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Data from the Michelson Doppler Imager (MDI) and Helioseismic and Magnetic Imager (HMI) are analyzed from 1996 to 2023 to investigate tilt angles (γ) of bipolar magnetic regions and Joy's law for Solar Cycles 23 and 24 and a portion of Cycle 25. The HMI radial magnetic field (B r ) and MDI magnetogram (B los) data are used to calculate (γ) using the flux-weighted centroids of the positive and negative polarities. Each active region (AR) is only sampled once. The analysis includes only Beta (β)-class ARs since computing γ of complex ARs is less meaningful. During the emergence of the ARs, we find that the average tilt angle ( γ ¯ ) increases from 3.°30 ± 0.75 when 20% of the flux has emerged to 6.°79° ± 0.66 when the ARs are at their maximum flux. Cycle 24 has a larger average tilt, γ ¯ 24 =6.67 ± 0.66, than Cycle 23, γ ¯ 23 = 5.11 ± 0.61. No significant difference is found in the slope of Joy's law or γ ¯ when sampling the ARs at the time of maximum flux or central meridian crossing. There are persistent differences in γ ¯ in the hemispheres, with the Sun's southern hemisphere having higher γ ¯ in Cycles 23 and 24, but the uncertainties are such that these differences are not statistically significant. [ABSTRACT FROM AUTHOR]

Meridional flow is crucial in generating the solar poloidal magnetic field by facilitating poleward transport of the field from decayed bipolar magnetic regions (BMRs). As the meridional circulation changes with the stellar rotation rate, the properties of stellar magnetic cycles are expected to be influenced by this flow. In this study, we explore the role of meridional flow in generating magnetic fields in the Sun and Sun-like stars using the STABLE (surface flux transport and Babcock–Leighton) dynamo model. We find that a moderate meridional flow increases the polar field by efficiently driving the trailing polarity flux toward the pole, while a strong flow tends to transport both polarities of BMRs poleward, potentially reducing the polar field. Our findings are in perfect agreement with what one can expect from the surface flux transport model. Similarly, the toroidal field initially increases with moderate flow speeds and then decreases beyond a certain value. This trend is due to the competitive effects of shearing and diffusion. Furthermore, our study highlights the impact of meridional flow on the strength and duration of stellar cycles. By including the meridional flow from a mean-field hydrodynamics model in STABLE, we show that the magnetic field strength initially increases with the stellar rotation rate and then declines in rapidly rotating stars, offering an explanation of the observed variation of stellar magnetic field with rotation rate. [ABSTRACT FROM AUTHOR]

Sunspots and active regions observed on the solar surface are widely believed to be manifestations of compact predominantly toroidal magnetic field structures ("flux tubes") that emerge by magnetic buoyancy from the deeper interior of the Sun. Much work has examined the evolution of such magnetic structures, typically considering them as idealized isolated magnetic entities and not as more realistic magnetic concentrations in a volume-filling background magnetic field. Here, we report results that explore the buoyant rise dynamics of magnetic concentrations in a volume-filling field in the full three dimensions. Earlier 2.5D work in this series established the remarkable fact that the twist orientation of a flux concentration relative to the background field affected its likelihood to rise and emerge, regardless of whether the buoyant rise took place in the absence or presence of convection. The contrasting dynamics between structures with differing orientations lead to a selection mechanism that reproduces characteristics of the "solar hemispheric helicity rule(s)" observations strikingly well. Here, we show that this two-dimensional selection mechanism persists in the face of the added complexity of three-dimensional dynamics. Arching of the magnetic structure in the third dimension, as might be expected in the solar application, is introduced. The role of tension force leading to this selection mechanism is elucidated and subtle differences that arise due to the three-dimensional geometry are discussed. [ABSTRACT FROM AUTHOR]

Using Helioseismic and Magnetic Imager/Solar Dynamics Observatory data, we search for a relationship between kinetic helicity and magnetic helicity in solar active regions (ARs) using a sample of 62 ARs from 2010 May to 2015 May. The sample includes 32 mature ARs and 30 emerging ARs. We calculate kinetic helicity in the interior in the depth range from 0.6 to 11.6 Mm, magnetic helicity in the corona, helicity flux across the photosphere, and the magnetic twist and magnetic writhe of the ARs at the photosphere. From these data, relationships are found between magnetic helicity, helicity flux, and magnetic twist. However, magnetic writhe appears not to be related to the other magnetic quantities. No relationship is found between the kinetic helicity and any magnetic quantity. In particular, no relationship is found between the kinetic helicity and any of the following: magnetic helicity, magnetic helicity flux, magnetic twist, or magnetic writhe. These results suggest that (1) the magnetic helicity in the corona above ARs is mainly derived from the magnetic twist, and (2) the flow dynamics in the region from 0.6 to 11.6 Mm below the photosphere is not the primary source for the generation of magnetic helicity in ARs. [ABSTRACT FROM AUTHOR]

