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.     

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 Periodicity of High-Latitude Solar Activity

The periodicity of high-latitude solar activity has been studied with the use of the Carte Synoptique solar filaments archive. The Morlet wavelet is utilized to analyze the periodicity of the number of solar filaments at latitudes over 50° during Carrington solar rotations 876 – 1823. For solar filaments at latitudes over 50°, the most eminent periods are about 10.23 and 10.90 years, which correspond to the Schwabe period of high-latitude solar activity, and the these periods make-up a highly significant proportion of the time span considered. The periods of 1.3 and 1.7 years and the quasi-biennial 2 – 3-year oscillation often mentioned in the literature are not found to be a feature of every solar cycle but seem to appear only from time to time.     

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.     

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.     

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.     

Differential rotation of the sun determined tracing sunspots and oscillations of sunspot tilt angle

The time and spatial characteristics of 324 large sunspots (S50 millionths of the solar hemisphere) selected from the Abastumani Astrophysical Observatory photoheliogram collection (1950–1990) have been studied. The variations of sunspot angular rotation velocity residuals and oscillations of sunspot tilt angle were analyzed. It has been shown that the differential rotation rate of selected sunspots correlates on average with the solar cycle. The deceleration of differential rotation of large sunspots begins on the ascending arm of the activity curve and ends on the descending arm reaching minimum near the epochs of solar activity maxima. This behavior disappears during the 21st cycle. The amplitudes and periods of sunspot tilt-angle oscillations correlate well with the solar activity cycle. Near the epochs of activity maximum there appear sunspots with large amplitudes and periods showing a significant scatter while the scatter near the minimum is rather low. We also found evidence of phase difference between the sunspot angular rotation velocity and the amplitudes and periods of tilt-angle oscillations.     

ALMA as the ideal probe of the solar chromosphere

The very nature of the solar chromosphere, its structuring and dynamics, remains far from being properly understood, in spite of intensive research. Here we point out the potential of chromospheric observations at millimeter wavelengths to resolve this long-standing problem. Computations carried out with a sophisticated dynamic model of the solar chromosphere due to Carlsson and Stein demonstrate that millimeter emission is extremely sensitive to dynamic processes in the chromosphere and the appropriate wavelengths to look for dynamic signatures are in the range 0.8–5.0 mm. The model also suggests that high resolution observations at mm wavelengths, as will be provided by ALMA, will have the unique property of reacting to both the hot and the cool gas, and thus will have the potential of distinguishing between rival models of the solar atmosphere. Thus, initial results obtained from the observations of the quiet Sun at 3.5 mm with the BIMA array (resolution of 12″) reveal significant oscillations with amplitudes of 50–150 K and frequencies of 1.5–8 mHz with a tendency toward short-period oscillations in internetwork and longer periods in network regions. However higher spatial resolution, such as that provided by ALMA, is required for a clean separation between the features within the solar atmosphere and for an adequate comparison with the output of the comprehensive dynamic simulations.     

A Study of the Frequency of Occurrence of Large-Fluence Solar Proton Events and the Strength of the Interplanetary Magnetic Field

It has been shown previously that the number of very-large-fluence solar proton events inferred for the period since 1561 were more frequent at times of low solar activity (e.g., following the recovery from the Maunder minimum), than in the present epoch of high solar activity. An inverse dependence is demonstrated between the probability of observation of the very large-fluence solar proton events and the strength of the interplanetary magnetic field derived from empirical predictions. Using the observed dependence, it is predicted and demonstrated that large-fluence solar proton events have been observed at Earth more frequently near the recurrent minima of the solar activity cycle in the past than during the present epoch. We show that these results are explicable in terms of the linear dependence of the Alfvén velocity upon the strength of the interplanetary magnetic field, leading to higher shock compression ratios in the past. These results indicate that this aspect of “solar weather” will be significantly influenced by the prevailing strength of the interplanetary magnetic field, and that recurrence of solar conditions similar to those of the solar activity minimum of solar cycles 12–14 (1878.9–1913.6) would be accompanied by a factor of ∼4 increase in the occurrence of large-fluence solar proton events.     

