the Solar Activity

This paper considers the indices characterizing the minimum activity epoch, according to the data of large-scale magnetic fields and polar activity. Such indices include: dipole–octopole index, area and average latitude of the field with dominant polarity in each hemisphere, polar activity seen in polar faculae and Ca?ii K line bright points, coronal emission line intensity (5303?Å) and others. We studied the correlation between these indices and the amplitude of the following sunspot cycle, and the relation between the duration of the cycle of large-scale magnetic fields and the duration of the sunspot cycle. The obtained relationships allow us to presume that the polar field is formed from the sources of both preceding and the current activity cycles during the decay phase and at the activity minimum. The balance in these sources would therefore determine the features of the following sunspot cycle. The prediction for the 24th activity cycle using these results leads to W=102±13.     

Latitude variations of photospheric activity areas with particular reference to solar faculae

Detailed studies of the development of photospheric activity centres for two solar cycles show that Spörer's Law holds in a very similar form to that applying to sunspots for the faculae which inhabit the sunspot zones. Similar differences between the two solar hemispheres can arise, and it seems to be confirmed that the average latitude of faculae tends to be a few degrees poleward of that of sunspots throughout a given cycle. It is shown that the normal averaging process involved in deriving Spörer's Law obscures a detail which is revealed in a breakdown into the variations within successive narrow latitude strips. These show the existence within a cycle of three separate maxima of activity occurring at different epochs and with different preferred latitudes. The main properties of these maxima are discussed.Now at NOAA, Environmental Data Service, NGSTDC, Boulder, Colo. 80302, U.S.A.     

A Detailed Comparison of Cosmic Ray Gaps with solar Gnevyshev Gaps

After increasing almost monotonically from sunspot minimum, sunspot activity near maximum falters and remains in a narrow grove for several tens of months. During the 2–3 years of turmoil near sunspot maximum, sunspots depict several peaks (Gnevyshev peaks). The spaces between successive peaks are termed as Gnevyshev Gaps (GG). An examination showed that the depths of the troughs varied considerably from one GG to the next in the same cycle, with magnitudes varying in a wide range (<1% to ∼20%). In any cycle, the sunspot patterns were dissimilar to those of other solar parameters, qualitatively as well as quantitatively, indicating a general turbulence, affecting different solar parameters differently. The solar polar magnetic field reversal does not occur at the beginning of the general turmoil; it occurs much later. For cosmic ray (CR) modulation which occurs deep in the heliosphere, one would have thought that the solar open magnetic field flux would play a crucial role, but observations show that the sunspot GGs are not reflected well in the solar open magnetic flux, where sometimes only one peak occurred (hence no GG at all), not matching with any sunspot peak and with different peaks in the northern and southern hemispheres (north – south asymmetry). Gaps are seen in interplanetary parameters but these do not match exactly with sunspot GGs. For CR data available only for five cycles (19 – 23), there are CR gaps in some cycles, but the CR gaps do not match perfectly with gaps in the solar open magnetic field flux or in interplanetary parameters or with sunspot GGs. Durations are different and/or there are variable delays, and magnitudes of the sunspot GGs and CR gaps are not proportional. Solar polar magnetic field reversal intervals do not coincide with either sunspot GGs or CR gaps, and some CR gaps start before magnetic field reversals, which should not happen if the magnetic field reversals are the cause of the CR gaps.     

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.     