• Sunspot number (SN) is linearly relating with sunspot-group area (WSGA). • A decreasing trend exists in the slope of this relation during Solar Cycles 12–24. • In the cases of Solar Cycles 14, 17, and 24 a nonlinear fit is better than linear fit. • A 77-year cycle is found in the ratio SN/WSGA at the maximum epoch of Solar cycle. • We predicted that Solar Cycle 25 will be larger than both Cycles 24 and 26. • Using an our earlier methods we predicted 141 and 127 for the amplitude of Solar Cycle 25. • We predicted Solar Cycle 25 will have similar shape as Solar Cycle 13. • Hence, we predicted 135 for the amplitude of Solar Cycle 25. • We predicted March/2024 for the maximum epoch of Solar Cycle 25. • We predicted March/2032 will be the end of Solar Cycle 25 with SN 4. Prediction of the amplitude of solar cycle is important for understanding the mechanism of solar cycle and solar activity influence on space-weather. We analysed the combined data of sunspot groups from Greenwich Photoheliographic Results (GPR) during the period 1874–1976 and Debrecen Photoheliographic Data (DPD) during 1977–2017 and determined the monthly mean, annual mean, and 13-month smoothed monthly mean whole sphere sunspot-group area (WSGA). We also analysed the monthly mean, annual mean, and 13-month smoothed monthly mean version 2 of international sunspot number ( SN T ) during the period 1874–2017. We fitted the annual mean WSGA and SN T data during each of Solar Cycles 12–24 separately to the linear and nonlinear (parabola) forms. In the cases of Solar Cycles 14, 17, and 24 the nonlinear fits are found better than the linear fits. We find that there exists a secular decreasing trend in the slope of the WSGA– SN T linear relation during Solar Cycles 12–24. A secular decreasing trend is also seen in the coefficient of the first order term of the nonlinear relation. The existence of ≈ 77-year variation is clearly seen in the ratio of the amplitude to WSGA at the maximum epoch of solar cycle. From the pattern of this long-term variation of the ratio we inferred that Solar Cycle 25 will be larger than both Solar Cycles 24 and 26. Using an our earlier method (now slightly revised), i.e. using high correlations of the amplitude of a solar cycle with the sums of the areas of sunspot groups in 0– 10 ° latitude intervals of the northern hemisphere during 3.75-year interval around the minimum–and the southern hemisphere during 0.4-year interval near the maximum–of the corresponding preceding solar cycle, we predicted 127 ± 26 and 141 ± 19 for the amplitude of Solar Cycle 25, respectively. Based on ≈ 130-year periodicity found in the cycle-to-cycle variation of the amplitudes of Solar Cycles 12–24 we find the shape of Solar Cycle 25 would be similar to that of Solar Cycle 13 and predicted for Solar Cycle 25 the amplitude 135 ± 8 , maximum epoch 2024.21 (March 2024) ± 6-month, and the following minimum epoch 2032.21 (March 2032) ± 6-month with SN T ≈ 4. [ABSTRACT FROM AUTHOR]

The details of the dynamo process in the Sun are an important aspect of research in solar-terrestrial physics and astrophysics. The surface part of the dynamo can be constrained by direct observations, but the subsurface part lacks direct observational constraints. The torsional oscillations, a small periodic variation of the Sun's rotation with the solar cycle, are thought to result from the Lorentz force of the cyclic magnetic field generated by the dynamo. In this study, we aim to discriminate between three Babcock–Leighton dynamo models by comparing the zonal acceleration of the three models with the observed one. The property that the poleward and equatorward branches of the torsional oscillations originate from about ±55° latitudes with their own migration time periods serves as an effective discriminator that could constrain the configuration of the magnetic field in the convection zone. The toroidal field, comprising poleward and equatorward branches separated at about ±55° latitudes, can generate the two branches of the torsional oscillations. The alternating acceleration and deceleration bands in time are the other property of the torsional oscillations that discriminates between the dynamo models. To reproduce this property, the phase difference between the radial (B r ) and toroidal (B ϕ ) components of the magnetic field near the surface should be about π /2. [ABSTRACT FROM AUTHOR]

Abstract In this study, we, for the first time, compiled all publicly available annually or biannually resolved $$^{14}$$ 14 C records, which fully covers 7 grand solar minima at an annual and bi-annual resolution. Our results from 7 grand solar minima showed a clear relationship between the rate of decrease (increase) in solar activity levels and how long the onset (termination) of the grand solar minima will last. Additionally, we show a weaker relationship between the durations of onsets and terminations and between the rate of increase and decrease of solar activity levels. Our results also suggest there might be two or more types of grand solar minima.

In this study, we, for the first time, compiled all publicly available annually or biannually resolved 14 C records, which fully covers 7 grand solar minima at an annual and bi-annual resolution. Our results from 7 grand solar minima showed a clear relationship between the rate of increase (decrease) in solar activity levels and how long the onset (termination) of the grand solar minima will last. Additionally, we show a weaker relationship between the durations of onsets and terminations and between the rate of increase and decrease of solar activity levels. Our results also suggest there might be two or more types of grand solar minima. [ABSTRACT FROM AUTHOR]

