Group Sunspot Number Research Articles

A Recount of Sunspot Groups on Staudach’s Drawings

We have examined the more than 1100 drawings of the solar disk made by the German amateur astronomer Johann Caspar Staudach during 1749 – 1799 and counted the spots on each image. Using the modern perception of how to group spots into active regions, we regrouped the spots as a modern observer would. The resulting number of groups was found to be higher on average by 25 % than the first count of groups performed by Wolf in 1857, which was used by Hoyt and Schatten (Solar Phys. 181, 491, 1998) in their construction of the group sunspot number. Compared to other observers at the time, Staudach’s drawings have a very low average number, about two, of spots per group, possibly indicating an inferior telescope that probably suffered from spherical and chromatic aberration, as would be typical of amateur telescopes of the day. We have initiated an ongoing project aiming at observing sunspots with antique telescopes having similar defects in order to determine the factor necessary to bring the Staudach observations onto a modern scale.

Dependence of the Sunspot-Group Size on the Level of Solar Activity and its Influence on the Calibration of Solar Observers

The distribution of the sunspot group size (area) and its dependence on the level of solar activity is studied. It is shown that the fraction of small groups is not constant but decreases with the level of solar activity so that high solar activity is largely defined by big groups. We study the possible influence of solar activity on the ability of a realistic observer to see and report the daily number of sunspot groups. It is shown that the relation between the number of sunspot groups as seen by different observers with different observational acuity thresholds is strongly non-linear and cannot be approximated by the traditionally used linear scaling ($k-$factors). The observational acuity threshold [$A_{\rm th}$] is considered to quantify the quality of each observer, instead of the traditional relative $k-$factor. A nonlinear $c-$factor based on $A_{\rm th}$ is proposed, which can be used to correct each observer to the reference conditions. The method is tested on a pair of principal solar observers, Wolf and Wolfer, and it is shown that the traditional linear correction, with the constant $k-$factor of 1.66 to scale Wolf to Wolfer, leads to an overestimate of solar activity around solar maxima.

Preface to Topical Issue: Recalibration of the Sunspot Number

This topical issue contains articles on the effort to recalibrate the sunspot number (SN) that was initiated by the Sunspot Number Workshops. These workshops led to a revision of the Wolf sunspot number (WSN) and a new construction of the group sunspot number (GSN), both published herein. In addition, this topical issue includes three independently proposed alternative SN time series (two Wolf and one group), as well as articles providing historical context, critical assessments, correlative analyses, and observational data, both historical and modern, pertaining to the sunspot-number time series. The ongoing effort to understand and reconcile the differences between the various new sunspot number series is briefly discussed.

The New Sunspot Number: Assembling All Corrections

The Sunspot Number, created by R.Wolf in 1849, provides a direct long-term record of solar activity from 1700 to the present. In spite of its central role in multiple studies of the solar dynamo and of the past Sun-Earth relations, it was never submitted to a global critical revision. However, various discrepancies with other solar indices recently motivated a full re-calibration of this series. Based on various diagnostics and corrections established in the framework of several Sunspot Number Workshops and described in Clette et al. 2014, we assembled all corrections in order to produce a new standard version of this reference time series. In this paper, we explain the three main corrections and the criteria used to choose a final optimal version of each correction factor or function, given the available information and published analyses. We then discuss the good agreement obtained with the Group sunspot Number derived from a recent reconstruction. Among the implications emerging from this re-calibrated series, we also discuss the absence of a rising secular trend in the newly-determined solar cycle amplitudes, also in relation with contradictory indications derived from cosmogenic radionuclides. As conclusion, we introduce the new version management scheme now implemented at the World Data Center - SILSO, which reflects a major conceptual transition: beyond the re-scaled numbers, this first revision of the Sunspot Number also transforms the former locked data archive into a living observational series open to future improvements.

