Group Sunspot Number Research Articles

THE MAUNDER MINIMUM IS NOT AS GRAND AS IT SEEMED TO BE

The Maunder Minimum (MM), which occurred between 1645 and 1715, is mainly known as an almost spotless period on the Sun. We analyze the nominal number of sunspot groups for each observer individually. Comparing the sunspot drawings and textual reports, we conclude that the latter underestimate the number of sunspots. We also argue that the different points of view of observers in the seventeenth century on the origin of sunspots resulted in the underestimation of sunspot groups or even gaps in observational reports. We demonstrate that Jean Picard and Giovanni Domenico Cassini of the Paris Observatory did not report any sunspots, while other observers reported on the occurrence of spots. Moreover, compared with other observers, La Hire underestimated the solar activity. The MM looks like an ordinary secular minimum with a depressed 11 yr solar cyclicity.

STOCHASTIC DESCRIPTION OF THE HIGH-FREQUENCY CONTENT OF DAILY SUNSPOTS AND EVIDENCE FOR REGIME CHANGES

The irregularity index λ is applied to the high-frequency content of daily sunspot numbers ISSN. This λ is a modification of the standard maximal Lyapunov exponent. It is computed here as a function of embedding dimension m, within four-year time windows centered at the maxima of Schwabe cycles. The λ(m) curves form separate clusters (pre-1923 and post-1933). This supports a regime transition and narrows its occurrence to cycle 16, preceding the growth of activity leading to the Modern Maximum. The two regimes are reproduced by a simple autoregressive process AR(1), with the mean of Poisson noise undergoing 11 yr modulation. The autocorrelation a of the process (linked to sunspot lifetime) is a ≈ 0.8 for 1850-1923 and ≈0.95 for 1933-2013. The AR(1) model suggests that groups of spots appear with a Poisson rate and disappear at a constant rate. We further applied the irregularity index to the daily sunspot group number series for the northern and southern hemispheres, provided by the Greenwich Royal Observatory (RGO), in order to study a possible desynchronization. Correlations between the north and south λ(m) curves vary quite strongly with time and indeed show desynchronization. This may reflect a slow change in the dimension of an underlying dynamical system. The ISSN and RGO series of group numbers do not imply an identical mechanism, but both uncover a regime change at a similar time. Computation of the irregularity index near the maximum of cycle 24 will help in checking whether yet another regime change is under way.

The heliospheric Hale cycle over the last 300 years and its implications for a “lost” late 18th century solar cycle

A Hale cycle, one complete magnetic cycle of the Sun, spans two complete Schwabe cycles (also referred to as sunspot and, more generally, solar cycles). The approximately 22-year Hale cycle is seen in magnetic polarities of both sunspots and polar fields, as well as in the intensity of galactic cosmic rays reaching Earth, with odd- and even-numbered solar cycles displaying qualitatively different waveforms. Correct numbering of solar cycles also underpins empirical cycle-to-cycle relations which are used as first-order tests of stellar dynamo models. There has been much debate about whether the unusually long solar cycle 4 (SC4), spanning 1784–1799, was actually two shorter solar cycles combined as a result of poor data coverage in the original Wolf sunspot number record. Indeed, the group sunspot number does show a small increase around 1794–1799 and there is evidence of an increase in the mean latitude of sunspots at this time, suggesting the existence of a cycle “4b”. In this study, we use cosmogenic radionuclide data and associated reconstructions of the heliospheric magnetic field (HMF) to show that the Hale cycle has persisted over the last 300 years and that data prior to 1800 are more consistent with cycle 4 being a single long cycle (the “no SC4b” scenario). We also investigate the effect of cycle 4b on the HMF using an open solar flux (OSF) continuity model, in which the OSF source term is related to sunspot number and the OSF loss term is determined by the heliospheric current sheet tilt, assumed to be a simple function of solar cycle phase. The results are surprising; Without SC4b, the HMF shows two distinct peaks in the 1784–1799 interval, while the addition of SC4b removes the secondary peak, as the OSF loss term acts in opposition to the later rise in sunspot number. The timing and magnitude of the main SC4 HMF peak is also significantly changed by the addition of SC4b. These results are compared with the cosmogenic isotope reconstructions of HMF and historical aurora records. These data marginally favour the existence of SC4b (the “SC4b” scenario), though the result is less certain than that based on the persistence of the Hale cycle. Thus while the current uncertainties in the observations preclude any definitive conclusions, the data favour the “no SC4b” scenario. Future improvements to cosmogenic isotope reconstructions of the HMF, through either improved modelling or additional ice cores from well-separated geographic locations, may enable questions of the existence of SC4b and the phase of Hale cycle prior to the Maunder minimum to be settled conclusively.