Relative sunspot numbers in the first half of eighteenth century

We revised relative sunspot numbers in the time interval 1700–1748 for which Wolf derived their annual means. The frequency of daily observations, counting simultaneously the number of sunspots and the number of sunspot groups necessary for determinating Wolf's relative sunspot numbers, is in this time interval very low and covers, on average, 4.8% of the number of all days only. There also exist incomplete observations not convenient to determine relative sunspot numbers. To enlarge the number of daily relative sunspot numbers we used the nonlinear, two-step interpolation method derived earlier by Letfus (1996, 1999). After interpolation, the mean value increased to 13.8%. Waldmeier (1968) found that the scaling factor k can be derived directly from the observed number of spots f and from the number of sunspot groups g. From the observations made at Zürich (Wolf and his assistants, Wolfer), at Peckeloh, and at Moncalieri during the years 1861–1928, we derived a new, more correct empirical relation. The resulting annual relative sunspot numbers are given in Table II. However, only for 26 years (53.0%) from the total number of 49 years was it possible to derive annual relative sunspot numbers. The observations were missing for the other years. This corresponds with results of Wolf, which gives the annual relative sunspot numbers for all 49 years. For the years when the data were missing, he marked these values as interpolated or very uncertain ones. Most of the observations originate from two data series (Kirch, Plantade), for which Wolf derived a higher scaling factor (k=2.0) than followed from the newly derived relation (k=1.40). The investigated time interval covers four solar cycles. After our results, the height of the first cycle (No. –4), given by Wolf, should be lowered by about two-thirds, the following two cycles (Nos. –3 and –2) lowered by one-third, as given by Wolf, and only the height of the fourth one (No. –1) should be unchanged. The activity levels of the cycles, as represented by group sunspot numbers, are lower by about one-fourth and, in the case of the first one (No. –4) even by two-thirds of the levels derived by us. The group sunspot numbers, derived from a much greater number of observations, have also greater credibility than other estimates. The shapes of the cycles, as given by Wolf, can be considered only as their more or less idealized form.     

Do polar faculae on the sun predict a sunspot cycle?

The paper reports the results of the analysis of the data on polar faculae for three solar cycles (1960–1986) at the Kislovodsk Station of the Pulkovo Observatory and on polar bright points in Ca ii K line for two solar cycles (1940–1957) at the Kodaikanal Station of the Indian Institute of Astrophysics. We have noticed that the monthly numbers of polar faculae and polar bright points in Ca ii K line and monthly sunspot areas in each hemisphere of the following solar cycle have a correlation with each other. A new cycle of polar faculae and polar bright points in the Ca ii K line begins after the polar magnetic field reversal. We find that the smaller the period between the ending of the polar field reversal and the beginning of a new sunspot cycle is, the more intense is the cycle itself. The intensity of the forthcoming solar cycle (cycle 22) and the periods of strong fluctuations in activity expected in this cycle are also discussed.     

The Relative Phase Asynchronization between Sunspot Numbers and Polar Faculae

The monthly sunspot numbers compiled by Temmer et al. and the monthly polar faculae from observations of the National Astronomical Observatory of Japan, for the interval of March 1954 to March 1996, are used to investigate the phase relationship between polar faculae and sunspot activity for total solar disk and for both hemispheres in solar cycles 19, 20, 21 and 22. We found that (1) the polar faculae begin earlier than sunspot activity, and the phase difference exhibits a consistent behaviour for different hemispheres in each of the solar cycles, implying that this phenomenon should not be regarded as a stochastic fluctuation; (2) the inverse correlation between polar faculae and sunspot numbers is not only a long-term behaviour, but also exists in short time range; (3) the polar faculae show leads of about 50–71 months relative to sunspot numbers, and the phase difference between them varies with solar cycle; (4) the phase difference value in the northern hemisphere differs from that in the southern hemisphere in a solar cycle, which means that phase difference also existed between the two hemispheres. Moreover, the phase difference between the two hemispheres exhibits a periodical behaviour. Our results seem to support the finding of Hiremath (2010).     

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.     

On the latitude migration of polar faculae in the solar activity cycle period: 1970–1978

Coordinates of polar faculae have been measured and processed using daily photoheliograms of the Kislovodsk Station of the Pulkovo observatory with the final goal of studying their latitude distribution during the solar cycles 20–21. The results obtained are as follows:

1. The first polar faculae emerge immediately after the polarity inversion of the solar magnetic field at the latitudes from 40° to 70° with the average ?-55°.
2. The zone of the emergence of polar faculae migrates poleward during the period between the neighbouring polarity inversions of the solar magnetic field. This migration is about 20° for 8 years, which corresponds to a velocity of 0.5 m s^-1.
3. The maximum number of polar faculae was reached at the activity minimum (1975–1976).
4. The last polar faculae were observed in the second half of 1978 at the latitudes from 70° to 80°.

