Grand Minima Research Articles

Evaluating solar-like behavior in turbulent alpha and Babcock-Leighton mechanisms using non-kinematic nonlinear flux-transport solar dynamos.

In this study, we simulate 30,000years of solar activity using turbulent-alpha (TA) and Babcock-Leighton (BL) mechanisms in a non-kinematic, nonlinear mean field flux-transport solar dynamo model. We evaluate their performances against observational data from proxies, like C, and direct solar observations. Both the TA and BL dynamos generate Schwabe-like variations, with the TA dynamo also generating periods that can be related to the QBOs and the Gleissberg cycle. The TA dynamo spends 13.3% (12.2%) of its time in a grand minimum (maximum) state, closely match the historical solar activity reconstructions from proxy records, while the BL dynamo underperforms. For the TA dynamo, the Schwabe cycle length variations during grand minima and the latitudinal and radial dependencies of the amplitude of variations both in Schwabe and QBO timescales align well with C data and solar observations, whereas the BL dynamo fails to reproduce these features.

Most of the Long-Term Solar Radiation Forcing on the Climate Is Due to the Strong Feedback Mechanisms

The main interactions of the Total Solar Irradiance (TSI) variations with the climatic system are considered. This research introduced new physically based indexes for 11-year cycles: the integral relative energetic power of the cycles solar activity (SA) and TSI, as well as the cycle-weighted mean value both of the TSI and sunspot number. The observed cycle-average TSI value in cycles XXII–XXIV has decreased by more than 0.5 W/m2, indicating its quasi-bicentennial decline. The onset of the Maunder-type Grand minimum phase of the SA and TSI of the quasi-bicentennial cycle (BCC) is expected in the 27th or 28th 11-year cycle in 2042 or 2053. The Earth's thermal inertia will cause a temperature reduction of around 0.25 K due to the deficit in TSI during the declining phase of the bicentennial cycle due to its negative impact on Earth's energy imbalance. As a result, the Bond's albedo will increase, and the abundance of atmospheric water vapor and carbon dioxide will decrease as a response to a direct solar forcing. BCC feedback mechanisms will also continue operating during both its minimum and maximum phases. The feedback mechanisms will continue further in short periods (about 30 years) at the beginning of BCC's growth and decline phases. These long-term self-reinforcing feedback effects will act as a response to the TSI, forcing in such a way as to trigger a strong amplification of the initial direct input to the corresponding temperature changes. They will lead to a significant increasing cooling in 2070 or 2080. Variations of the galactic cosmic rays and cloud cover practically do not affect the climate. The quasi-bicentennial cyclicity of the TSI also provides simultaneous climate variations on all Solar system planets.

Weakened Magnetic Braking in the Exoplanet Host Star 51 Peg

The consistently low activity level of the old solar analog 51 Peg not only facilitated the discovery of the first hot Jupiter, but also led to the suggestion that the star could be experiencing a magnetic grand minimum. However, the 50 yr time series showing minimal chromospheric variability could also be associated with the onset of weakened magnetic braking (WMB), where sufficiently slow rotation disrupts cycling activity and the production of large-scale magnetic fields by the stellar dynamo, thereby shrinking the Alfvén radius and inhibiting the efficient loss of angular momentum to magnetized stellar winds. In this Letter, we evaluate the magnetic evolutionary state of 51 Peg by estimating its wind braking torque. We use new spectropolarimetric measurements from the Large Binocular Telescope to reconstruct the large-scale magnetic morphology, we reanalyze archival X-ray measurements to estimate the mass-loss rate, and we detect solar-like oscillations in photometry from the Transiting Exoplanet Survey Satellite, yielding precise stellar properties from asteroseismology. Our estimate of the wind braking torque for 51 Peg clearly places it in the WMB regime, driven by changes in the mass-loss rate and the magnetic field strength and morphology that substantially exceed theoretical expectations. Although our revised stellar properties have minimal consequences for the characterization of the exoplanet, they have interesting implications for the current space weather environment of the system.