Sunspot Numbers and Areas from the Madrid Astronomical Observatory (1876 – 1986)

The solar program of the Astronomical Observatory of Madrid started in 1876. For ten solar cycles, observations were made in this institution to determine sunspot numbers and areas. The program was completed in 1986. The resulting data have been published in various Spanish scientific publications. The metadata allowed four periods of this program (with different observers and instruments) to be identified. In the present work, the published data were retrieved and digitized. Their subsequent analysis showed that most of these data can be considered reliable given their very high correlation with international reference indices (International Sunspot Number, Group Sunspot Number, and Sunspot Area). An abrupt change emerged in the spots/groups ratio in 1946 which lasted until 1972.

Centennial variations in sunspot number, open solar flux, and streamer belt width: 1. Correction of the sunspot number record since 1874

AbstractWe analyze the widely used international/Zürich sunspot number record, R, with a view to quantifying a suspected calibration discontinuity around 1945 (which has been termed the “Waldmeier discontinuity”). We compare R against the composite sunspot group data from the Royal Greenwich Observatory network and the Solar Optical Observing Network, using both the number of sunspot groups, NG, and the total area of the sunspots, AG. In addition, we compare R with the recently developed interdiurnal variability geomagnetic indices IDV and IDV(1d). In all four cases, linearity of the relationship with R is not assumed and care is taken to ensure that the relationship of each with R is the same before and after the putative calibration change. It is shown the probability that a correction is not needed is of order 10−8 and that R is indeed too low before 1945. The optimum correction to R for values before 1945 is found to be 11.6%, 11.7%, 10.3%, and 7.9% using AG, NG, IDV, and IDV(1d), respectively. The optimum value obtained by combining the sunspot group data is 11.6% with an uncertainty range 8.1–14.8% at the 2σ level. The geomagnetic indices provide an independent yet less stringent test but do give values that fall within the 2σ uncertainty band with optimum values are slightly lower than from the sunspot group data. The probability of the correction needed being as large as 20%, as advocated by Svalgaard (2011), is shown to be 1.6 × 10−5.

Centennial variations in sunspot number, open solar flux and streamer belt width: 3. Modeling

AbstractFrom the variation of near‐Earth interplanetary conditions, reconstructed for the mid‐19th century to the present day using historic geomagnetic activity observations, Lockwood and Owens (2014) have suggested that Earth remains within a broadened streamer belt during solar cycles when the Open Solar Flux (OSF) is low. From this they propose that the Earth was immersed in almost constant slow solar wind during the Maunder minimum (c. 1650–1710). In this paper, we extend continuity modeling of the OSF to predict the streamer belt width using both group sunspot numbers and corrected international sunspot numbers to quantify the emergence rate of new OSF. The results support the idea that the solar wind at Earth was persistently slow during the Maunder minimum because the streamer belt was broad.

Centennial variations in sunspot number, open solar flux, and streamer belt width: 2. Comparison with the geomagnetic data

AbstractWe investigate the relationship between interdiurnal variation geomagnetic activity indices, IDV and IDV(1d), corrected sunspot number, RC , and the group sunspot number RG . RC uses corrections for both the “Waldmeier discontinuity,” as derived in Paper 1, and the “Wolf discontinuity” revealed by Leussu et al. (2013). We show that the simple correlation of the geomagnetic indices with RCn or RGn masks a considerable solar cycle variation. Using IDV(1d) or IDV to predict or evaluate the sunspot numbers, the errors are almost halved by allowing for the fact that the relationship varies over the solar cycle. The results indicate that differences between RC and RG have a variety of causes and are highly unlikely to be attributable to errors in either RG alone, as has recently been assumed. Because it is not known if RC or RG is a better predictor of open flux emergence before 1874, a simple sunspot number composite is suggested which, like RG , enables modeling of the open solar flux for 1610 onward in Paper 3 but maintains the characteristics of RC .

