Overlooked sunspot observations by Hevelius in the early Maunder Minimum, 1653–1684

In the bookMachina Coelestis (1679), Johannes Hevelius lists his daily solar observations from 1653 to 1679. He mentions 19 sunspot groups during this interval, of which 14 are unique to Hevelius and five are confirmed by other observers. There are an additional 9 sunspot groups during this interval that were not observed by Hevelius. In five cases he was not observing, but in the other four cases he did observe but failed to comment upon sunspots. The spots he missed or failed to observe tend to occur near the end of his career. This suggests Hevelius occasionally missed sunspots but usually was a reliable observer. These observations are important because they provide us the only known daily listing of solar observations during the early years of the Maunder Minimum. They are also important because they were overlooked by Wolf, Spoerer, Maunder, Eddy, and others in their study of solar activity in the seventeenth century. They provide us the best record of the sunspot maximum of 1660 when one sunspot lasted at least 86 days as it traversed the solar disk four times. The same region was active for seven solar rotations.     

Could a Hexagonal Sunspot Have Been Observed During the Maunder Minimum?

The Maunder Minimum is the period between 1645 and 1715. Its main characteristic is abnormally low and prolonged solar activity. However, some authors have doubted the low level of solar activity during that period by questioning the accuracy and objectivity of the observers. This work presents a particular case of a sunspot observed during the Maunder Minimum with an unusual shape of its umbra and penumbra: a hexagon. This sunspot was observed by Cassini in November 1676, just at the core of the Maunder Minimum. This historical observation is compared with a twin case that occurred recently in May 2016. The conclusion reached is that Cassini’s record is another example of the good quality of the observations that were made during the Maunder Minimum, showing the meticulousness of the astronomers of that epoch. This sunspot observation made by Cassini does not support the conclusions of Zolotova and Ponyavin (Astrophys. J. 800, 42, 2015) that professional astronomers in the seventeenth century only registered round sunspots. Finally, a discussion is given of the importance of this kind of unusual sunspot record for a better assessment of the true level of solar activity in the Maunder Minimum.     

Solar Rotation in the 17th century

Sunspot drawings made by Galileo Galilei in 1612 are used to derive the law of differential rotation at that time. The main interest of the work is during the time of observations, just at the beginning of telescopic observations and some decades before the Maunder Minimum (1645 – 1715), a period where the sunspots almost disappeared from the solar surface. For this purpose we have carried out careful corrections of the different sources of errors derived from the observing technique. By comparing with other results of the same century, a significant difference is only detected by comparing with data corresponding to the deep Maunder Minimum (Paris Observatory drawings). The characteristics of the solar differential rotation, and extrapolating the behavior of solar activity, did not differ before or after the Maunder Minimum. We also include an analysis of hitherto ignored sunspot drawings by N. Bion made in October and November 1672.     

Cosmogenic Isotope Variability During the Maunder Minimum: Normal 11-year Cycles Are Expected

The amplitude of the 11-year cycle measured in the cosmogenic isotope ¹⁰Be during the Maunder Minimum is comparable to that during the recent epoch of high solar activity. Because of the virtual absence of the cyclic variability of sunspot activity during the Maunder Minimum this seemingly contradicts an intuitive expectation that lower activity would result in smaller solar-cycle variations in cosmogenic radio-isotope data, or in none, leading to confusing and misleading conclusions. It is shown here that large 11-year solar cycles in cosmogenic data observed during periods of suppressed sunspot activity do not necessarily imply strong heliospheric fields. Normal-amplitude cycles in the cosmogenic radio-isotopes observed during the Maunder Minimum are consistent with theoretical expectations because of the nonlinear relation between solar activity and isotope production. Thus, cosmogenic-isotope data provide a good tool to study solar-cycle variability even during grand minima of solar activity.     