A Phenomenological Study of the Cosmic Ray Variations over the Past 9400 Years, and Their Implications Regarding Solar Activity and the Solar Dynamo

Two 9400-year long ¹⁰Be data records from the Arctic and Antarctic and a ¹⁴C record of equal length were used to investigate the periodicities in the cosmic radiation incident on Earth throughout the past 9400 years. Fifteen significant periodicities between 40 and 2320 years are observed in the ¹⁰Be and ¹⁴C records, there being close agreement between the periodicities in each record. We found that the periodic variations in the galactic cosmic radiation are the primary cause for periods <?250 years, with minor contributions of terrestrial origin possible >?250 years. The spectral line for the Gleissberg (87-year) periodicity is narrow, indicating a stability of ≈?0.5 %. The 9400-year record contains 26 Grand Minima (GM) similar to the Maunder Minimum, most of which occurred as sequences of 2?–?7 GM with intervals of 800?–?1200 years in between, in which there were no GM. The intervals between the GM sequences are characterised by high values of the modulation function. Periodicities <?150 years are observed in both the GM intervals and the intervals in between. The longer-period variations such as the de Vries (208-year) cycle have high amplitudes during the GM sequences and are undetectable in between. There are three harmonically related pairs of periodicities (65 and 130 years), (75 and 150 years), and (104 and 208 years). The long periodicities at 350, 510, and 708 years closely approximate 4, 6, and 8 times the Gleissberg period (87 years). The well-established properties of cosmic-ray modulation theory and the known dependence of the heliospheric magnetic field on the solar magnetic fields lead us to speculate that the periodicities evident in the paleo-cosmic-ray record are also present in the solar magnetic fields and in the solar dynamo. The stable, narrow natures of the Gleissberg and other periodicities suggest that there is a strong “frequency control” in the solar dynamo, in strong contrast to the variable nature (8?–?15 years) of the Schwabe (11-year) solar cycle.     

Study of bi-orthogonal modes in magnetic butterflies

We present a bi-orthogonal decomposition of the temporal and latitudinal distribution of solar magnetic fields from synoptic magnetograms. Results are compared with a similar decomposition of the distribution of sunspots since 1874. We show that the butterfly diagrams can be interpreted as the result of approximately constant amplitudes and phases of two oscillations with periods close to 22 years. A clear periodicity of 7 years can also be identified in the most energetic modes of both spatio-temporal series. These results can be used to obtain relevant information concerning the physics of the solar dynamo.     

Torsional oscillations of umbra and penumbra of sunspots

Torsional oscillations of seven single spots are studied based on the observations of the longitudinal magnetic field and the field of radial velocities in the photospheric Fe I λ 525.3 nm line. The periods of umbra and penumbra oscillations are 2.2–7.1 and 3.3–7.7 days, respectively. The spots at a greater solar latitude are characterized by a longer period of oscillations and a smaller axial strength of the magnetic field. The periods of umbra and penumbra oscillations increase with an increase in the period and amplitude of the sunspot umbra oscillations. The obtained results can point to a unitary mechanism of torsional oscillations of umbra and penumbra of single spots and a connection of these oscillations with the differential rotation of the Sun.     

What the Sunspot Record Tells Us About Space Climate

The records concerning the number, sizes, and positions of sunspots provide a direct means of characterizing solar activity over nearly 400 years. Sunspot numbers are strongly correlated with modern measures of solar activity including: 10.7-cm radio flux, total irradiance, X-ray flares, sunspot area, the baseline level of geomagnetic activity, and the flux of galactic cosmic rays. The Group Sunspot Number provides information on 27 sunspot cycles, far more than any of the modern measures of solar activity, and enough to provide important details about long-term variations in solar activity or “Space Climate.” The sunspot record shows: 1) sunspot cycles have periods of 131± 14 months with a normal distribution; 2) sunspot cycles are asymmetric with a fast rise and slow decline; 3) the rise time from minimum to maximum decreases with cycle amplitude; 4) large amplitude cycles are preceded by short period cycles; 5) large amplitude cycles are preceded by high minima; 6) although the two hemispheres remain linked in phase, there are significant asymmetries in the activity in each hemisphere; 7) the rate at which the active latitudes drift toward the equator is anti-correlated with the cycle period; 8) the rate at which the active latitudes drift toward the equator is positively correlated with the amplitude of the cycle after the next; 9) there has been a significant secular increase in the amplitudes of the sunspot cycles since the end of the Maunder Minimum (1715); and 10) there is weak evidence for a quasi-periodic variation in the sunspot cycle amplitudes with a period of about 90 years. These characteristics indicate that the next solar cycle should have a maximum smoothed sunspot number of about 145 ± 30 in 2010 while the following cycle should have a maximum of about 70 ± 30 in 2023.     