Statistical analysis of sunspot groups and flares for solar maximum and minimum

Based on the NOAA/SWPC data, by choosing two separative periods with successive 12 months, that is, 2005 July–2006 June(during the solar minimum) and 2011 July–2012 June(during the solar maximum), we analyze the activity of flares and compare the statistical results between the two periods for studying their evolution with time, sunspot distribution, sunspot lifetime and magnetic field types. The main conclusions are:(1) The time variation of sunspot groups number is random for both the solar minimum and maximum periods. The sunspot number during the solar maximum is about 1.5 times larger than during the solar minimum. The flare number shows good correlation with the sunspot group number. During solar maximum there may be very few flares for some months, while during solar minimum there can be plenty of flares for some months, indicating the importance of keeping monitoring for solar activities even during the solar minimum period.(2) The δ-sunspot groups have the highest flare productivity(the ratio of flare amount to sunspot group number) for both solar minimum and maximum, while the β-sunspot groups have produced the most flares. The flare productivity of sunspot groups has close relation with magnetic field type, and it has no obvious relation with the state of solar cycle.(3) There is serious asymmetry in the distribution for flares, especially for X-class flares. The increase of the flares number from solar minimum to maximum is mainly caused by C- and M-class flares.(4) The number of sunspot groups has no obvious correlation with their lifetime, while the flare productivity shows well correlation with sunspot lifetime for all periods.

Properties of the sunspot latitudinal distribution skewness

The properties of the sunspot latitudinal distributions related to skewness have been studied based on the data of the extended Greenwich catalog for 1874–2011. The results of the performed analysis indicate that a significant skewness is present in most annual latitudinal distributions of the sunspot index. In this case, the distribution skewness increases near the 11-year cycle maximum phase. An increase in the sunspot group number is also accompanied by an increase in skewness. In particular, when the sunspot index is large, the number of groups located below midlatitudes is mostly larger than the number of groups above these latitudes and this imbalance increases with increasing total sunspot activity level. In medium and large 11-year cycles, the average distribution skewness for a cycle is always positive and its value is related to the cycle amplitude. This results agree with the theoretical models of the 11-year cycle, where the specific features of the low-latitude meridional circulation are related to the sunspot activity level.

Long-term variations in sunspot characteristics

Relative variations in the number of sunspots and sunspot groups in activity cycles have been analyzed based on data from the Kislovodsk Mountain Astronomical Station and international indices. The following regularities have been established: (1) The relative fraction of small sunspots decreases linearly and that of large sunspots increase with increasing activity cycle amplitude. (2) The variation in the average number of sunspots in one group has a trend, and this number decreased from ∼12 in cycle 19 to ∼7.5 in cycle 24. (3) The ratio of the sunspot index (Ri) to the sunspot group number index (G gr) varies with a period of about 100 years. (4) An analysis of the sunspot group number index (G gr) from 1610 indicates that the Gnevyshev-Ohl rule reverses at the minimums of secular activity cycles. (5) Ratio of the total area to area of Ssp/Sum nuclei has long-term variation with a period approximately 8 cycles. Minimum ratio falls on 16–17 cycles of activity. (6) It has been indicated that the magnetic field intensity and sunspot area in the current cycle are related to the amplitude of the next activity cycle.

Inconsistency of the Wolf sunspot number series around 1848

Aims. Sunspot number is a benchmark series in many studies, but may still contain inhomogeneities and inconsistencies. In particular, an essential discrepancy exists between the two main sunspot number series, Wolf (WSN) and group (GSN) sunspot numbers, before 1848. The source of this discrepancy has so far remained unresolved. However, the recently digitized series of solar observations in 1825-1867 by Samuel Heinrich Schwabe, who was the primary observer of the WSN before 1848, makes such an assessment possible. Methods. We construct sunspot series, similar to WSN and GSN, but using only Schwabe's data. These series, called WSN-S and GSN-S, respectively, were compared with the original WSN and GSN series for the period 1835-1867 to look for possible inhomogeneities. Results. We show that: (1) The GSN series is homogeneous and consistent with the Schwabe data throughout the entire studied period; (2) The WSN series decreases by roughly ~20% around 1848 caused by the change of the primary observer from Schwabe to Wolf and an inappropriate individual correction factor used for Schwabe in the WSN; (3) This implies a major inhomogeneity in the WSN, which needs to be corrected by reducing its values by 20% before 1848; (4) The corrected WSN series is in good agreement with the GSN series. This study supports the earlier conclusions that the GSN series is more consistent and homogeneous in the earlier part than the WSN series.

One Possible Reason for Double-Peaked Maxima in Solar Cycles: Is a Second Maximum of Solar Cycle 24 Expected?

