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.     

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.     

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 Analysis of Solar Global Activity

This article proposes a unified observational model of solar activity based on sunspot number and the solar global activity in the rotation of the structures, both per 11-year cycle. The rotation rates show a variation of a half-century period and the same period is also associated to the sunspot amplitude variation. The global solar rotation interweaves with the observed global organisation of solar activity. An important role for this assembly is played by the Grand Cycle formed by the merging of five sunspot cycles: a forgotten discovery by R. Wolf. On the basis of these elements, the nature of the Dalton Minimum, the Maunder Minimum, the Gleissberg Cycle, and the Grand Minima are presented.     

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.     

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.     

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.     

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.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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 Sun’s Strange Behavior: Maunder Minimum or Gleissberg Cycle?

During the last few years the Sun and solar wind have shown a behavior that was so unexpected that the phenomena was described as “the strange solar minimum”. It has been speculated that the 23/24 solar cycle minimum may have indicated the onset of a Maunder-Minimum-type Grand Minimum. Here we review what is known from 1500 years of proxy data about Maunder-type Grand Minima and the minima of the cyclic Centennial Gleissberg variations. We generate criteria that distinguish between the two types of event. Applying these criteria to the observed solar terrestrial data we conclude that the unexpected behavior began well before the solar cycle 23/24 minimum. The data do not support the Maunder Minimum conjecture. However, the behavior can be understood as a minimum of the Centennial Gleissberg Cycle that previously minimized in the beginning of the 20th century. We conclude that the Centennial Gleissberg Cycle is a persistent variation that has been present 80% of the time during the last 1500 years and should be explained by solar dynamo theory.     

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.     

Did the Sun’s Prairie Ever Stop Burning?

The presence of the red flash at total solar eclipses requires the existence of an extended chromosphere and therefore of a photospheric magnetic network that gives rise to spicules. We draw attention to the earliest historical reports of a red flash at the 1706 and 1715 eclipses, which therefore imply a substantial, widespread photospheric field during at least the last decade of the Maunder Minimum. Our finding is consistent with reports of a persistent photospheric field throughout the Maunder Minimum from analyses of ¹⁰Be radioisotope evidence. We note, however, that the last decade may not be representative of conditions throughout the roughly 1645 – 1715 extent of that prolonged activity minimum.     

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.     

Solar differential rotation derived from sunspot observations

Sunspot drawings obtained at National Astronomical Observatory of Japan during the years 1954–1986 were used to determine the differential rotation of the Sun. From the limited data set of three solar cycles it was found that three factors (the level of cycle activity, the cycle phase, and sunspot type) affect the solar rotation rate. The differential rotation varies from cycle to cycle in such a way that the rotation velocity in the low activity cycle (cycle 20) is higher than in the high-activity cycle (cycle 19). The equatorial rotation rate shows a systematic variation within each cycle. The rate is higher at the beginning of the cycle and decreases subsequently. Although quite small, the variation of solar differential rotation with respect to Zürich sunspot type was found. The H and J types show the slowest rotation among all the sunspot types.     

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.     

Study of Multiple Coronal Mass Ejections at Solar Minimum Conditions

Solar activity alternates between active and quiet phases with an average period of 11?years, and this is known as the Schwabe cycle. Additionally, solar activity occasionally falls into a prolonged quiet phase (grand solar minimum), as represented by the Maunder Minimum in the 17th century, when sunspots were almost absent for 70?years and the length of the Schwabe cycle increased to 14?years. To examine the consistency of the cycle length characteristics during the grand solar minima, the carbon-14 contents in single-year tree rings were measured using an accelerator mass spectrometer as an index of the solar variability during the grand solar minimum of the 4th century BC. The signal of the Schwabe cycle was detected with a statistical confidence level of higher than 95?% by wavelet analysis. This is the oldest evidence for the Schwabe cycle at the present time, and the cycle length is considered to have increased to approximately 16?years during the grand solar minimum of the 4th century BC. This result confirms the association between the increase of the Schwabe cycle length and the weakening of solar activity, and indicates the possible prolonged absence of sunspots in the 4th century BC as during the Maunder Minimum. Theoretical implications from solar dynamo theory are discussed in order to identify the trigger of prolonged sunspot absence. A possible association between the long-term solar variation around the 4th century BC and terrestrial cooling in this period is also discussed.