Meticulous study of sunspots on the Sun's photosphere over the centuries has led to the conclusion that they are areas of high magnetism that contribute to solar activities. High and low activities associated with their polarities were recognized in a cyclical pattern, therefore questioning the mechanisms behind the Sun's predictive nature. The solar dynamo model was put forth in the 1960s and provided an understanding of the generation of the Sun's intense magnetic field; however, they were missing one critical ingredient. The tachocline was found with helioseismology in 1992 by measuring oscillations that travel throughout the Sun. Most solar physicists agree that the magnetic field is generated in the tachocline due to shearing forces of the convection zone acting against the rigid radiative zone. The poloidal field at the start of a cycle becomes distorted throughout the progression due to the Sun's differential rotation and pulls these field lines around the Sun. This creates a toroidal field, in which the stretching of the lines permits them to grow in strength. Turbulent convective flows cause them to twist and produce magnetic flux tubes. As the tubes expand, they become less dense and achieve magnetic buoyancy, which then rises and emerges out of the photosphere, appearing as sunspots with a bipolar nature. [ABSTRACT FROM AUTHOR]

The solar tachocline is an internal region of the Sun possessing strong radial and latitudinal shears straddling the base of the convective envelope. Based on helioseismic inversions, the tachocline is known to be thin (less than 5% of the solar radius). Since the first theory of the solar tachocline in 1992, this thinness has not ceased to puzzle solar physicists. In this review, we lay out the grounds of our understanding of this fascinating region of the solar interior. We detail the various physical mechanisms at stake in the solar tachocline, and put a particular focus on the mechanisms that have been proposed to explain its thinness. We also examine the full range of MHD processes including waves and instabilities that are likely to occur in the tachocline, as well as their possible connection with active region patterns observed at the surface. We reflect on the most recent findings for each of them, and highlight the physical understanding that is still missing and that would allow the research community to understand, in a generic sense, how the solar tachocline and stellar tachocline are formed, are sustained, and evolve on secular timescales. [ABSTRACT FROM AUTHOR]

Abstract One obvious feature of the solar cycle is its variation from one cycle to another. In this article, we review the dynamo models for the long-term variations of the solar cycle. By long-term variations, we mean the cycle modulations beyond the 11-year periodicity and these include, the Gnevyshev–Ohl/Even–Odd rule, grand minima, grand maxima, Gleissberg cycle, and Suess cycles. After a brief review of the observed data, we present the dynamo models for the solar cycle. By carefully analyzing the dynamo models and the observed data, we identify the following broad causes for the modulation: (1) magnetic feedback on the flow, (2) stochastic forcing, and (3) time delays in various processes of the dynamo. To demonstrate each of these causes, we present the results from some illustrative models for the cycle modulations and discuss their strengths and weakness. We also discuss a few critical issues and their current trends. The article ends with a discussion of our current state of ignorance about comparing detailed features of the magnetic cycle and the large-scale velocity from the dynamo models with robust observations.

Clette recently showed that F _10.7 systematically approaches a quiet Sun daily value of 67 solar flux units (sfu) at solar minima as the number of spotless days on the Sun increases. Previously, a floor of ∼2.8 nT had been proposed for the solar wind (SW) magnetic field strength (B). F _10.7 , which closely tracks the Sun's unsigned photospheric magnetic flux, and SW B exhibit different relationships to their floors at 11 yr solar minima during the last ∼50 yr. While F _10.7 approaches 67 sfu at each minimum, the corresponding SW B is offset above ∼2.8 nT by an amount approximately proportional to the solar polar field strength—which varied by a factor of ∼2.5 during this interval. This difference is substantiated by ∼130 yr of reconstructed F _10.7 (via the range of the diurnal variation of the East-component (rY) of the geomagnetic field) and SW B (based on the interdiurnal variability geomagnetic activity index). For the last ∼60 yr, the contribution of the slow SW to SW B has exhibited a floor-like behavior at ∼2 nT, in contrast to the contributions of coronal mass ejections and high-speed streams that vary with the solar cycle. These observations, as well as recent SW studies based on Parker Solar Probe and Solar Dynamics Observatory data, suggest that (1) the Sun has a small-scale turbulent dynamo that is independent of the 11 yr sunspot cycle; and (2) the small-scale magnetic fields generated by this nonvarying turbulent dynamo maintain a constant open flux carried to the heliosphere by the Sun's floor-like slow SW.

The minimum value of the geomagnetic aa index has served as a remarkably successful predictor of solar cycle amplitude. This value is reached near or just after sunspot minimum, when both the near-Earth solar wind speed and interplanetary magnetic field (IMF) strength fall to their lowest values. At this time, the heliospheric current sheet is flattened toward the heliographic equator and the dominant source of the IMF is the Sun’s axial dipole moment, which, in turn, has its source in the polar fields. As recognized previously, the success of ${{aa}}_{\min }$ as solar cycle precursor provides support for dynamo models in which the sunspots of a given cycle are produced by winding up the poloidal field built up during the previous cycle. Because they are highly concentrated toward the poles by the surface meridional flow, the polar fields are difficult to measure reliably. Here we point out that the observed value of the radial IMF strength at solar minimum can be used to constrain the polar field measurements, and that this parameter, which is directly proportional to the Sun’s axial dipole strength, may be an even better solar cycle predictor than geomagnetic activity.

Abstract The presence of grand minima, characterized by significantly reduced solar and stellar activity, brings a challenge to the understanding of solar and stellar dynamo. The Maunder Minimum (1645–1715 AD) is a representative grand solar minimum. The cyclic variation of solar activity, especially the cycle length during this period, is critical to understand the solar dynamo but remains unknown. By analyzing the variations in solar activity‐related equatorial auroras recorded in Korean historical books in the vicinity of a low‐intensity paleo‐West Pacific geomagnetic anomaly, we find clear evidence of an 8‐year solar cycle rather than the normal 11‐year cycle during the Maunder Minimum. This result provides a key constraint on solar dynamo models and the generation mechanism of grand solar minima.