Tests of Sunspot Number Sequences: 4. Discontinuities Around 1946 in Various Sunspot Number and Sunspot-Group-Number Reconstructions

We use 5 test data series to quantify putative discontinuities around 1946 in 5 annual-mean sunspot number or group number sequences. The series tested are: the original and new versions of the Wolf/Zurich/International sunspot number composite [$R_{ISNv1}$ and $R_{ISNv2}$] ; the corrected version of $R_{ISNv1}$ [$R_C$]; the backbone group number [$R_{BB}$]; and the group number composite [$R_{UEA}$]. The test data are: the group number $N_G$ and total sunspot area $A_G$ from the RGO photoheliographic data; the CaK index from re-analysis of MWO CaII K spectroheliograms; the group number from the MWO sunspot drawings, $N_{MWO}$; and ionospheric critical frequencies at Slough [$foF2$]. The test data all vary with sunspot numbers, in some cases non-linearly. Tests use both before-and-after fit-residual comparison and correlation methods, applied to intervals iterated to minimise errors and eliminate the effect of the discontinuity date. It is not assumed that the correction required is by a constant factor, nor even linear in sunspot number. A non-linear correction is required by $R_C$, $R_{BB}$ and $R_{ISNv1}$, but not by $R_{ISNv2}$ or $R_{UEA}$. The test datasets give very similar results in all cases. By multiplying the probability distribution functions together we obtain the optimum correction for each data series that must be applied to pre-discontinuity data to make them consistent with the post-discontinuity data. It is shown that, on average, values for 1932-1943 are too small (relative to later values) by about 12.3% for $R_{ISNv1}$ but are too large for $R_{ISNv2}$ and $R_{BB}$ by 3.8% and 5.2%. The correction applied to generate $R_C$ from $R_{ISNv1}$ reduces this average factor to 0.5% but does not remove the non-linear variation, and other errors remain uncorrected. A test is provided by $R_{UEA}$, which is identical to the RGO $N_G$ values over the interval used.

A Revised Collection of Sunspot Group Numbers

We describe a revised collection of the number of sunspot groups from 1610 to the present. This new collection is based on the work of Hoyt and Schatten (Solar Phys. 179, 189, 1998). The main changes are the elimination of a considerable number of observations during the Maunder Minimum (hereafter, MM) and the inclusion of several long series of observations. Numerous minor changes are also described. Moreover, we have calculated the active-day percentage during the MM from this new collection as a reliable index of the solar activity. Thus, the level of solar activity obtained in this work is greater than the level obtained using the original Hoyt and Schatten data, although it remains compatible with a grand minimum of solar activity. The new collection is available in digital format.

Historical Heliophysical Series of the Ebro Observatory

We present the contents of the historical heliophysical series collected at the Ebro Observatory, as well as the actions carried out to restore and save these data and to conserve the physical media containing the data and the telescopes that helped to obtain them. We also discuss the results obtained with these measurements, describe how we disseminated them, and report on the investigations that we have carried out with this information. We show the evolution of the local solar indices such as the Ebro Sunspot Number (ESN), the Ebro Group Sunspot Number (EGSN), or the Ebro Sunspot Area (ESA), which are derived directly from our data. For verification purposes, these local solar indices have been compared to the international sunspot numbers published by SILSO. Our data are reliable and correlate well with the respective international series. Finally, as an example of the possibilities that the Ebro series offer, we explain the use of these data to elucidate one of the recent problems in solar physics: the discontinuity in international data known as the Waldmeier discontinuity and, in general, the ratio between sunspots and sunspot groups. In the Ebro Observatory series, no discontinuity such as this is detected. We instead observe a rather stable ratio in the spot or group rates. This result is in agreement with the hypothesis of Svalgaard (2010, ASP CS-428, 297) that the Waldmeier discontinuity is produced only on a procedural level, perhaps by a change in the criteria used in Zurich by Waldmeier or by changing external conditions.