The Maunder Minimum and the Sun as the Possible Source of Particles Creating Increased Abundance of the <Superscript>14</Superscript>C Carbon Isotope

The Maunder Minimum was the time during the second part of the 17th century, nominally from 1645 to 1717 AD, when unusually low numbers of sunspots were observed. On the basis of numerous recorded observations of auroras in the early 18th century, the end of the Minimum could be regarded as around 1700, but details of sunspot observations by Jan Heweliusz (Heweliusz, Machina Coelestis, 1679), John Flamsteed and Philippe de La Hire in 1684 allow us to interpret the Maunder Minimum as the period without a significant cessation of activity. This Minimum was also recognized in ¹⁴C data from trees which grew during the second part of 17th century. The variation in the production rate of radioactive carbon isotope ¹⁴C is due to modulation of the cosmic ray flux producing it by the changing level of solar activity and solar magnetic flux. Stronger magnetic fields in the solar wind make it more difficult for cosmic rays to reach the Earth, causing a drop in the production rate of ¹⁴C. However, more detailed analyses of ¹⁴C data indicate that the highest isotope abundances do not occur at the time of sunspot minima, as would be expected on the basis of modulation of the cosmic ray flux by the solar magnetic field, but two years after the sunspot number maximum. This time difference (or phase delay) can be accounted for if in fact there are both solar and non-solar cosmic ray contributions. Solar flares could also contribute high-energy particles and produce ¹⁴C and are generally not most frequent at the time of the highest sunspot numbers in the cycle.     

Sunspot and Auroral Activity During Maunder Minimum

The extremely low sunspot activity during the period of the Maunder minimum 1645–1715 was confirmed by group sunspot numbers, a new sunspot index constructed by Hoyt and Schatten (1998a,b). Neither sunspots nor auroral data time behavior indicate the presence of 11-year solar cycles as stated by Eddy (1976). The evidence for solar cycles was found in the butterfly diagram, constructed from observations made at Observatoire de Paris. After Clivier, Boriakoff, and Bounar (1998) the solar cycles were reflected also in geomagnetic activity. Results are supported by the variation of cosmogenic isotopes ¹⁰Be and ¹⁴C. The majority of the observed 14 naked-eye sunspots occurred on days when telescopic observations were not available. A part of them appeared in the years when no spot was allegedly observed. Two-ribbon flares appear in plages with only very small or no sunspots. Some of these flares are geoactive. Most aurorae (90%), which were observed during the Maunder minimum, appeared in years when no spot was observed. Auroral events as a consequence of proton flares indicate that regions with enhanced magnetic field can occur on the Sun when these regions do not produce any sunspots.     

The Maunder Minimum and the Solar Dynamo

Based on archival observations of solar activity, we suggest a scenario for the Maunder minimum, and compare to what extent this is reproduced by dynamo models of Grand minima. In particular, we argue that the transition into the Maunder minimum was very abrupt, while the end of Maunder minimum was gradual, however, rather rapid as well.     

Solar Activity during the Maunder Minimum: Comparison with the Dalton Minimum

The solar modulation potential has been reconstructed from data on the ¹⁰Be concentration in south and central Greenland ice over more than 500 last years. These two reconstructions, along with fourteen others obtained by various authors from data on the cosmogenic isotopes ¹⁴C and ¹⁰Be, have been investigated in the time interval 1630–1840 encompassing the Maunder and Dalton minima. The information contained in these sixteen paleoreconstructions has been generalized. The available data on the concentration of cosmogenic isotopes in terrestrial archives suggest that the solar activity in the first part of theMaunder minimum (1645–1680) was lower than that at the Dalton minimum (1792–1827), while in the second part (1680–1715) it was considerably lower. At the same time, at the beginning of theMaunder minimum (1645–1660) the solar activity could reach levels exceeding noticeably the estimates based on telescopic observations. Possible causes of these discrepancies and the directions of further research are discussed.     

Sunspot Positions and Areas from Observations by Galileo Galilei

Sunspot records in the seventeenth century provide important information on the solar activity before the Maunder minimum, yielding reliable sunspot indices and the solar butterfly diagram. Galilei’s letters to Cardinal Francesco Barberini and Marcus Welser contain daily solar observations on 3?–?11 May, 2 June?–?8 July, and 19?–?21 August 1612. These historical archives do not provide the time of observation, which results in uncertainty in the sunspot coordinates. To obtain them, we present a method that minimizes the discrepancy between the sunspot latitudes. We provide areas and heliographic coordinates of 82 sunspot groups. In contrast to Sheiner’s butterfly diagram, we found only one sunspot group near the Equator. This provides a higher reliability of Galilei’s drawings. Large sunspot groups are found to emerge at the same longitude in the northern hemisphere from 3 May to 21 August, which indicates an active longitude.     