An Overview of Sunspot Observations in the Early Maunder Minimum: 1645–1659

Abstract Within four centuries of sunspot observations, the Maunder Minimum (MM) in 1645–1715 has been considered a unique grand minimum with weak solar cycles in group numbers of sunspots and hemispheric asymmetry in sunspot positions. However, the early part of the MM (1645–1659) is poorly understood in terms of its source records and has accommodated diverse reconstructions of the contemporaneous group number. This study identified their source records, classidied them in three different categories (datable observations, general descriptions, and misinterpreted records), and revised their data. On this basis, we estimated the yearly mean group number using the brightest star method, derived the active day fraction (ADF), reconstructed the sunspot number based on ADF, and compared them with proxy reconstructions from the tree-ring data sets. Our results revised the solar activity in the early MM downward in yearly mean group numbers using the brightest star method and upward in the active day fraction and sunspot number estimates. Our results are consistent with the proxy reconstruction for 1645–1654 and show more realistic values for 1657–1659 (against the unphysical negative sunspot number). These records have paid little attention to sunspot positions, except for Hevelius' report on a sunspot group in the northern solar hemisphere in 1652 April. Therefore, slight caveats are required to discuss if the sunspot positions are located purely in the southern solar hemisphere throughout the MM.

Long-term forcing of the Sun’s coronal field, open flux, and cosmic ray modulation potential during grand minima, maxima, and regular activity phases by the solar dynamo mechanism

ABSTRACT Magnetic fields generated in the Sun’s interior by the dynamo mechanism drive solar activity over a range of time-scales. Direct sunspot observations exist for a few centuries; reconstructed variations based on cosmogenic isotopes in the solar open flux and cosmic ray flux exist over thousands of years. While such reconstructions indicate the presence of extreme solar activity fluctuations in the past, causal links between millennia scale dynamo activity, consequent coronal field, solar wind, open flux and cosmic ray flux variations remain elusive; a lack of coronal field observations compounds this issue. By utilizing a stochastically forced solar dynamo model and potential field source surface extrapolation, we perform long-term simulations to illuminate how dynamo generated magnetic fields govern the structure of the solar corona and the state of the heliosphere – as indicated by variations in the open flux and cosmic ray modulation potential. We establish differences in the nature of the large-scale structuring of the solar corona during grand maximum, minimum, and regular solar activity phases and simulate how the open flux and cosmic ray modulation potential vary across these different phases of activity. We demonstrate that the power spectrum of simulated and observationally reconstructed solar open flux time series are consistent with each other. Our study provides the theoretical foundation for interpreting long-term solar cycle variations inferred from cosmogenic isotope based reconstructions and establishes causality between solar internal variations to the forcing of the state of the heliosphere.

Nonlinearity, time delay, and Grand Maxima in supercritical Babcock-Leighton dynamos

The physical origin of centennial and millennial-scale variations in solar activity remains ill-understood. Although stochastic fluctuations of the solar dynamo are unavoidable in view of the turbulent nature of the solar convection zone, the quasiperiodic long timescale modulations revealed by the cosmogenic radioisotope records are suggestive of a deterministic process. In this paper, we investigate the nonlinear behavior of two solar cycle models based on the Babcock-Leighton mechanism, with particular emphasis on deterministic amplitude modulation patterns materializing in the moderately to strongly supercritical dynamo regimes. Although formulated quite differently, both models show common long timescale modulation patterns arising from the interaction between the time-delay dynamics inherent to these flux transport dynamos, with the threshold non-linearity characterizing the Babcock-Leighton mechanism of poloidal field regeneration. In particular, we demonstrate the existence of multiple co-existing dynamo branches in the supercritical regime, each retaining a finite-sized basin of attraction over a substantial range in dynamo number. The transition from one branch to another is shown to be possible via the introduction of low-amplitude stochastic noise with short coherence time. On this basis, we propose a novel physical scenario potentially accounting for the occurrence of both Grand Minima and Maxima of solar activity.

An Overview of Sunspot Observations in 1727–1748

Solar activity generally exhibits cyclic behavior in terms of sunspot group number and sunspot positions every ≈11 yr. These sunspot data have therefore played key roles in numerous analyses of solar–terrestrial physics. However, their reconstructions prior to the 1830s have remained controversial and included significant data gaps, especially from the 1720s to the 1740s. Therefore, this study reviewed contemporary sunspot observations for 1727–1748 to add several forgotten records by Van Coesfelt in 1728–1729, Dûclos in 1736, Martin in 1737, and Cassini and Maraldi in 1748. On the basis of these records, this study revised the sunspot group number and newly derived the sunspot positions in this interval. The results show clearer solar cycles in sunspot group number than those of previous studies and indicate regular solar cycles with limited hemispheric asymmetry over Solar Cycles 0 to −2. The sunspot positions also show sunspot groups mostly at heliographic latitude φ fulfilling ∣φ∣ < 35° in both solar hemispheres, with slight equatorward motions. Furthermore, the solar minima between Solar Cycles −2 and −1 and between Solar Cycles −1 and 0 have been located around 1733.5 ± 0.5 and 1743 ± 0.5, indicating cycle lengths of 11.7 ± 0.5 yr and 10.0 ± 1.0 yr, respectively. Our results provide a chronological missing link between the Maunder Minimum and the regular solar cycles observed since Staudach’s observations from 1749 onward. This lets us better understand the transition of solar activity from the grand minimum to the regular solar cycles.

