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.     

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.     

A Measure of the Solar Rotation During the Maunder Minimum

In this paper we present a measure of the synodic solar rotation rate derived from an analysis of a Flamsteed drawing, corroborating the decrease of the solar rotation in the deep Maunder minimum (1666–1700).     

A Reconstruction of Ultraviolet Spectral Irradiance During the Maunder Minimum

We present a reconstruction of the solar spectrum in the near and mid-ultraviolet spectral range during the Maunder Minimum, a period of strongly suppressed magnetic activity spanning the second half of the 17th century. This spectral reconstruction is based on an extension of the Monte Carlo Solar Spectral Irradiance Model (MOCASSIM). The new version of the model, documented in this paper, extends its spectral range down to 150 nm, its temporal range back to 1610, includes a secular modulation of the quiet-Sun emissivity based on a total solar irradiance reconstruction, and uses the Atmospheric Laboratory for Applications and Science-3 (ATLAS-3) spectrum as a reconstruction baseline. The model is validated against the ATLAS-1 spectrum for 29 March 1992, showing a general agreement varying from ～?1 % in the 300?–?400 nm range, up to 3?–?5 % below 200 nm, the largest discrepancies occurring in emission lines formed in the chromosphere and transition region. We also reconstruct ultraviolet spectra for May 2008 and March 2009, spanning the extended phase of low activity separating Cycles 23 and 24. Our results suggest that despite the unusually long temporal extent of this activity minimum, the ultraviolet emission still remained slightly higher than during the Maunder Minimum, due to the lingering presence of decay products from active regions having emerged in the late descending phase of Cycle 23.     

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.     

Bayesian Methods for Reconstructing Sunspot Numbers Before and During the Maunder Minimum

The Maunder Minimum (MM) was an extended period of reduced solar activity in terms of yearly sunspot numbers (SSN) during 1610?–?1715. The reality of this “grand minimum” is generally accepted in the scientific community, but the statistics of the SSN record suggest a need for data reconstruction. The MM data show a nonstandard distribution compared with the entire SSN signal (1610?–?2014). The pattern does not satisfy the weakly stationary solar dynamo approximation, which characterizes many natural events spanning centuries or even millennia, including the Sun and the stars. Over the entire observation period (1610?–?2014), the reported SSN exhibits statistically significant regime switches, departures from autoregressive stationarity, and growing trends. Reconstruction of the SSN during the pre-MM and MM periods is performed using five novel statistical procedures in support of signal analysis. A Bayesian–Monte Carlo backcast technique is found to be most reliable and produces an SSN signal that meets the weak-stationarity requirement. The computed MM signal for this reconstruction does not show a “grand” minimum or even a “semi-grand” minimum.     

Solar rotation during the Maunder Minimum

We have measured solar surface rotation from sunspot drawings made in a.d. 1642–1644 and find probable differences from present-day rates. The 17th century sunspots rotated faster near the equator by 3 or 4%, and the differential rotation between 0 and ±20° latitude was enhanced by about a factor 3. These differences are consistent features in both spots and groups of spots and in both northern and southern hemispheres. We presume that this apparent change in surface rotation was related to the ensuing dearth of solar activity (the Maunder Minimum) which persisted until about 1715.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Observations of sunspots by Flamsteed during the Maunder Minimum

In the bookHistoria Coelestis Brittannica, John Flamsteed (1725) lists his daily solar observations from 1676 onwards. Coupled with his comments in thePhilosophical Transactions of the Royal Society and his letters to William Derham in the Cambridge University Library, it is possible to reconstruct a daily chronology of his solar and sunspot observations from 1676 to 1700. These observations are important because, coupled with daily logs of observations by Picard, La Hire, Eimmart, and others, a detailed record of the observations during a portion of the Maunder Minimum can be constructed. For example, for 1691, a typical year, the longest gap between observations is only four days. Flamsteed's observations are also important because they add to the data gathered by Wolf, Spoerer, Maunder, Eddy, and others in their study of solar activity in the seventeenth century. Flamsteed's observations are summarized here and a sample of his observations is presented.     

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.     

An Active Sun Throughout the Maunder Minimum

Measurements of ¹⁰Be concentration in the Dye 3 ice core show that magnetic cycles persisted throughout the Maunder Minimum, although the Sun's overall activity was drastically reduced and sunspots virtually disappeared. Thus the dates of maxima and minima can now be reliably estimated. Similar behaviour is shown by a nonlinear dynamo model, which predicts that, after a grand minimum, the Sun's toroidal field may switch from being antisymmetric to being symmetric about the equator. The presence of cyclic activity during the Maunder Minimum limits estimates of the solar contribution to climatic change.     

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.     

Redefining the limit dates for the Maunder Minimum

The Maunder Minimum corresponds to a prolonged minimum of solar activity a phenomenon that is of particular interest to many branches of natural and social sciences commonly considered to extend from 1645 until 1715. However, our knowledge of past solar activity has improved significantly in recent years and, thus, more precise dates for the onset and termination of this particularly episode of our Sun can be established. Based on the simultaneous analysis of distinct proxies we propose a redefinition of the Maunder Minimum period with the core “Deep Maunder Minimum” spanning from 1645 to 1700 (that corresponds to the Grand Minimum state) and a wider “Extended Maunder Minimum” for the longer period 1618–1723 that includes the transition periods.     

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.     

Polar magnetic field reversals of the Sun in Maunder Minimum

A possible scenario of polar magnetic field reversal of the Sun during the Maunder Minimum (1645–1715) is discussed using data of magnetic field reversals of the Sun for 1880–1991 and the¹⁴ C content variations in the bi-annual rings of the pine-trees in 1600–1730 yrs.     

Solar Magnetic Activity and Total Irradiance Since the Maunder Minimum

We develop a model for estimating solar total irradiance since 1600 AD using the sunspot number record as input, since this is the only intrinsic record of solar activity extending back far enough in time. Sunspot number is strongly correlated, albeit nonlinearly with the 10.7-cm radio flux (F _10.7), which forms a continuous record back to 1947. This enables the nonlinear relationship to be estimated with usable accuracy and shows that relationship to be consistent over multiple solar activity cycles. From the sunspot number record we estimate F _10.7 values back to 1600 AD. F _10.7 is linearly correlated with the total amount of magnetic flux in active regions, and we use it as input to a simple cascade model for the other magnetic flux components. The irradiance record is estimated by using these magnetic flux components plus a very rudimentary model for the modulation of energy flow to the photosphere by the subphotospheric magnetic flux reservoir feeding the photospheric magnetic structures. Including a Monte Carlo analysis of the consequences of measurement and fitting errors, the model indicates the mean irradiance during the Maunder Minimum was about 1 ± 0.4 W m⁻² lower than the mean irradiance over the last solar activity cycle.     

Radiocarbon content variations and Maunder Minimum of solar activity

We summarize our experimental data on radiocarbon variations in tree rings covering the last several hundred years. Special attention was devoted to the Maunder Minimum of solar activity which is displayed in ¹⁴C. It is shown that the modulation of galactic cosmic rays at Wolf numbersW 0 does really exist and that the 22-yr periodicity at that period is more pronounced than the 11-yr periodicity. The properties of future theoretical models of solar activity are briefly discussed.     

The Rotation of Sunspots During Activity Cycle 22

The solar rotation rate derived from the measurements of daily sunspot positions during activity cycle 22 (1988–1996) are presented. The averaged differential rotation is nearly symmetric with respect to the equator. The comparisons of our measurement with those for previous cycles show that the equatorial rotation rate gradually increases from cycle 18 to 22.