Comparison of New and Old Sunspot Number Time Series

Four new sunspot number time series have been published in this Topical Issue: a backbone-based group number in Svalgaard and Schatten (Solar Phys., 2016; referred to here as $\mathit{SS}$ , 1610 – present), a group number series in Usoskin et al. (Solar Phys., 2016; UEA, 1749 – present) that employs active day fractions from which it derives an observational threshold in group spot area as a measure of observer merit, a provisional group number series in Cliver and Ling (Solar Phys., 2016; $\mathit{CL}$ , 1841 – 1976) that removed flaws in the Hoyt and Schatten (Solar Phys. 179, 189, 1998a; 181, 491, 1998b) normalization scheme for the original relative group sunspot number ( $R_{\mathrm{G}}$ , 1610 – 1995), and a corrected Wolf (international, $R_{\mathrm{I}}$ ) number in Clette and Lefevre (Solar Phys., 2016; $S_{\mathrm{N}}$ , 1700 – present). Despite quite different construction methods, the four new series agree well after about 1900. Before 1900, however, the UEA time series is lower than $\mathit{SS}$ , $\mathit{CL}$ , and $S_{\mathrm{N}}$ , particularly so before about 1885. Overall, the UEA series most closely resembles the original $R_{\mathrm{G}}$ series. Comparison of the UEA and SS series with a new solar wind $B$ time series (Owens et al. in J. Geophys. Res., 2016; 1845 – present) indicates that the UEA time series is too low before 1900. We point out incongruities in the Usoskin et al. (Solar Phys., 2016) observer normalization scheme and present evidence that this method under-estimates group counts before 1900. In general, a correction factor time series, obtained by dividing an annual group count series by the corresponding yearly averages of raw group counts for all observers, can be used to assess the reliability of new sunspot number reconstructions.

Tests of Sunspot Number Sequences: 2. Using Geomagnetic and Auroral Data

We compare four sunspot-number data sequences against geomagnetic and terrestrial auroral observations. The comparisons are made for the original SIDC composite of Wolf-Zurich-International sunspot number [$R_{ISNv1}$], the group sunspot number [$R_{G}$] by Hoyt and Schatten (Solar Phys., 1998), the new "backbone" group sunspot number [$R_{BB}$] by Svalgaard and Schatten (Solar Phys., 2016), and the "corrected" sunspot number [$R_{C}$] by Lockwood at al. (J.G.R., 2014). Each sunspot number is fitted with terrestrial observations, or parameters derived from terrestrial observations to be linearly proportional to sunspot number, over a 30-year calibration interval of 1982-2012. The fits are then used to compute test sequences, which extend further back in time and which are compared to $R_{ISNv1}$, $R_{G}$, $R_{BB}$, and $R_{C}$. To study the long-term trends, comparisons are made using averages over whole solar cycles (minimum-to-minimum). The test variations are generated in four ways: i) using the IDV(1d) and IDV geomagnetic indices (for 1845-2013) fitted over the calibration interval using the various sunspot numbers and the phase of the solar cycle; ii) from the open solar flux (OSF) generated for 1845 - 2013 from four pairings of geomagnetic indices by Lockwood et al. (Ann. Geophys., 2014) and analysed using the OSF continuity model of Solanki at al. (Nature, 2000) which employs a constant fractional OSF loss rate; iii) the same OSF data analysed using the OSF continuity model of Owens and Lockwood (J.G.R., 2012) in which the fractional loss rate varies with the tilt of the heliospheric current sheet and hence with the phase of the solar cycle; iv) the occurrence frequency of low-latitude aurora for 1780-1980 from the survey of Legrand and Simon (Ann. Geophys., 1987). For all cases, $R_{BB}$ exceeds the test terrestrial series by an amount that increases as one goes back in time.