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.     

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.     

A Maunder Minimum Scenario Based on Cross-Hemispheric Coupling and Intermittency

A novel scenario for Maunder minimum-like grand minima epochs of reduced solar activity is proposed, based on diffusive coupling between both solar hemispheres, each susceptible to stochastically-driven intermittent behavior. After introducing cross-hemispheric coupling into a well-validated reduced model of the solar cycle based on the Babcock–Leighton mechanism for poloidal field regeneration, simulations are presented demonstrating that even weak coupling can lead to a high degree of synchronicity between the two hemispheres. This is in qualitative agreement with the similar onset and recovery times of sunspot activity at and around the Maunder minimum. Moreover, even weak coupling manages to greatly reduce the frequency and duration of quiescent episodes, again in qualitative agreement with the relative paucity of grand minima in the sunspot and radioisotope records.     

Does sunspot activity originate in slow global oscillations of the sun?

We present preliminary results of a spherical-harmonic-Fourier analysis of sunspot activity during the twenty-two years 1933–1954. The results indicate that the sunspot activity might be originating in global solar oscillations with periods of years and decades. However, except for the axisymmetric mode of degree 6, the set of other axisymmetric modes showing ∼ 11 yr periodicities are different from one sunspot cycle to another. A more detailed analysis, preferably with larger data series, will be needed to arrive at a more definite conclusion.     

Dynamo hysteresis and grand minima of solar activity

A nonlinear dynamo model that allows for the dependence of the turbulent diffusivity on the magnetic field shows the phenomenon of a hysteresis. In a certain range of dynamo numbers, two types of solutions are possible: decaying oscillations of weak fields and magnetic cycles with a constant and large amplitude, which are settled depending on the initial conditions. Fluctuations in α-parameter cause transitions between these two regimes and calculations show the intermittency of magnetic cycles with a relatively large amplitude and epochs of weak magnetic fields. This behavior can serve as a model of grand minima of solar activity like the well-known Maunder minimum.     

Solar activity cycles,north/south asymmetries,and differential rotation associated with solar spin-orbit variations

The possible role of the Sun's planetary-induced spin-orbit dynamics in the generation of various solar oscillations is examined using simple approaches and heuristic models. Theoretically, the 22.5-yr dipole inversion magnetic cycle and the recently described 17-yr neutral line topology cycle can be derived from the non-linear mixing of two oscillations with periods of approximately 20 and 165 years. Oscillations with such periods are observed in two aspects of the Sun's spin-orbit dynamics. The 20-yr oscillation is the fundamental variation in the angular momentum of the solar body with respect to the solar system center-of-mass, while the 165-yr oscillation is the lowest-frequency component of the spin projection variations. It is shown that these two oscillations when mixed non-linearly yield, to a 1st-order approximation, the correct phase and frequency of the observed 17.5- and 22.5-yr magnetic cycles. By allowing an asymmetric shape to the 165-yr oscillation, the frequency modulation inherent in the Hale cycle (and sunspot cycle) is reproduced, yielding a more accurate estimate of solar activity. The asymmetric 165-yr oscillation matches the combination of the two lowest frequency components (165- and 84-yr periods) of the spin projection variations. Hemispheric sunspot asymmetry cycles, north/south differences in convective zone rotational velocities, and meridional flows are also shown to be expected byproducts of classical spin-orbit effects. Finally, the problem of low activity epochs (e.g., Maunder minimum) can be seen as a natural outcome of the interactions among the driving and driven oscillations involved in the conservation of solar system angular momentum.