The dynamic activity of stars such as the Sun influences (exo)planetary space environments through modulation of stellar radiation, plasma wind, particle and magnetic fluxes. Energetic solar-stellar phenomena such as flares and coronal mass ejections act as transient perturbations giving rise to hazardous space weather. Magnetic fields – the primary driver of solar-stellar activity – are created via a magnetohydrodynamic dynamo mechanism within stellar convection zones. The dynamo mechanism in our host star – the Sun – is manifest in the cyclic appearance of magnetized sunspots on the solar surface. While sunspots have been directly observed for over four centuries, and theories of the origin of solar-stellar magnetism have been explored for over half a century, the inability to converge on the exact mechanism(s) governing cycle to cycle fluctuations and inconsistent predictions for the strength of future sunspot cycles have been challenging for models of the solar cycles. This review discusses observational constraints on the solar magnetic cycle with a focus on those relevant for cycle forecasting, elucidates recent physical insights which aid in understanding solar cycle variability, and presents advances in solar cycle predictions achieved via data-driven, physics-based models. The most successful prediction approaches support the Babcock-Leighton solar dynamo mechanism as the primary driver of solar cycle variability and reinforce the flux transport paradigm as a useful tool for modelling solar-stellar magnetism. [ABSTRACT FROM AUTHOR]

One obvious feature of the solar cycle is its variation from one cycle to another. In this article, we review the dynamo models for the long-term variations of the solar cycle. By long-term variations, we mean the cycle modulations beyond the 11-year periodicity and these include, the Gnevyshev–Ohl/Even–Odd rule, grand minima, grand maxima, Gleissberg cycle, and Suess cycles. After a brief review of the observed data, we present the dynamo models for the solar cycle. By carefully analyzing the dynamo models and the observed data, we identify the following broad causes for the modulation: (1) magnetic feedback on the flow, (2) stochastic forcing, and (3) time delays in various processes of the dynamo. To demonstrate each of these causes, we present the results from some illustrative models for the cycle modulations and discuss their strengths and weakness. We also discuss a few critical issues and their current trends. The article ends with a discussion of our current state of ignorance about comparing detailed features of the magnetic cycle and the large-scale velocity from the dynamo models with robust observations. [ABSTRACT FROM AUTHOR]

Using time–distance local helioseismology flow maps within 1 Mm of the solar photosphere, we detect inflows toward activity belts that contribute to solar-cycle scale variations in the near-surface meridional flow. These inflows stretch out as far as 30° away from the active region centroids. If active region neighborhoods are excluded, the solar-cycle-scale variation in the background meridional flow diminishes to below 2 m s−1, but still shows systematic variations in the absence of active regions between sunspot cycles 24 and 25. We therefore propose that the near-surface meridional flow is a three-component flow made up of a constant baseline flow profile that can be derived from quiet-Sun regions, variations due to inflows around active regions, and solar-cycle-scale variation of about 2 m s−1. Torsional oscillation, on the other hand, is found to be a global phenomenon, i.e., exclusion of active region neighborhoods does not significantly affect its magnitude or phase. This nonvariation in torsional oscillation with distance away from active regions and the three-component breakdown of the near-surface meridional flow serve as vital constraints for solar dynamo models and surface flux-transport simulations. [ABSTRACT FROM AUTHOR]

Here we review present knowledge of the long-term behaviour of solar activity on a multi-millennial timescale, as reconstructed using the indirect proxy method. The concept of solar activity is discussed along with an overview of the dedicated indices used to quantify different aspects of variable solar activity, with special emphasis on sunspot numbers. Over long timescales, quantitative information about past solar activity is historically obtained using a method based on indirect proxies, such as cosmogenic isotopes 14 C and 10 Be in natural stratified archives (e.g., tree rings or ice cores). We give a historical overview of the development of the proxy-based method for past solar-activity reconstruction over millennia, as well as a description of the modern state of the art. Special attention is paid to the verification and cross-calibration of reconstructions. It is argued that the method of cosmogenic isotopes makes a solid basis for studies of solar variability in the past on a long timescale (centuries to millennia) during the Holocene (the past ∼ 12 millennia). A separate section is devoted to reconstructions of extremely rare solar eruptive events in the past, based on both cosmogenic-proxy data in terrestrial and lunar natural archives, as well as statistics of sun-like stars. Finally, the main features of the long-term evolution of solar magnetic activity, including the statistics of grand minima and maxima occurrence, are summarized and their possible implications, especially for solar/stellar dynamo theory, are discussed. [ABSTRACT FROM AUTHOR]