Sunspot Observations of Rudolf Wolf from 1849 – 1893

The sunspot observations of Rudolf Wolf form the core of the Wolf series of sunspot relative numbers, or Wolf numbers, since his observations define the original scale of the series and also the main course of solar activity from 1849 to 1893. Unfortunately, the raw data for the years 1856 to 1869 were never published in full detail. The heritage group of the Rudolf Wolf Society in Switzerland digitized parts of the hitherto unpublished original source book of the Wolf series and put it on its website . Now, the Wolf numbers from 1849 to 1876, as provided by the World Data Center for Solar Index and Long-term Solar Observations (WDC-SILSO), can be reconstructed in every detail, since the source book contains all the raw sunspot group and individual spot numbers as well as the implemented calibration and interpolation methods. Thus, the observations made by Rudolf Wolf with the 83/1320 mm Fraunhofer refractor and with the 40/700 mm Parisian refractor as well as those made by Heinrich Schwabe can be identified and separated now. In this article, we describe Wolf’s instruments and methods of observation. An inspection of the source book and other published sources reveals that the calibration factor of the 40/700 mm Parisian refractor should probably be lowered. Since no appropriate comparison observations are available, the scale transfer from Heinrich Schwabe to Rudolf Wolf has to be analyzed further.

North-south asymmetry in small and large sunspot group activity and violation of even-odd solar cycle rule

According to Gnevyshev-Ohl (G-O) rule an odd-numbered cycle is stronger than its preceding even-numbered cycle. In the modern time the cycle pair (22, 23) violated this rule. By using the combined Greenwich Photoheliographic Results (GPR) and Solar Optical Observing Network (SOON) sunspot group data during the period 1874-2015, and Debrecen Photoheliographic Data (DPD) of sunspot groups during the period 1974-2015, here we have found that the solar cycle pair (22, 23) violated the G-O rule because, besides during cycle 23 a large deficiency of small sunspot groups in both the northern and the southern hemispheres, during cycle 22 a large abundance of small sunspot groups in the southern hemisphere. In the case of large and small sunspot groups the cycle pair (22, 23) violated the G-O rule in the northern and southern hemispheres, respectively, suggesting the north-south asymmetry in solar activity has a significant contribution in the violation of G-O rule. The amplitude of solar cycle 24 is smaller than that of solar cycle 23. However, Coronal Mass Ejections (CMEs) rate in the rising phases of the cycles 23 and 24 are almost same (even slightly large in cycle 24). From both the SOON and the DPD sunspot group data here we have also found that on the average the ratio of the number (counts) of large sunspot groups to the number of small sunspot groups is larger in the rising phase of cycle 24 than that in the corresponding phase of cycle 23. We suggest this could be a potential reason for the aforesaid discrepancy in the CME rates during the rising phases of cycles 23 and 24. These results have significant implication on solar cycle mechanism

The Greenwich Photo-heliographic Results (1874 – 1885): Observing Telescopes, Photographic Processes, and Solar Images

Potential sources of inhomogeneity in the sunspot measurements published by the Royal Observatory, Greenwich, during the early interval 1874 – 1885 are examined critically. Particular attention is paid to inhomogeneities that might arise because the sunspot measurements were derived from solar photographs taken at various contributing solar observatories, which used different telescopes, experienced different seeing conditions, and employed different photographic processes. The procedures employed in the Solar Department at the Royal Greenwich Observatory (RGO), Herstmonceux, during the final phase of sunspot observations provide a modern benchmark for interpreting the early sunspot measurements. The different observing telescopes used at the contributing solar observatories during the interval 1874 – 1885 are discussed in detail, using information gleaned from the official RGO publications and other relevant historical documents. Likewise, the different photographic processes employed at the different solar observatories are reviewed carefully. The procedures used by RGO staff to measure the positions and areas of sunspot groups on photographs of the Sun having a nominal radius of either four or eight inches are described. It is argued that the learning curve for the use of the Kew photoheliograph at the Royal Observatory, Greenwich, actually commenced in 1858, not 1874. The RGO daily number of sunspot groups is plotted graphically and analysed statistically. Similarly, the changes of metadata at each solar observatory are shown on the graphical plots and analysed statistically. It is concluded that neither the interleaving of data from the different solar observatories nor the changes in metadata invalidates the RGO count of the number of sunspot groups, which behaves as a quasi-homogeneous time series. Furthermore, it is emphasised that the correct treatment of days without photographs is quite crucial to the correct calculation of Group Sunspot Numbers.