Reconstruction of Subdecadal Changes in Sunspot Numbers Based on the NGRIP 10Be Record

Sunspot observations since 1610 A.D. show that the solar magnetic activity displays long-term changes, from Maunder Minimum-like low-activity states to Modern Maximum-like high-activity episodes, as well as short-term variations, such as the pronounced 11-year periodicity. Information on changes in solar activity levels before 1610 relies on proxy records of solar activity stored in natural archives, such as ¹⁰Be in ice cores and ¹⁴C in tree rings. These cosmogenic radionuclides are produced by the interaction between Galactic cosmic rays (GCRs) and atoms in the Earth’s atmosphere; their production rates are anti-correlated with the solar magnetic activity. The GCR intensity displays a distinct 11-year periodicity due to solar modulation of the GCRs in the heliosphere, which is inversely proportional to, but out of phase with, the 11-year solar cycle. This implies a time lag between the actual solar cycles and the GCR intensity, which is known as the hysteresis effect. In this study, we use the North Greenland Ice Core Project (NGRIP) records of the ¹⁰Be flux to reconstruct the solar modulation strength (Φ), which describes the modulation of GCRs throughout the heliosphere, to reconstruct both long-term and subdecadal changes in sunspot numbers (SSNs). We compare three different approaches for reconstructing subdecadal-scale changes in SSNs, including a linear approach and two approaches based on the hysteresis effect, i.e. models with ellipse–linear and ellipse relationships between Φ and SSNs. We find that the ellipse approach provides an amplitude-sensitive reconstruction and the highest cross-correlation coefficients in comparison with the ellipse–linear and linear approaches. The long-term trend in the reconstructed SSNs is computed using a physics-based model and agrees well with the other group SSN reconstructions. The new empirical approach, combining a physics-based model with ellipse-modeling of the 11-year cycle, therefore provides a method for reconstructing SSNs during individual solar cycles based on ¹⁰Be in ice cores. This, in turn, represents a new window for studying short-term changes in solar activity on unprecedented timescales, which may help improve our understanding of the solar dynamo.     

A Simple Method to Check the Reliability of Annual Sunspot Number in the Historical Period 1610 – 1847

A simple method to detect inconsistencies in low annual sunspot numbers based on the relationship between these values and the annual number of active days is described. The analysis allowed for the detection of problems in the annual sunspot number series clustered in a few explicit periods, namely: i) before Maunder minimum, ii) the year 1652 during the Maunder minimum, iii) the year 1741 in Solar Cycle −1, and iv) the so-called “lost” solar cycle in the 1790s and the subsequent onset of the Dalton Minimum.     

The Solar Spectral Irradiance as a Function of the Mg <Emphasis Type="SmallCaps">ii</Emphasis> Index for Atmosphere and Climate Modelling

We present a new method to reconstruct the solar spectrum irradiance in the Ly α – 400 nm region, and its variability, based on the Mg ii index and neutron-monitor measurements. Measurements of the solar spectral irradiance available in the literature have been made with different instruments at different times and different spectral ranges. However, climate studies require harmonised data sets. This new approach has the advantage of being independent of the absolute calibration and aging of the instruments. First, the Mg ii index is derived using solar spectra from Ly α (121 nm) to 410 nm measured from 1978 to 2010 by several space missions. The variability of the spectra with respect to a chosen reference spectrum as a function of time and wavelength is scaled to the derived Mg ii index. The set of coefficients expressing the spectral variability can be applied to the chosen reference spectrum to reconstruct the solar spectra within a given time frame or Mg ii index values. The accuracy of this method is estimated using two approaches: direct comparison with particular cases where solar spectra are available from independent measurements, and calculating the standard deviation between the measured spectra and their reconstruction. From direct comparisons with measurements we obtain an accuracy of about 1 to 2%, which degrades towards Ly α. In a further step, we extend our solar spectral-irradiance reconstruction back to the Maunder Minimum introducing the relationship between the Mg ii index and the neutron-monitor data. Consistent measurements of the Mg ii index are not available prior to 1978. However, we remark that over the last three solar cycles, the Mg ii index shows strong correlation with the modulation potential determined from the neutron-monitor data. Assuming that this correlation can be applied to the past, we reconstruct the Mg ii index from the modulation potential back to the Maunder Minimum, and obtain the corresponding solar spectral-irradiance reconstruction back to that period. As there is no direct measurement of the spectral irradiance for this period we discuss this methodology in light of the other proposed approaches available in the literature. The use of the cosmogenic-isotope data provides a major advantage: it provides information about solar activity over several thousands years. Using technology of today, we can calibrate the solar irradiance against activity and thus reconstruct it for the times when cosmogenic-isotope data are available. This calibration can be re-assessed at any time, if necessary.     