We have used high-resolution zoom-in simulations of direct collapse to supermassive black hole (SMBH) seeds within dark mater halos in the presence of magnetic fields generated during the collapse, down to 10 ^−5 pc or 2 au. We confirm an efficient amplification of magnetic field during collapse, the formation of a geometrically thick self-gravitating accretion disk inside 0.1 pc, and damping of fragmentation in the disk by the field. This disk differs profoundly from SMBH accretion disks. We find the following: (1) The accretion disk is subject to the magnetorotational instability, which further amplifies the field to near equipartition. No artificial seeding of the disk field has been used. (2) The equipartition toroidal field changes its polarity in the midplane. (3) The nonlinear Parker instability develops, accompanied by the vertical buckling of the field lines, which injects material above the disk, leading to an increase in the disk scale height. (4) With the Coriolis force producing a coherent helicity above the disk, the vertical poloidal field has been generated and amplified. (5) We estimate that the associated outflow will be most probably squashed by accretion. The resulting configuration consists of a magnetized disk with β ≳ 0.1 and its magnetosphere with β ≪ 1, where β = P _th / P _B is the ratio of thermal to magnetic energy density. (6) The disk is highly variable, due to feeding by variable accretion flow, and strong vortical motions are present. (7) Finally, the negative gradient of the total vertical stress drives an equatorial outflow sandwiched by an inward accretion flow.

Data from the Michelson Doppler Imager (MDI) and Helioseismic and Magnetic Imager (HMI) are analyzed from 1996 to 2023 to investigate tilt angles ( γ ) of bipolar magnetic regions and Joy’s law for Solar Cycles 23 and 24 and a portion of Cycle 25. The HMI radial magnetic field ( B _r ) and MDI magnetogram ( B _los ) data are used to calculate ( γ ) using the flux-weighted centroids of the positive and negative polarities. Each active region (AR) is only sampled once. The analysis includes only Beta ( β )-class ARs since computing γ of complex ARs is less meaningful. During the emergence of the ARs, we find that the average tilt angle ( $\bar{\gamma }$ ) increases from 3.°30 ± 0.75 when 20% of the flux has emerged to 6.°79° ± 0.66 when the ARs are at their maximum flux. Cycle 24 has a larger average tilt, ${\bar{\gamma }}_{24}$ =6.67 ± 0.66, than Cycle 23, ${\bar{\gamma }}_{23}$ = 5.11 ± 0.61. No significant difference is found in the slope of Joy’s law or $\bar{\gamma }$ when sampling the ARs at the time of maximum flux or central meridian crossing. There are persistent differences in $\bar{\gamma }$ in the hemispheres, with the Sun's southern hemisphere having higher $\bar{\gamma }$ in Cycles 23 and 24, but the uncertainties are such that these differences are not statistically significant.

In solar physics, a long-unanswered question is whether or not there are local dynamos acting in sunspot regions. Here we report an observed pattern of magnetic evolution that makes the sunspots alive with ample complexity and energy. This anomalous pattern manifests as peculiar bipolar magnetic emergences (BMEs), exhibiting the following characteristics: (1) the BMEs persistently appear beyond the penumbra, encircling the sunspot in an end-to-end configuration; (2) each BME gradually grows and separates its two polarities along an arc trajectory centered on the sunspot; (3) a circular brightening belt is manifested in the ultraviolet/extreme-ultraviolet radiations during the BMEs’ evolution; and (4) the sunspot regions with such an evolution pattern often exhibit vigorous solar activity, such as homogeneous major flares. The magnetic evolving pattern and relevant flare activity indicate the presence of a local dynamo, and we characterize it as a twisting-reconnecting dynamo.

Based on the data from the Kodaikanal and Mount Wilson observatories, we investigate the relationships of the tilt angles of sunspot groups, including the mean tilt angle and the tilt-angle scatter, during the declining phase with the parameters of the next solar cycle (SC). The main findings are summarized in the following three points. (1) During the declining phase, the correlation between the mean tilt angle and the tilt-angle scatter is statistically insignificant. (2) Six quantities measured during the declining phase show significant anticorrelations with the strength and amplitude of the next SC and positive correlations with the duration of the ascending phase of the next SC: the standard deviation of the tilt angles, the rms tilt angle, the mean absolute value of the tilt angles, the area-weighted absolute value of the tilt angles, the latitude-weighted absolute value of the tilt angles, and the area- and latitude-weighted absolute value of the tilt angles. (3) The correlations of the mean tilt angle, the area-weighted tilt angle, the latitude-weighted tilt angle, and the area- and latitude-weighted tilt angle during the declining phase with the strength, amplitude, and duration of the ascending phase of the next SC are statistically insignificant. These findings demonstrate that the modulation of the parameters of the next SC by the tilt-angle scatter during the declining phase plays a vital role in regulating SC variability.

Meridional flow is crucial in generating the solar poloidal magnetic field by facilitating poleward transport of the field from decayed bipolar magnetic regions (BMRs). As the meridional circulation changes with the stellar rotation rate, the properties of stellar magnetic cycles are expected to be influenced by this flow. In this study, we explore the role of meridional flow in generating magnetic fields in the Sun and Sun-like stars using the STABLE (surface flux transport and Babcock–Leighton) dynamo model. We find that a moderate meridional flow increases the polar field by efficiently driving the trailing polarity flux toward the pole, while a strong flow tends to transport both polarities of BMRs poleward, potentially reducing the polar field. Our findings are in perfect agreement with what one can expect from the surface flux transport model. Similarly, the toroidal field initially increases with moderate flow speeds and then decreases beyond a certain value. This trend is due to the competitive effects of shearing and diffusion. Furthermore, our study highlights the impact of meridional flow on the strength and duration of stellar cycles. By including the meridional flow from a mean-field hydrodynamics model in STABLE, we show that the magnetic field strength initially increases with the stellar rotation rate and then declines in rapidly rotating stars, offering an explanation of the observed variation of stellar magnetic field with rotation rate.