Re-examination of the Daily Number of Sunspot Groups for the Royal Observatory, Greenwich (1874 – 1885)

The daily number of sunspot groups on the solar disk, as recorded by the programme of sunspot observations performed under the aegis of the Royal Observatory, Greenwich, UK, and subsequently the Royal Greenwich Observatory (RGO), is re-examined for the interval 1874 – 1885. The motivation for this re-examination is the key role that the RGO number of sunspot groups plays in the calculation of Group Sunspot Numbers (Hoyt and Schatten in Solar Phys. 179, 189, 1998a; Solar Phys. 181, 491, 1998b). A new dataset has been derived for the RGO daily number of sunspot groups in the interval 1874 – 1885. This new dataset attempts to achieve complete consistency between the sunspot data presented in the three main sections of the RGO publications and also incorporates all known errata and additions. It is argued that days for which no RGO solar photograph was acquired originally should be regarded, without exception, as being days without meaningful sunspot data. The daily number of sunspot groups that Hoyt and Schatten assign to days without RGO photographs is frequently just a lower limit. Moreover, in the absence of a solar photograph, the daily number of sunspot groups is inevitably uncertain because of the known frequent occurrence of sunspot groups that exist for just a single day. The elimination of days without photographs changes the list of inter-comparison days on which both the primary RGO observer and a specified secondary comparison observer saw at least one sunspot group. The resulting changes in the personal correction factors of secondary observers then change the personal correction factors of overlapping tertiary observers, etc. In this way, numerical changes in the personal correction factors of secondary observers propagate away from the interval 1874 – 1885, thereby potentially changing the arithmetical calculation of Group Sunspot Numbers over an appreciably wider time interval.

Tests of Sunspot Number Sequences: 3. Effects of Regression Procedures on the Calibration of Historic Sunspot Data

We use sunspot group observations from the Royal Greenwich Observatory (RGO) to investigate the effects of intercalibrating data from observers with different visual acuities. The tests are made by counting the number of groups $R_B$ above a variable cut-off threshold of observed total whole-spot area (uncorrected for foreshortening) to simulate what a lower acuity observer would have seen. The synthesised annual means of $R_B$ are then re-scaled to the observed RGO group number $R_A$ using a variety of regression techniques. It is found that a very high correlation between $R_A$ and $R_B$ ($r_{AB}$ > 0.98) does not prevent large errors in the intercalibration (e.g. sunspot maximum values can be over 30% too large even for such levels of $r_{AB}$). In generating the backbone sunspot number, Svalgaard and Schatten [2015] force regression fits to pass through the scatter plot origin which generates unreliable fits (the residuals do not form a normal distribution) and causes sunspot cycle amplitudes to be exaggerated in the intercalibrated data. It is demonstrated that the use of Quantile-Quantile (Q-Q) plots to test for a normal distribution is a useful indicator of erroneous and misleading regression fits. Ordinary least squares linear fits, not forced to pass through the origin, are sometimes reliable (although the optimum method used is shown to be different when matching peak and average sunspot group numbers). However other fits are only reliable if non-linear regression is used. From these results it is entirely possible that the inflation of solar cycle amplitudes in the backbone group sunspot number as one goes back in time, relative to related solar-terrestrial parameters, is entirely caused by the use of inappropriate and non-robust regression techniques to calibrate the sunspot data.