Erratum to: Width of Sunspot Generating Zone and Reconstruction of Butterfly Diagram

Based on the extended Greenwich – NOAA/USAF catalogue of sunspot groups, it is demonstrated that the parameters describing the latitudinal width of the sunspot generating zone (SGZ) are closely related to the current level of solar activity, and the growth of the activity leads to the expansion of the SGZ. The ratio of the sunspot number to the width of the SGZ shows saturation at a certain level of the sunspot number, and above this level the increase of the activity takes place mostly due to the expansion of the SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes of solar activity. Using the obtained relations and the group sunspot numbers by Hoyt and Schatten (Solar Phys. 179, 189, 1998), the latitude distribution of sunspot groups (“the Maunder butterfly diagram”) for the eighteenth and the first half of the nineteenth centuries is reconstructed and compared with historical sunspot observations.     

Modulation of Atmospheric 14C Concentration by the Solar Wind and Irradiance Components of the Hale and SCHWABE Solar Cycles

¹⁴C abundance on the Earth can be modulated by both the solar wind and irradiance components of the solar cycle. The magnetic field component of the solar wind modulates ¹⁴C production whereas the irradiance component can result in a change in the exchange rate between the various reservoirs of the carbon biogeochemical cycle. The effects would be nearly synchronous and difficult to separate. The 0.1% amplitude of irradiance variation during the two most recent solar cycles is well known. A 22-yr cycle exists also in the measured global temperature record.We have divided the University of Washington high-precision data on¹⁴C in tree rings into three 91-yr intervals: AD 1540–1630, 1630–1720 and 1715–1805, before, during and after the Maunder Minimum. Unfortunately the AD 1540–1630 interval includes part of the Spörer Minimum as well as the intermediate interval of high solar activity. These data were analyzed by the DFT, MEM and MTM methods of spectral time series analysis. The ca. 22-yr cycle is prominent during the Maunder Minimum, whereas the 11-yr cycle is most prominent after the Maunder Minimum but totally suppressed during the Maunder Minimum. The lesser amplitude of the 11-yr cycle before the Maunder Minimum is most probably due to overlap with the Spörer Minimum.Vasiliev and Kocharov VK83 have previously suggested that the 22-yr cycle persists through the Maunder Minimum whereas the 11-yr cycle is suppressed. Our calculations show that irradiance forcing of the carbon cycle during the 11-yr cycle is negligible, so the observed 11-yr cycle in¹⁴ C must be the result of production rate changes. The presence of the 22-yr cycle and suppression of the 11-yr cycle during the Maunder Minimum is in accord with a model by Jokipii Jok91.     

An Upper Limit on Sunspot Activity During the Maunder Minimum

We have estimated the upper and lower limits of sunspot activity, in terms of active day fraction during the Maunder minimum (1645–1710), using raw information on individual daily observations (Hoyt and Schatten, 1998). Establishing the relation between the sunspot activity and active day fraction after 1850, we evaluate the upper limit of annual group sunspot number during the deep Maunder minimum (1645–1700) which does not exceed 4. The earlier finding of a dominant 22-year periodicity during the Maunder minimum is verified and shown to be robust. Also we confirm that the start of the Maunder minimum was very abrupt.     