HD 166620: Portrait of a Star Entering a Grand Magnetic Minimum

HD 166620 was recently identified as a Maunder minimum candidate based on nearly 50 years of Ca ii H and K activity data from Mount Wilson and Keck HIRES. These data showed clear cyclic behavior on a 17 yr timescale during the Mount Wilson survey that became flat when picked up later with Keck HIRES planet-search observations. Unfortunately, the transition between these two data sets—and therefore the transition into the candidate Maunder minimum phase—contained little to no data. Here, we present additional Mount Wilson data not present in Baum et al., along with photometry over a nearly 30 yr baseline that definitively traces the transition from cyclic activity to a prolonged phase of flat activity. We present this as conclusive evidence of the star entering a grand magnetic minimum and therefore the first true Maunder minimum analog. We further show that neither the overall brightness nor the chromospheric activity level (as measured by S HK) is significantly lower during the grand magnetic minimum than its activity cycle minimum, implying that an anomalously low mean or instantaneous activity levels are not a good diagnostic or criterion for identifying additional Maunder minimum candidates. Intraseasonal variability in S HK, however, is lower in the star’s grand minimum; this may prove a useful symptom of the phenomenon.

Centennial Total Solar Irradiance Variation

Total Solar Irradiance (TSI) quantifies the solar energy received by the Earth and therefore is of direct relevance for a possible solar influence on climate change on Earth. We analyse the TSI space measurements from 1991 to 2021, and we derive a regression model that reproduces the measured daily TSI variations with a Root Mean Square Error (RMSE) of 0.17 W/m2. The daily TSI regression model uses the MgII core to wing ratio as a facular brightening proxy and the Photometric Sunspot Index (PSI) as a measure of sunspot darkening. We reconstruct the annual mean TSI backwards to 1700 based on the Sunspot Number (SN), calibrated on the space measurements with an RMSE of 0.086 W/m2. The analysis of the 11 year running mean TSI reconstruction confirms the existence of a 105 year Gleissberg cycle. The TSI level of the current grand minimum is only about 0.15 W/m2 higher than the TSI level of the grand minimum in the beginning of the 18th century.

A candidate auroral report in the Bamboo Annals, indicating a possible extreme space weather event in the early 10th century BCE

Historical auroral reports extend our knowledge of solar eruptions and long-term solar variability in the millennial time scale beyond the chronological coverage of instrumental observations, in the decadal to centennial time scales. Such chronological extensions benefit the scientific community, increasing the number of case studies on extreme space weather events with lower frequency but higher potential impact on modern technological infrastructure. So far, the earliest known datable reports of candidate aurorae have reached back to the 7th century BCE. Beyond this time series, we have analysed a celestial report in the Chinese Bamboo Annals that has attracted little scientific interest, probably owing to the controversial interpretations for the physical identity and the chronology of the event. Our philological analysis establishes its probable auroral nature. The textual description can be compared with early modern accounts of visual auroral observations for the multi-colour aurorae. We have located the observational site around Hàojīng (N34°14′, E108°46′) and dated the event to 977 ± 1 or 957 ± 1 BCE. On this basis, we have computed the equatorward extension of the auroral visibility as ≤39.0° in magnetic latitude and reconstructed the equatorward boundary of the auroral oval as ≤45.5° in invariant latitude. Our investigations empirically associate this candidate aurora with an extreme geomagnetic storm. We have compared this space weather event with proxy-based reconstructions of long-term solar variability and characterised it as a unique space-weather reference before the Neo-Assyrian Grand Minimum (alternatively Homeric Grand Minimum) in ca. 810 – 720 BCE.