Solar differential rotation exhibits a prominent feature: its cyclic variations over the solar cycle, referred to as zonal flows or torsional oscillations, are observed throughout the convection zone. Given the challenge of measuring magnetic fields in subsurface layers, understanding deep torsional oscillations becomes pivotal in deciphering the underlying solar dynamo mechanism. In this study, we address the critical question of identifying specific signatures within helioseismic frequency-splitting data associated with the torsional oscillations. To achieve this, a comprehensive forward modeling approach is employed to simulate the helioseismic data for a dynamo model that, to some extent, reproduces solar-cycle variations of magnetic fields and flows. We provide a comprehensive derivation of the forward modeling process utilizing generalized spherical harmonics, as it involves intricate algebraic computations. All estimated frequency-splitting coefficients from the model display an 11 yr periodicity. Using the simulated splitting coefficients and realistic noise, we show that it is possible to identify the dynamo wave signal present in the solar zonal flow from the tachocline to the solar surface. By analyzing observed data, we find similar dynamo wave patterns in the observational data from the Michelson Doppler Imager, Helioseismic Magnetic Imager, and Global Oscillation Network Group. This validates the earlier detection of dynamo waves and holds potential implications for the solar dynamo theory models.

Using Helioseismic and Magnetic Imager/Solar Dynamics Observatory data, we search for a relationship between kinetic helicity and magnetic helicity in solar active regions (ARs) using a sample of 62 ARs from 2010 May to 2015 May. The sample includes 32 mature ARs and 30 emerging ARs. We calculate kinetic helicity in the interior in the depth range from 0.6 to 11.6 Mm, magnetic helicity in the corona, helicity flux across the photosphere, and the magnetic twist and magnetic writhe of the ARs at the photosphere. From these data, relationships are found between magnetic helicity, helicity flux, and magnetic twist. However, magnetic writhe appears not to be related to the other magnetic quantities. No relationship is found between the kinetic helicity and any magnetic quantity. In particular, no relationship is found between the kinetic helicity and any of the following: magnetic helicity, magnetic helicity flux, magnetic twist, or magnetic writhe. These results suggest that (1) the magnetic helicity in the corona above ARs is mainly derived from the magnetic twist, and (2) the flow dynamics in the region from 0.6 to 11.6 Mm below the photosphere is not the primary source for the generation of magnetic helicity in ARs.

Sunspots and active regions observed on the solar surface are widely believed to be manifestations of compact predominantly toroidal magnetic field structures (“flux tubes”) that emerge by magnetic buoyancy from the deeper interior of the Sun. Much work has examined the evolution of such magnetic structures, typically considering them as idealized isolated magnetic entities and not as more realistic magnetic concentrations in a volume-filling background magnetic field. Here, we report results that explore the buoyant rise dynamics of magnetic concentrations in a volume-filling field in the full three dimensions. Earlier 2.5D work in this series established the remarkable fact that the twist orientation of a flux concentration relative to the background field affected its likelihood to rise and emerge, regardless of whether the buoyant rise took place in the absence or presence of convection. The contrasting dynamics between structures with differing orientations lead to a selection mechanism that reproduces characteristics of the “solar hemispheric helicity rule(s)” observations strikingly well. Here, we show that this two-dimensional selection mechanism persists in the face of the added complexity of three-dimensional dynamics. Arching of the magnetic structure in the third dimension, as might be expected in the solar application, is introduced. The role of tension force leading to this selection mechanism is elucidated and subtle differences that arise due to the three-dimensional geometry are discussed.

The details of the dynamo process in the Sun are an important aspect of research in solar-terrestrial physics and astrophysics. The surface part of the dynamo can be constrained by direct observations, but the subsurface part lacks direct observational constraints. The torsional oscillations, a small periodic variation of the Sun's rotation with the solar cycle, are thought to result from the Lorentz force of the cyclic magnetic field generated by the dynamo. In this study, we aim to discriminate between three Babcock–Leighton dynamo models by comparing the zonal acceleration of the three models with the observed one. The property that the poleward and equatorward branches of the torsional oscillations originate from about ±55° latitudes with their own migration time periods serves as an effective discriminator that could constrain the configuration of the magnetic field in the convection zone. The toroidal field, comprising poleward and equatorward branches separated at about ±55° latitudes, can generate the two branches of the torsional oscillations. The alternating acceleration and deceleration bands in time are the other property of the torsional oscillations that discriminates between the dynamo models. To reproduce this property, the phase difference between the radial ( B _r ) and toroidal ( B _ϕ ) components of the magnetic field near the surface should be about π /2.