We investigate solar activity by focusing on double maxima in solar cycles and try to estimate the shape of the current solar cycle (Cycle 24) during its maximum. We analyzed data for Solar Cycle 24 by using Learmonth Solar Observatory sunspot group data since 2008. All sunspot groups (SGs) recorded during this time interval were separated into two groups: The first group includes small SGs [A, B, C, H, classes by the Zurich classification], and the second group consists of large SGs [D, E, and F]. We then calculated small and large sunspot group numbers, their sunspot numbers [SSN] and Zurich numbers [Rz] from their daily mean numbers as observed on the solar disk during a given month. We found that the temporal variations for these three different separations behave similarly. We also analyzed the general shape of solar cycles from Cycle 1 to 23 by using monthly International Sunspot Number [ISSN] data and found that the durations of maxima were about 2.9 years. Finally, we used ascending time and SSN relationship and found that the maximum of the Cycle 24 should be later than 2011. Thus, we conclude that i) one possible reason for a double maximum in solar cycles is the different behavior of large and small sunspot groups, and ii) a double maximum is coming for Solar Cycle 24.

Instrumental data on the sunspot formation in the 17th–18th centuries: Correct information or approximations

The available data on the sunspot number derived from telescopic observations are analyzed. It has been indicated that uncertainty in the data on the number of sunspot groups is close to 30% for the 17th century-the early 19th century and reaches a factor of 2 and more in individual years. This means that the above data include limited information on solar activity in the 17th–18th centuries and it is necessary to use external sources (first of all, the data of paleoastrophysics) in order to study this activity in the indicated epoch. Only from the middle of the 19th century, information obtained based on instrumental observations became sufciently accurate for reliable quantitative estimates.

Revised Group Sunspot Number Values for 1640, 1652, and 1741

Some studies have shown that our knowledge on solar activity in the years 1640, 1652, and 1741 can be improved. In this contribution, we revise the annual group sunspot numbers for these years from original observations. For the years 1640, 1652 and 1741, we have obtained the corrected values 15.2, 1.8, and 27.3, respectively (instead of the original values 15.0, 4.0, and 57.7).

The Greenwich Photo-heliographic Results (1874 – 1976): Initial Corrections to the Printed Publications

A new sunspot and faculae digital dataset for the interval 1874 – 1955 has been prepared under the auspices of the NOAA National Geophysical Data Center (NGDC). This digital dataset contains measurements of the positions and areas of both sunspots and faculae published initially by the Royal Observatory, Greenwich, and subsequently by the Royal Greenwich Observatory (RGO), under the title Greenwich Photo-heliographic Results (GPR), 1874 – 1976. Quality control (QC) procedures based on logical consistency have been used to identify the more obvious errors in the RGO publications. Typical examples of identifiable errors are North versus South errors in specifying heliographic latitude, errors in specifying heliographic (Carrington) longitude, errors in the dates and times, errors in sunspot group numbers, arithmetic errors in the summation process, and the occasional omission of solar ephemerides. Although the number of errors in the RGO publications is remarkably small, an initial table of necessary corrections is provided for the interval 1874 – 1917. Moreover, as noted in the preceding companion papers, the existence of two independently prepared digital datasets, which both contain information on sunspot positions and areas, makes it possible to outline a preliminary strategy for the development of an even more accurate digital dataset. Further work is in progress to generate an extremely reliable sunspot digital dataset, based on the long programme of solar observations supported first by the Royal Observatory, Greenwich, and then by the Royal Greenwich Observatory.

Long-term temporal variations in the areas of sunspot groups

Recently, ħ0125protectJavaraiah2012a) analyzed the combined Greenwich and Solar Optical Observing Network (SOON) sunspot group data during the period 1874–2011 and studied variations in the annual numbers (counts) of the small (maximum area AM<100 millionth of solar hemisphere, msh), large (100⩽AM<300msh), and big (AM⩾300msh) sunspot groups. Here that analysis is extended and studied variations in the mean maximum sizes (the mean values of maximum areas) of the aforementioned three classes of sunspot groups and also their combination. It is found that there is no significant correlation between the mean maximum size of any class of sunspot groups and the International Sunspot Number (RZ), probably due to in a given time interval small sunspot groups/sunspots outnumber the large ones. A pattern of an approximate 9-year period cycle is seen in the variations of the mean maximum sizes of the large and the big sunspot groups during a solar cycle. On long-time scales it is found that there exists a strong 130 or more years cycle in the variation of the mean size of the small sunspot groups, whereas there is a hint on the existence of ≈44-year cycles in the variations of the mean maximum sizes of the large and the big sunspot groups. During the decline phase of cycle 23, there was a scarcity in the sunspot groups whose AM⩽37msh, which may be related to the slow growth of sunspot groups during this period. During the minimum between cycles 23 and 24 may be due to the presence of a number of small sunspot groups whose AM>37 was larger than that of whose AM⩽37, the relatively large size coronal holes were present at low-latitudes and the total solar irradiance was very low.