Динамика растительности юга Приморья при климатической ритмике малого ледникового периода

Six stages of vegetation development have been identified on the basis of a palynological study of floodplain deposits of the Tsukanovka River (southern Primorye). The first stage is transitional from the medieval warm period, the next four stages are comparable with the climatic phases of the Little Ice Age. The sixth stage in the development of vegetation reflects the modern warming in the 20th century, when modern landscapes have been formed with the participation of the anthropogenic factor. The specific development of a complex of atmospheric-hydrospheric processes, which developed under the direct influence of long-term variations in solar activity, was the reason for the emergence of the Little Ice Age. The coldest phase in the territory of southern Primorye occurred at the end of the 17th century and coincided with the Maunder Grand Minimum of solar activity (1645–1715), it is also characterized by a decrease in humidity. The development of forest vegetation in the valley of the Tsukanovka River recorded alternating warm and cold episodes during the Little Ice Age. In relatively warm phases, the proportion of oak and other broad-leaved trees increased in the forest vegetation in southern Primorye, while in cold phases the proportion of alder increased. In the first half of the XVI century on the territory of southern Primorye, an increase in humidity due to an increase in precipitation is noted. The correlation of paleoclimatic rhythms identified on the basis of spore-pollen analysis results during the Little Ice Age in southern Primorye, with dendrochronological data for the southern Sikhote-Alin and other regions of the northern hemisphere, as well as with historical evidence from neighboring China, has showed the synchronism of the onset of climatic events in the regions, which reflects their global nature and global scale.

Can Stochastic Resonance Explain Recurrence of Grand Minima?

Abstract The amplitude of the 11 yr solar cycle is well known to be subject to long-term modulation, including sustained periods of very low activity known as Grand Minima. Stable long-period cycles found in proxies of solar activity have given new momentum to the debate about a possible influence of the tiny planetary tidal forcing. Here, we study the solar cycle by means of a simple zero-dimensional dynamo model, which includes a delay caused by meridional circulation as well as a quenching of the α-effect at toroidal magnetic fields exceeding an upper threshold. Fitting this model to the sunspot record, we find a set of parameters close to the bifurcation point at which two stable oscillatory modes emerge. One mode is a limit cycle resembling normal solar activity including a characteristic kink in the decaying limb of the cycle. The other mode is a weak sub-threshold cycle that could be interpreted as Grand Minimum activity. Adding noise to the model, we show that it exhibits Stochastic Resonance, which means that a weak external modulation can toss the dynamo back and forth between these two modes, whereby the periodicities of the modulation get strongly amplified.

Shaken and Stirred: When Bond Meets Suess\u2013de Vries and Gnevyshev\u2013Ohl

We argue that the most prominent temporal features of the solar dynamo, in particular the Hale cycle, the Suess–de Vries cycle (associated with variations of the Gnevyshev–Ohl rule), Gleissberg-type cycles, and grand minima can all be explained by combined synchronization with the 11.07-year periodic tidal forcing of the Venus–Earth–Jupiter system and the (mainly) 19.86-year periodic motion of the Sun around the barycenter of the solar system. We present model simulations where grand minima, and clusters thereof, emerge as intermittent and non-periodic events on millennial time scales, very similar to the series of Bond events which were observed throughout the Holocene and the last glacial period. If confirmed, such an intermittent transition to chaos would prevent any long-term prediction of solar activity, notwithstanding the fact that the shorter-term Hale and Suess–de Vries cycles are clocked by planetary motion.

Solar cyclic activity over the last millennium reconstructed from annual 14C data

Aims. The 11-year solar cycle (Schwabe cycle) is the dominant pattern of solar magnetic activity reflecting the oscillatory dynamo mechanism in the Sun’s convection zone. Solar cycles have been directly observed since 1700, while indirect proxy data suggest their existence over a much longer period of time, but generally without resolving individual cycles and their continuity. Here we reconstruct individual solar cycles for the last millennium using recently obtained 14C data and state-of-the-art models. Methods. Starting with the 14C production rate determined from the so far most precise measurements of radiocarbon content in tree rings, solar activity was reconstructed in the following three physics-based steps: (1) correction of the 14C production rate for the changing geomagnetic field; (2) computation of the open solar magnetic flux; and (3) conversion into sunspot numbers outside of grand minima. All known uncertainties, including both measurement and model uncertainties, were straightforwardly accounted for by a Monte-Carlo method. Results. Cyclic solar activity is reconstructed for the period 971–1900 (85 individual cycles) along with its uncertainties. This more than doubles the number of solar cycles known from direct solar observations. We found that the lengths and strengths of well-defined cycles outside grand minima are consistent with those obtained from the direct sunspot observations after 1750. The validity of the Waldmeier rule (cycles with fast-rising phase tend to be stronger) is confirmed at a highly significant level. Solar activity is found to be in a deep grand minimum when the activity is mostly below the sunspot formation threshold for about 250 years. Therefore, although considerable cyclic variability in 14C is seen even during grand minima, individual solar cycles can hardly be reliably resolved therein. Three potential solar particle events, ca. 994, 1052, and 1279 AD, are shown to occur around the maximum phases of solar cycles. Conclusions. A new approximately 1000-year-long solar activity reconstruction, in the form of annual (pseudo) sunspot numbers with the full assessment of all known uncertainties, is presented based on new high-precision Δ14C measurements and state-of-the-art models, more than doubling the number of individually resolved solar cycles. This forms a solid basis for new, more detailed studies of solar variability.