The Discontinuity Circa 1885 in the Group Sunspot Number

On average, the international sunspot number ( $R_{\mathrm{I}}$ ) is 44 % higher than the group sunspot number ( $R_{\mathrm{G}}$ ) from 1885 to the beginning of the $R_{\mathrm{I}}$ series in 1700. This is the principal difference between $R_{\mathrm{I}}$ and $R_{\mathrm{G}}$ . Here we show that this difference is primarily due to an inhomogeneity in the Royal Greenwich Observatory (RGO) record of sunspot groups (1874 – 1976) used to derive observer normalization factors (called $k$ -factors) for $R_{\mathrm{G}}$ . Specifically, annual RGO group counts increase relative to those of Wolfer and other long-term observers from 1876 – 1915. A secondary contributing cause is that the $k$ -factors for observers who began observing before 1884 and overlapped with RGO for any years during 1874 – 1883 were not based on direct comparison with RGO but were calculated using one or more intermediary or additional observers. We introduce $R_{\mathrm{GC}}$ by rectifying the RGO group counts from 1874 – 1915 and basing $k$ -factors on direct comparison with RGO across the 1885 discontinuity, which brings the $R_{\mathrm{G}}$ and $R_{\mathrm{I}}$ series into reasonable agreement for the 1841 – 1885 interval (after correcting $R_{\mathrm{I}}$ for an inhomogeneity from 1849 – 1867 (to give $R_{\mathrm{IC}}$ )). Comparison with an independently derived backbone-based reconstruction of $R_{\mathrm{G}}$ ( $R_{\mathrm{BB}}$ ) indicates that $R_{\mathrm{GC}}$ over-corrects $R_{\mathrm{BB}}$ by 4 % on average from 1841 – 1925. Our analysis suggests that the maxima of Cycles 10 (in 1860), 12 (1883/1884), and 13 (1893) in the $R_{\mathrm{IC}}$ series are too low by ≈ 10 %.

A continuous ice-core 10Be record from Mongolian mid-latitudes: Influences of solar variability and local climate

High-resolution 10Be records used for studies of detailed changes in atmospheric 10Be production rates predominantly derive from polar ice cores. In this study, we present the first 10Be record from a mid-latitude ice core. The ice core derives from the Tsambagarav mountain range located in the Mongolian Altai region. The new 10Be concentration record spans the period from AD 1550 to 2009, while the flux record extends from AD 1816 to 2009. The 10Be concentration in the Tsambagarav ice core ranges between ∼1.5×104 and ∼10×104 atomsg−1, whereas the 10Be flux changes from ∼0.02 to ∼0.15 atoms cm−2 s−1. The average 10Be flux at Tsambagarav is four times higher than the average 10Be flux recorded in the NGRIP and Dome Fuji ice cores, which is in accordance with model predictions. In general, the long-term trends observed in the Tsambagarav 10Be concentration and flux records are reasonably similar to those observed in the NGRIP ice core. A comparison between the Tsambagarav 10Be record, group sunspot numbers (GSNs), and solar modulation potentials based on 14C in tree rings suggests that the Maunder Minimum was associated with a prolonged maximum in 10Be concentrations at Tsambagarav, whereas the Dalton Minimum was associated with a minor increase in the 10Be concentration and flux that was delayed relative to the primary minimum in GSNs. The sulphate record from Tsambagarav shows that large positive anomalies in the sulphate concentration are associated with negative anomalies in the 10Be concentration. A concurrent positive sulphate anomaly may explain why the main phase of the Dalton Minimum is subdued in the 10Be record from Tsambagarav. Spectral analysis indicates that the 11-yr solar-cycle signal may have influenced the new 10Be record, but the evidence supporting a direct link is ambiguous. Local and regional climatic changes, such as cyclonic versus anticyclonic conditions and related storm tracks, most likely played a significant role for the 10Be deposition in the Tsambagarav region.

Amplitude–time relations at different latitudes in the 11-year cycle of solar activity

On the basis of sunspots data for cycles 12–23, it is shown that the correlation between the amplitude of the 11-year cycle and lengths of intervals that determine the location of the cyclic curve of average latitudes relative to the cycle’s maximum and minimums is strongly dependent on the latitude. The correlation extrema are reached at latitudes 15° and 20°, which are the most representative. The equations for calculating the amplitude of the 11-year cycle are composed based on the information on the intervals corresponding to latitude 15°. It is found that the correlation between the amplitude of the 11-year cycle and the latitude values of the sunspot group number index is significant at middle and high latitudes (15°–25°) and is small at low latitudes (5°–10°). This agrees with the statement that the level of sunspot activity is not correlated with the cycle amplitude at the declining phase of the 11-year cycle (for latitudes <12°) and depends only on the current value of the average latitude. A high correlation (R = 0.88 for latitudes ±8°) is found between the activity level of the current 11-year cycle at low latitudes and the amplitude of the next one. The amplitude of the 24th cycle in GSN units (GSN(24) = 91) is estimated by the corresponding regression equation.

