Solar cycles during the Maunder minimum

We have obtained new consistent versions of the 400-yr time series of the Wolf sunspot number W, the sunspot group number G, and the total sunspot area S (or the total sunspot magnetic flux Φ). We show that the 11-yr cycle did not cease during the Maunder minimum of solar activity. The characteristics of the extrema of individual 11-yr cycles in 1600–2005 have been determined in terms of the total sunspot area index. We provide arguments for using alternating (“magnetic”) time series of indices in investigating the solar cyclicity.     

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.     

Modeling a Maunder minimum

We introduce on/off intermittency into a mean field dynamo model by imposing stochastic fluctuations in either the alpha effect or through the inclusion of a fluctuating electromotive force. Sufficiently strong small scale fluctuations with time scales of the order of 0.3–3 years can produce long term variations in the system on time scales of the order of hundreds of years. However, global suppression of magnetic activity in both hemispheres at once was not observed. The variation of the magnetic field does not resemble that of the sunspot number, but is more reminiscent of the ¹⁰Be record. The interpretation of our results focuses attention on the connection between the level of magnetic activity and the sunspot number, an issue that must be elucidated if long term solar effects are to be well understood. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comments on the so-called Maunder minimum

Arguments are presented in favour of the operation of the 11-yr cycle during the Maunder minimum and before it. The laws of differential rotation (1642–1644 and 1899–1901) before the low cycle are shown to differ insignificantly. It is suggested that the Maunder minimum was a result of the 600-yr cycle effect (during its epoch of minimum) on the 80–90 yr cycle.     

Variation of solar irradiance and mode frequencies during Maunder minimum

Using the sunspot numbers reported during the Maunder minimum and the empirical relations between the mode frequencies and solar activity indices, the variations in the total solar irradiance and 10.7 cm radio flux for the period 1645 to 1715 is estimated. We find that the total solar irradiance and radio flux during the Maunder minimum decreased by 0.19% and 52% respectively, as compared to the values for solar cycle 22. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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.     

Period and phase of the 88-year solar cycle and the Maunder minimum: Evidence for a chaotic sun

The problem of whether the solar dynamo is quasi-periodic or chaotic is addressed by examining 1500 years of sunspot, geomagnetic and auroral activity cycles. We find sub-harmonics of the fundamental solar cycle period during the years preceding the Maunder minimum and loss of phase of the subharmonic on emergence from it. These phenomena are indicative of chaos. They indicate that the solar dynamo is chaotic and is operating in a region close to the transition between period doubling and chaos. Since Maunder type minima reoccur irregularly for millennia, it appears that the Sun remains close to this transition to and from chaos. We postulate this as a universal characteristic of solar type stars caused by feedback in the dynamo number.     

The revival of solar activity after Maunder minimum in reports and observations of E. Manfredi

We present information, published here for the first time, concerning observations of sunspots made at the beginning of the XVIIIth century. The information has been taken from specola's archives in Bologna. It concerns the years just after the end of the Maunder minimum. The data confirms the presence of a double maximum in 1704–1707, and shows a high asymmetry in sunspots latitude distribution, possibly related to the abnormal Sun activity in the second half of XVIIth century.     

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.     

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).     

Aurorae during the so-called Spörer minimum

It is shown that such data that exist on auroral observations in the period between 1450 and 1550 do not provide the conclusive evidence that some authors have claimed for the so-called ‘Spörer minimum’ in solar activity in this time.     

Ephemeral active regions during solar minimum

Ephemeral active regions (ER) identified on Kitt Peak daily full-disk magnetograms from April through November 1975 were analyzed and compared with larger active regions during the same interval. The 1975 ER were also compared with ER data from 1970, 1973, 1976, and 1977. ER were found to vary approximately with the sunspot cycle. However, a minimum in the number of ER occurred at least one year prior to sunspot minimum. All evidence to date indicates that the early ER minimum was due to the rise of solar cycle 21 primarily in the form of ER. ER were statistically identified as belonging to both outgoing solar cycle 20 and incoming cycle 21 by maxima in their distribution in latitude and by their statistically dominant orientation as a function of latitude. From the identification of ER with specific solar cycles and the persistent presence of high latitude ER maxima since 1970, it is suggested that the outgoing and incoming solar cycles may co-exist on the sun longer than the 0–3 year period of overlap between successive cycles already known from the properties of large sunspot-producing active regions.Presently associated with Solar Physics Research Corporation, Tucson, Arizona and Visiting Astronomer at Kitt Peak National Observatory, operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

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.