Gradual onset of the Maunder Minimum revealed by high-precision carbon-14 analyses

The Sun exhibits centennial-scale activity variations and sometimes encounters grand solar minimum when solar activity becomes extremely weak and sunspots disappear for several decades. Such an extreme weakening of solar activity could cause severe climate, causing massive reductions in crop yields in some regions. During the past decade, the Sun’s activity has tended to decline, raising concerns that the Sun might be heading for the next grand minimum. However, we still have an underdeveloped understanding of solar dynamo mechanisms and hence precise prediction of near-future solar activity is not attained. Here we show that the 11-year solar cycles were significantly lengthened before the onset of the Maunder Minimum (1645–1715 CE) based on unprecedentedly high-precision data of carbon-14 content in tree rings. It implies that flow speed in the convection zone is an essential parameter to determine long-term solar activity variations. We find that a 16 year-long cycle had occurred three solar cycles before the onset of prolonged sunspot disappearance, suggesting a longer-than-expected preparatory period for the grand minimum. As the Sun has shown a tendency of cycle lengthening since Solar Cycle 23 (1996–2008 CE), the behavior of Solar Cycle 25 can be critically important to the later solar activity.

Sunspot Observations at the Eimmart Observatory and in Its Neighborhood during the Late Maunder Minimum (1681–1718)

Abstract The Maunder Minimum (1645–1715; hereafter MM) is generally considered as the only grand minimum in the chronological coverage of telescopic sunspot observations. Characterized by scarce sunspot occurrences and their asymmetric concentrations in the southern solar hemisphere, the MM has frequently been associated with a special state of solar dynamo activity. As such, it is important to analyze contemporary observational records and improve our understanding of this peculiar interval, whereas the original records are frequently preserved in historical archives and can be difficult to access. In this study, we consult historical archives in the National Library of Russia, St. Petersburg, and analyze a series of sunspot observations conducted at the Eimmart Observatory from 1681 to 1709, which is the second-richest sunspot data set produced during the MM, following La Hire's series, among existing data sets. We have further extended our analyses to neighboring observations to extend our investigations up to 1718. We first analyze source documents and descriptions of observational instruments. Our analyses have significantly revised the existing data set, removed contaminations, and updated and labeled them as Eimmart Observatory (78 days), Altdorf Observatory (4 days), Hoffmann (22 days), and Wideburg (25 days). The revisions have updated the temporal coverage of the contemporary sunspot observations from 73.4% to 66.9% from 1677 to 1709. We have also derived the positions of the observed sunspot groups in comparison with contemporary observations. Our results indicate hemispheric asymmetry in the MM and recovery of sunspot groups in both hemispheres after 1716, supporting the common paradigm of the MM.

Candidate Auroral Observations Indicating a Major Solar–Terrestrial Storm in 1680: Implication for Space Weather Events during the Maunder Minimum