Sunspots During the Maunder Minimum from Machina Coelestis by Hevelius

We revisited the sunspot observations published by Johannes Hevelius in his book Machina Coelestis (1679) corresponding to the period 1653-1675 (just in the middle of the Maunder Minimum). We show detailed translations of the original Latin texts describing the sunspot records and provide the general context of these sunspot observations. From this source only, we present an estimate of the annual values of the Group Sunspot Number based only on the records that explicitly inform about the presence or absence of sunspots. Although we obtain very low values of the Group Sunspot Number, in accordance with a grand minimum of solar activity, these values are significantly higher in general than the values provided by Hoyt and Schatten (1998) for the same period.

Newly found sunspot observations by Peter Becker from Rostock for 1708, 1709, and 1710

AbstractWe present a few newly found old sunspot observations from the years AD 1708, 1709, and 1710, which were obtained by Peter Becker from Rostock, Germany. For 1709, Becker gave a detailed drawing: he observed a sunspot group made up of two spots on January 5, 6, and 7, and just one of the two spots was observed on January 8 and 9. We present his drawing and his explanatory text. We can measure the latitude and longitude of these two spots and estimate their sizes for all five days. While the spots and groups in 1708 and the spot on four of the five days in January 1709 were known before from other observers (e.g. Hoyt &amp; Schatten 1998), the location of the spots in early January 1709 were not known before, so that they can now be considered in reconstructed butterfly diagrams. The sunspots detected by Becker on 1709 January 5 and 1710 September 10 were not known before at all, as the only observer known for those two dates, La Hire, did not detect that spot (group). We estimate new group sunspot numbers for the relevant days, months, and years. The time around 1708–1710 is important, because it documents the recovery of solar activity towards the end of the Maunder Grand Minimum. We also show two new spot observations from G. Kirch for 1708 September 13 and 14 as described in his letter to Wurzelbaur (dated Berlin AD 1708 December 19). (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Level and length of cyclic solar activity during the Maunder minimum as deduced from the active-day statistics

The Maunder minimum (MM) of greatly reduced solar activity took place in 1645-1715, but the exact level of sunspot activity is uncertain as based, to a large extent, on historical generic statements of the absence of spots on the Sun. Here we aim, using a conservative approach, to assess the level and length of solar cycle during the Maunder minimum, on the basis of direct historical records by astronomers of that time. A database of the active and inactive days (days with and without recorded sunspots on the solar disc respectively) is constructed for three models of different levels of conservatism (loose ML, optimum MO and strict MS models) regarding generic no-spot records. We have used the active day fraction to estimate the group sunspot number during the MM. A clear cyclic variability is found throughout the MM with peaks at around 1655--1657, 1675, 1684 and 1705, and possibly 1666, with the active day fraction not exceeding 0.2, 0.3 or 0.4 during the core MM, for the three models. Estimated sunspot numbers are found very low in accordance with a grand minimum of solar activity. We have found, for the core MM (1650-1700), that: (1) A large fraction of no-spot records, corresponding to the solar meridian observations, may be unreliable in the conventional database. (2) The active day fraction remained low (below 0.3-0.4) throughout the MM, indicating the low level of sunspot activity. (3) The solar cycle appears clearly during the core MM. (4) The length of the solar cycle during the core MM appears $9\pm 1$ years, but there is an uncertainty in that. (5) The magnitude of the sunspot cycle during MM is assessed to be below 5-10 in sunspot numbers; A hypothesis of the high solar cycles during the MM is not confirmed.