Hale Cyclicity of Solar Activity and Its Relation to Climate Variability

The periodicity of climatic processes along the Russian Arctic Ocean coast has been studied by analyzing the tree-ring chronologies for the regions close to the northern timberline. The wavelet analysis of annual series of conifer tree rings for the period 1458–1975 has revealed climatic oscillations with periods of 20–25 years. The amplitudes and periods of climatic oscillations in the region of Russian Arctic Ocean proved to exhibit appreciable changes. Especially strong climatic variations in comparison with the recent ones were found to occur during the Maunder minimum epoch when the period of oscillations increased from 22–23 years to 24–29 years, and oscillations with periods of 15 years appeared. After the Maunder minimum, the periods of oscillations and their amplitudes again decreased, and the 15–16-year maximum disappeared. Analysis of solar activity based on of radiocarbon (¹⁴C) concentration in annual tree rings has revealed a similar pattern in changes of periodicity before, during, and after the Maunder minimum. This suggests that quasi-bidecadal climatic oscillations and variations in solar activity can be connected with each other. A possible solar forcing of periodic climatic processes and its nonlinear influence on the atmosphere-ocean-continental system are discussed. The intense quasi-bidecadal climatic oscillations can be, in all probability, interpreted as resulting from amplification of a weak solar signal in the atmosphere-ocean system that has its own noises whose frequencies are close to the 22–23-year solar cycles.     

The Solar Ultraviolet Spectrum Estimated Using the Mg <Emphasis Type="SmallCaps">ii</Emphasis> Index and Ca <Emphasis Type="SmallCaps">ii</Emphasis> K Disk Activity

As part of a program to estimate the solar spectrum back to the early twentieth century, we have generated fits to UV spectral irradiance measurements from 1 – 410 nm. The longer wavelength spectra (150 – 410 nm) were fit as a function of two solar activity proxies, the Mg ii core-to-wing ratio, or Mg ii index, and the total Ca ii K disk activity derived from ground based observations. Irradiance spectra at shorter wavelengths (1 – 150 nm) where used to generate fits to the Mg ii core-to-wing ratio alone. Two sets of spectra were used in these fitting procedures. The fits at longer wavelengths (150 to 410 nm) were derived from the high-resolution spectra taken by the Solar Ultraviolet Spectral Irradiance Monitor (SUSIM) on the Upper Atmospheric Research Satellite (UARS). Spectra measured by the Solar EUV Experiment (SEE) instrument on the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite were used for the fits at wavelengths from 1 to 150 nm. To generate fits between solar irradiance and solar proxies, this study uses the above irradiance data, the NOAA composite Mg ii index, and daily Ca ii K disk activity determined from images measured by Big Bear Solar Observatory (BBSO). In addition to the fitting coefficients between irradiance and solar proxies, other results from this study include an estimated relationship between the fraction of the disk with enhanced Ca ii K activity and the Mg ii index, an upper bound of the average solar UV spectral irradiance during periods where the solar disk contains only regions of the quiet Sun, as was believed to be present during the Maunder Minimum, as well as results indicating that slightly more than 60% of the total solar irradiance (TSI) variability occurs between 150 and 400 nm.     

The solar wind during the Maunder minimum

It is presently believed that the high speed solar wind originates almost entirely in coronal holes. Theory suggests that the origin of the high speeds is extended energy deposition in proportion to the magnetic field intensity in the holes and at 1.5–3.0 solar radii heliocentric distance. Evidence from the time of the Maunder Minimum, together with the above results, allows a hypothesis to be made for the state of the solar wind at that time. Firstly, carbon-14 data indicate an enhanced cosmic ray intensity, with the conclusion that the interplanetary magnetic field (IMF) was smooth and perhaps of low intensity. Secondly, the apparent absence of a corona during eclipses requires low coronal density, suggesting an absence of closed magnetic loops. Thirdly, the absence of sunspots eliminates the possibility of a solar maximum type of corona of low emission intensity and implies a low large-scale photospheric field intensity. Finally, the absence of mid-latitude aurorae implies either that the solar wind speed or the IMF intensity or both, were low and not irregular.A resulting self-consistent hypothesis is that the solar wind was of the simplest variety, analogous to that described in models of the so-called “quiet solar wind”. All closed coronal field regions would have been absent and extended energy deposition in the corona would have been far less important than today. At 1 a.u., the density and speed would have been less than 5 cm^?3 and 300 km^?1s, respectively. At the same time, there would have been a very low level of fluctuation all the way from the microscale up to the contrast between high and low speed solar wind streams. Also, if the IMF is the source of the 22 yr and magnetic sector associated modulations in the present terrestrial climate, these modulations may have been suppressed during the Maunder Minimum. Recently, it has been discovered that the 22 yr modulation in fact was suppressed during the Maunder Minimum (C. Stockton and M. Mitchell, personal communication), in support of the above suggestion.