Abstract The Maunder Minimum (MM; 1645–1715) is currently considered the only grand minimum within telescopic sunspot observations since 1610. During this epoch, the Sun was extremely quiet and unusually free from sunspots. However, despite a reduced frequency, candidate aurorae were reported in the mid-European sector during this period and have been associated with occurrences of interplanetary coronal mass ejections (ICMEs), although some of them have been identified as misinterpretations. Here, we have analyzed reports of candidate aurorae on 1680 June 1 with simultaneous observations in central Europe, and compared their descriptions with visual accounts of early modern aurorae. Contemporary sunspot drawings on 1680 May 22, 24, and 27 have shown a sunspot. This sunspot may have been a source of ICMEs, which caused the reported candidate aurorae. On the other hand, its intensity estimate shows that the geomagnetic storm during this candidate aurora was probably within the capability of the storms derived from the corotating interaction region (CIR). Therefore, we accommodate both ICMEs and CIRs as its possible origin. This interpretation is probably applicable to a number of candidate aurorae in the oft-cited Hungarian catalog, on the basis of the reconstructed margin of their equatorward auroral boundary. Moreover, this catalog itself has clarified that the considerable candidates during the MM were probably misinterpretations. Therefore, the frequency of the auroral visibility in Hungary was probably lower than previously considered and agrees more with the generally slow solar wind in the existing reconstructions, whereas sporadic occurrences of sunspots and coronal holes still caused occasional geomagnetic storms.

Some Features of the Present-day Transition Period in Solar Activity

Various geophysical indices and their prognostic value were analyzed in (Obridko et al., 2013; Kirov et al., 2013, 2015, 2017; Georgieva et al., 2015, 2018). Two indices have been selected for the analysis (total annual Dst values, and duration of a storm). It is important to note that, unlike the other indices of solar and geophysical activity, the summary Dst index does not show violation of the Gnevyshev-Ohl rule. The analysis of annual mean Dst values reveals a clearly pronounced decrease in activity, at least since the 1980-ies. This allows us to suggest that we are at the descending branch of a secular cycle or on the threshold of a Grand Minimum. The decrease in solar activity is corroborated by the analysis of Forbush effects, solar wind speed, and intensity of the near-Earth magnetic field.

Schwabe, Gleissberg, Suess-de Vries: Towards a consistent model of planetary synchronization of solar cycles

Aiming at a consistent planetary synchronization model of both short-term and long-term solar cycles, we start with an analysis of Schove's historical data of cycle maxima. Their deviations (residuals) from the average cycle duration of 11.07 years show a high degree of regularity, comprising a dominant 200-year period (Suess-de Vries cycle), and a few periods around 100 years (Gleissberg cycle). Encouraged by their robustness, we support previous forecasts of an upcoming grand minimum in the 21st century. To explain the long-term cycles, we enhance our tidally synchronized solar dynamo model by a modulation of the field storage capacity of the tachocline with the orbital angular momentum of the Sun, which is dominated by the 19.86-year periodicity of the Jupiter-Saturn synodes. This modulation of the 22.14 years Hale cycle leads to a 193-year beat period of dynamo activity which is indeed close to the Suess-de Vries cycle. For stronger dynamo modulation, the model produces additional peaks at typical Gleissberg frequencies, which seem to be explainable by the non-linearities of the basic beat process, leading to a bi-modality of the Schwabe cycle. However, a complementary role of beat periods between the Schwabe cycle and the Jupiter-Uranus/Neptune synodic cycles cannot be completely excluded.

Grand Minima in a spherical non-kinematicα2Ω mean-field dynamo model

We present a non-kinematic axisymetricα2Ω mean-field dynamo model in which the completeα-tensor and mean differential rotation profile are both extracted from a global magnetohydrodynamical simulation of solar convection producing cycling large-scale magnetic fields. The nonlinear backreaction of the Lorentz force on differential rotation is the only amplitude-limiting mechanism introduced in the mean-field model. We compare and contrast the amplitude modulation patterns characterizing this mean-field dynamo, to those already well-studied in the context of non-kinematicαΩ models using a scalarα-effect. As in the latter, we find that large quasi-periodic modulation of the primary cycle are produced at low magnetic Prandtl number (Pm), with the ratio of modulation period to the primary cycle period scaling inversely with Pm. The variations of differential rotation remain well within the bounds set by observed solar torsional oscillations. In this low-Pm regime, moderately supercritical solutions can also exhibit aperiodic Maunder Minimum-like periods of strongly reduced cycle amplitude. The inter-event waiting time distribution is approximately exponential, in agreement with solar activity reconstructions based on cosmogenic radioisotopes. Secular variations in low-latitude surface differential rotation during Grand Minima, as compared to epochs of normal cyclic behavior, are commensurate in amplitude with historical inferences based on sunspot drawings. Our modeling results suggest that the low levels of observed variations in the solar differential rotation in the course of the activity cycle may nonetheless contribute to, or perhaps even dominate, the regulation of the magnetic cycle amplitude.