     

Latitude-time distribution of 3 types of magnetic field activity in the global solar cycle

Large-scale solar activity is considered as a manifestation of 3 types of magnetic field activity which is demonstrated in the 22-year cycle (a) of small-scale flux emergence (polar faculae at latitudes > 40°), (b) of somewhat larger scale flux emergence (sunspots at latitudes < 40°), and (c) of the global magnetic neutral lines at all latitudes. The migration (poleward or equatorward) of the place of birth and/or of the phenomena themselves of these three types of manifestation of magnetic field is discussed. The poleward migration of the global field is explained in a phenomenological way.     

Correction to: Observation of a Flare and Filament Eruption in Lyman- α $\alpha $ on 8 September 2011 by the PRoject for OnBoard Autonomy/Large Yield Radiometer (PROBA2/LYRA)

In most of the solar cycles, activity in the northern and southern hemispheres peaks at different times. One hemisphere peaks well before the other, and at least one of the hemispheric maxima frequently does not coincide with the whole sphere maximum. Prediction of the maximum of a hemisphere and the corresponding north–south asymmetry of a solar cycle may help to understand the mechanisms of the solar cycle, the solar-terrestrial relationship, and solar-activity influences on space weather. Here we analysed the sunspot-group data from the Greenwich Photoheliographic Results (GPR) during 1874?–?1976 and Debrecen Photoheliographic Data (DPD) during 1977?–?2017 and studied the cycle-to-cycle variations in the values of 13-month smoothed monthly mean sunspot-group area in the whole sphere (WSGA), northern hemisphere (NSGA), and southern hemisphere (SSGA) at the epochs of maxima of Sunspot Cycles 12?–?24 and at the epochs of maxima of WSGA, NSGA, and SSGA Cycles 12?–?24 (note that solar-cycle variation of a parameter is expressed as a cycle of that parameter). The cosine fits to the values of WSGA, NSGA, and SSGA at the maxima of sunspot, WSGA, NSGA, and SSGA Cycles 12?–?24, and to the values of the corresponding north–south asymmetry, suggest the existence of a ≈132-year periodicity in the activity of the northern hemisphere, a 54?–?66-year periodicity in the activity of the southern hemisphere, and a 50?–?66 year periodicity in the north–south asymmetry in activity at all the aforementioned epochs. By extrapolating the best-fit cosine curves we predicted the amplitudes and the corresponding north–south asymmetry of the 25th WSGA, NSGA, and SSGA cycles. We find that on average Solar Cycle 25 in sunspot-group area would be to some extent smaller than Solar Cycle 24 in sunspot-group area. However, by inputting the predicted amplitudes of the 25th WSGA, NSGA, and SSGA cycles relationship between sunspot-group area and sunspot number we find that the amplitude (\(130\pm 12\)) of Sunspot Cycle 25 would be slightly larger than that of reasonably small Sunspot Cycle 24. Still it confirms that the beginning of the upcoming Gleissberg cycle would take place around Solar Cycle 25. We also find that except at the maximum of NSGA Cycle 25 where the strength of activity in the northern hemisphere would be dominant, the strength of activity in the southern hemisphere would be dominant at the maximum epochs of the 25th sunspot, WSGA, and SSGA cycles.

     

Solar cycle dependence of polar coronal holes

A study has been made of the polar coronal holes in relation to solar cycle activity. Important results obtained are: (i) the peak of the frequency distribution of coronal hole size shifts towards lower values as the solar cycle advances towards maximum, this being true for both the north and south polar holes, (ii) coronal hole size decreases with the increase of sunspot number.