The solar dynamo is essentially a cyclic process in which the toroidal component of the magnetic field is converted into the poloidal one and vice versa. This cyclic loop is disturbed by some nonlinear and stochastic processes mainly operating in the toroidal to poloidal part. Hence, the memory of the polar field decreases in every cycle. On the other hand, the dynamo efficiency and, thus, the supercriticality of the dynamo decreases with the Sun’s age. Previous studies have shown that the memory of the polar magnetic field decreases with the increase of supercriticality of the dynamo. In this study, we employ popular techniques of time series analysis, namely, compute Higuchi’s fractal dimension, Hurst exponent, and Multi-Fractal Detrended Fluctuation Analysis to the amplitude of the solar magnetic cycle obtained from dynamo models operating at near-critical and supercritical regimes. We show that the magnetic field in the near-critical regime is governed by strong memory, less stochasticity, intermittency, and breakdown of self-similarity. On the contrary, the magnetic field in the supercritical region has less memory, strong stochasticity, and shows a good amount of self-similarity. Finally, applying the same time series analysis techniques in the reconstructed sunspot data of 85 cycles and comparing their results with that from models, we conclude that the solar dynamo is possibly operating near the critical regime and not too much supercritical regime. Thus the Sun may not be too far from the critical dynamo transition.

We recently presented the first 3D numerical simulation of the solar interior for which tachocline confinement was achieved by a dynamo-generated magnetic field. In this follow-up study, we analyze the degree of confinement as the magnetic field strength changes (controlled by varying the magnetic Prandtl number) in a coupled radiative zone (RZ) and convection zone (CZ) system. We broadly find three solution regimes, corresponding to weak, medium, and strong dynamo magnetic field strengths. In the weak-field regime, the large-scale magnetic field is mostly axisymmetric with regular, periodic polarity reversals (reminiscent of the observed solar cycle) but fails to create a confined tachocline. In the strong-field regime, the large-scale field is mostly nonaxisymmetric with irregular, quasi-periodic polarity reversals and creates a confined tachocline. In the medium-field regime, the large-scale field resembles a strong-field dynamo for extended intervals but intermittently weakens to allow temporary epochs of strong differential rotation. In all regimes, the amplitude of poloidal field strength in the RZ is very well explained by skin-depth arguments, wherein the oscillating field that gives rise to the skin depth (in the medium- and strong-field cases) is a nonaxisymmetric field structure at the base of the CZ that rotates with respect to the RZ. These simulations suggest a new picture of solar tachocline confinement by the dynamo, in which nonaxisymmetric, very long-lived (effectively permanent) field structures rotating with respect to the RZ play the primary role, instead of the regularly reversing axisymmetric field associated with the 22 yr cycle.

We study the toroidal magnetic flux budget of the axisymmetric part of a data-driven 3D mean-field dynamo model of Solar Cycles 23 and 24. The model simulates the global solar dynamo that includes the effects of the formation and evolution of bipolar magnetic regions (BMRs) emerging on the solar surface. By applying Stokes’s theorem to the dynamo induction equation, we show that the hemispheric magnitude of the net axisymmetric toroidal magnetic field generation rate in the bulk of the convection zone can only partially be estimated from the surface parameters of the differential rotation and the axisymmetric radial magnetic field. The contribution of the radial integral along the equator, which is mostly due to the rotational radial shear at the bottom of the convection zone, has the same magnitude and is nearly in phase with the effect of the surface latitudinal differential rotation. Also, the toroidal field generation rate estimate strongly depends on the latitudinal profile of the surface radial magnetic field near the poles. This profile in our dynamo models significantly deviates from the polar magnetic field distribution observed during the minima of Solar Cycles 22, 23, and 24. The cause of this discrepancy requires further observational and theoretical studies. Comparing the 2D axisymmetric and the 3D nonaxisymmetric dynamo models, we find an increase in the toroidal field generation rate in the 3D model due to the surface effects of BMRs, resulting in an increase in the axisymmetric poloidal magnetic field magnitude.

• Active regions of solar cycles 23 and 24 were sorted out between two categories: regular bipolar (obeying Hale's polarity law, Joy's law, etc.) and irregular ARs. • Both regular and irregular regions exhibit strong N-S asymmetry. • Tendencies are discussed in terms of the interplay between the dipole and quadrupole components of the global magnetic field. We used the elaborated earlier catalog of the magneto-morphological classes (MMC) of active regions (ARs) to study 2046 ARs of the solar cycle (SC) 23 and 1507 ARs of the SC24. According to empiric rules for sunspot groups (Hale's polarity law, Joy's law, etc.) and MMC, all ARs (except for unipolar spots) were sorted out between two categories: A-type – regular bipolar ARs; B-type – all the rest irregular ARs. We found that the number of both regular and irregular ARs follows the cycle with the Pearson's correlation coefficient of 0.92 and 0.78, respectively. The regular ARs are distributed evenly between the two maxima of each cycle. The irregular ARs are also distributed evenly between the two maxima in the SC 23, however their number is enhanced in the second maximum of the SC 24. Both regular and irregular ARs exhibit strong north–south (N-S) asymmetry. The significance of asymmetry is confirmed using the Pearson's χ -square test and one more test based on the normal approximation to a binomial distribution. During the two maxima of a cycle, the peaks in two hemispheres for both regular and irregular ARs number do not vary synchronously. This can be explained by the fluctuations in Babcock-Leighton mechanism. In general, there are more irregular ARs in the S-hemisphere in both cycles, which might be the result of an additional weakening of the toroidal field due to interplay between the dipole and quadrupole components of the global magnetic field. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Information theory is used to characterize the solar active region periodicities and memories from the Carrington map images 1974–2021. The active regions typically evolve and move from one map to the next. In order to track these active region structures in sequences of images, an innovative method based on information theory is developed. Image entropy provides a measure of the organization of structures in the images. The entropy can also be used as a filter to identify structures and partition the active regions, which are then registered for each image. The partitions are used to compute the mutual information and measure the information flow from the active regions from one image to the next. Finally, conditional mutual information is used to give a measure of the information flow from one image to another given the third image. The results suggest the following: (1) there is a long-term memory of two cycles or more; (2) the coherence time of the active regions is ∼2 yr; and (3) the average active region structure scale size carrying the most information is approximately 118 × 10 ^3 –236 × 10 ^3 Mm ^2 . The study has implications to the short- and long-term predictability of active regions and sunspots as well as the nature of flux transport at the Sun. Finally, our innovative method can be similarly applied to stellar data to determine the dynamics of the active regions of stars.