Phase analysis of sunspot group numbers on both solar hemispheres

Cross-correlation analysis and wavelet transform methods are proposed to investigate the phase relationship between the monthly sunspot group numbers in the solar northern and southern hemispheres. It is found that (1) the monthly sunspot group numbers in the northern hemisphere begin two months earlier than those in the southern one, which should lead to phase asynchrony between them but with a slight effect; (2) the Schwabe cycle length for the monthly sunspot group numbers in the two hemispheres obviously differs from each other, and the mean Schwabe cycle length of the monthly sunspot group numbers in the northern hemisphere is slightly larger than that in the southern one; (3) the monthly sunspot group numbers in the northern hemisphere precede those in the southern hemisphere during the years of about 1874–1927, after which, the southern hemisphere leads the northern hemisphere in the years 1928–1964, and then the northern hemisphere leads in time till the present.

Missing solar cycle hypothesis and basic statistical regularities of solar cycles

The basic statistical properties of solar cycles, including the Gnevyshev-Ol’ rule, the Waldmeier effect, and the amplitude-period effect, are tested using data on the number of sunspot groups for 1700–1996, considering the hypothesis about a missing solar cycle in the late 18th century. The results show that the division of the long cycle of 1784–1800 into two short cycles—1784–1793 and 1793–1800—alters significantly the pattern of the solar cycles. The Gnevyshev-Ol’ cycle intensity effect becomes stronger, and almost all other statistical effects grow weaker. This change is due to the fact that the short and weak cycle of 1793–1800 is statistically very unusual and its features are very different from those of other solar cycles.

Change of Sunspot Groups Observed from 2002 to 2011 at ButterStar Observatory

Since the development of surface magnetic features should reflect the evolution of the solar magnetic field in the deep interior of the Sun, it is crucial to study properties of sunspots and sunspot groups to understand the physical processes working below the solar surface. Here, using the data set of sunspot groups observed at the ButterStar observatory for 3,364 days from 2002 October 16 to 2011 December 31, we investigate temporal change of sunspot groups depending on their Zurich classification type. Our main findings are as follows: (1) There are more sunspot groups in the southern hemisphere in solar cycle 23, while more sunspot groups appear in the northern hemisphere in solar cycle 24. We also note that in the declining phase of solar cycle 23 the decreasing tendency is apparently steeper in the solar northern hemisphere than in the solar southern hemisphere. (2) Some of sunspot group types make a secondary peak in the distribution between the solar maximum and the solar minimum. More importantly, in this particular data set, sunspot groups which have appeared in the solar southern hemisphere make a secondary peak 1 year after a secondary peak occurs in the solar northern hemisphere. (3) The temporal variations of small and large sunspot group numbers are disparate. That is, the number of large sunspot group declines earlier and faster and that the number of small sunspot group begins to rise earlier and faster. (4) The total number of observed sunspot is found to behave more likewise as the small sunspot group does. Hence, according to our findings, behaviors and evolution of small magnetic flux tubes and large magnetic flux tubes seem to be different over solar cycles. Finally, we conclude by briefly pointing out its implication on the space weather forecast.

The G–O Rule and Waldmeier Effect in the Variations of the Numbers of Large and Small Sunspot Groups

We have analyzed the combined Greenwich and Solar Optical Observing Network (SOON) sunspot group data during the period of 1874 – 2011 and determined variations in the annual numbers (counts) of the small (maximum area A M<100 millionth of solar hemisphere, msh), large (100≤A M<300 msh), and big (A M≥300 msh) spot groups. We found that the amplitude of an even-numbered cycle of the number of large groups is smaller than that of its immediately following odd-numbered cycle. This is consistent with the well known Gnevyshev and Ohl rule (G–O rule) of solar cycles, generally described by using the Zurich sunspot number (R Z). During cycles 12 – 21 the G–O rule holds good for the variation in the number of small groups also, but it is violated by cycle pair (22, 23) as in the case of R Z. This behavior of the variations in the small groups is largely responsible for the anomalous behavior of R Z in cycle pair (22, 23). It is also found that the amplitude of an odd-numbered cycle of the number of small groups is larger than that of its immediately following even-numbered cycle. This might be called the ‘reverse G–O rule’. In the case of the number of the big groups, both cycle pairs (12, 13) and (22, 23) violated the G–O rule. In many cycles the positions of the peaks of the small, large, and big groups are different, and considerably differ with respect to the corresponding positions of the R Z peaks. In the case of cycle 23, the corresponding cycles of the small and large groups are largely symmetric/less asymmetric (the Waldmeier effect is weak/absent) with their maxima taking place two years later than that of R Z. The corresponding cycle of the big groups is more asymmetric (strong Waldmeier effect) with its maximum epoch taking place at the same time as that of R Z.