Carbon‐14 in tree rings have suggested there had been multiple extreme solar proton events (SPEs) in the past. While the largest events such as in 774–775 CE can be significantly detected by the typical precision of accelerator mass spectrometry, smaller but possibly more frequent events have been difficult to be detected. Thus, the frequency or any characteristics of such relatively smaller events are still largely unknown. In this paper, we report that large SPEs had occurred in 1261–1262, 1268–1269, and 1279–1280 CE before the onset of the Wolf minimum based on high‐precision carbon‐14 analyses. It is suggested that they had occurred at the maximum and the declining phase of solar cycles, and that they had occurred during the transition time of solar activity into a deep minimum. We propose that this episode may provide a unique opportunity to elucidate a potential interaction between the solar dynamo and extreme solar flares. Plain Language Summary: The Sun is a magnetically active star and occasionally cause intense bursts that sometimes accompany the ejection of energetic protons, described as the solar proton events. In this paper, we report that there were three intense solar proton events in the thirteenth century, just before the onset of the Wolf grand minimum. We propose that these events may be related to the weakening of solar activity during that time. Key Points: Multiple abrupt increases in carbon‐14 content were found during the transition time of solar activity into the grand minimum stateThey occurred at solar activity maximum or at the declining phase of solar cycles, suggesting that they originate from solar proton eventsThe Wolf minimum may provide a unique opportunity to potentially deepen the understanding of the solar dynamo [ABSTRACT FROM AUTHOR]

Although wanting to become an astronomer from an early age, I ended up in solar physics purely by chance, after first working in high-energy astrophysics. I’ve never regretted switching from the pulsar to the solar magnetosphere, because solar physics has a great advantage over other areas of astrophysics—in the enormous amount of high-quality data available, much of it underutilized. I’ve often wondered why theoreticians and modelers don’t spent more time looking at these data (perhaps they feel that it is cheating, like taking a peek at the answers to a difficult homework assignment?). Conversely, I wonder why observers and data analysts aren’t more skeptical of the theoretical models—especially the fashionable ones.

Yearly sunspot cycle 24 (SC24) activity reached a minimum in December 2019. Timeline for SC25 is explored with data for sunspot numbers (SSNs) and geomagnetic indices (aa/Ap) using our time-tested heuristic methodology not based on any model. We infer SC25 may be as active as SC24, reaching its peak (Rmax) in February 2024 ± 6 months, ruling out Dalton-like minimum in 21st century as well as McIntosh et al. (2020) forecast that "SC25 could have a magnitude that rivals the top few since records began." Wide range of SC25 forecasts challenges our understanding of solar dynamo operation and reliability of future long-term space weather / climate forecasts. We cannot anticipate whether SC25 may have multiple peaks; no theory is tuned to predict fine structure of a SC. During ascending phase of SC24 a CME from the Sun barely missed the Earth. A direct hit by it could have caused damage of trillions of dollars, shutting down power grid and rendering satellites blind. [ABSTRACT FROM AUTHOR]

Using time–distance local helioseismology flow maps within 1 Mm of the solar photosphere, we detect inflows toward activity belts that contribute to solar-cycle scale variations in the near-surface meridional flow. These inflows stretch out as far as 30° away from the active region centroids. If active region neighborhoods are excluded, the solar-cycle-scale variation in the background meridional flow diminishes to below 2 m s ^−1 , but still shows systematic variations in the absence of active regions between sunspot cycles 24 and 25. We therefore propose that the near-surface meridional flow is a three-component flow made up of a constant baseline flow profile that can be derived from quiet-Sun regions, variations due to inflows around active regions, and solar-cycle-scale variation of about 2 m s ^−1 . Torsional oscillation, on the other hand, is found to be a global phenomenon, i.e., exclusion of active region neighborhoods does not significantly affect its magnitude or phase. This nonvariation in torsional oscillation with distance away from active regions and the three-component breakdown of the near-surface meridional flow serve as vital constraints for solar dynamo models and surface flux-transport simulations.

We have studied the large-scale dynamo forced with helical magnetic energy. Compared to the kinetic forcing process, the magnetic process is not clearly observed nor intuitive. However, it may represent the actual B field amplification in the stellar corona, accretion disk, plasma lab, or other magnetically dominated systems where the strong kinetic effect does not exist. The interaction between the magnetic field and the plasma is essentially nonlinear. However, when the plasma system is driven by helical energy, whether kinetic or magnetic, the nonlinear process can be linearized with pseudotensors a , β and the large-scale magnetic field $\overline{{\boldsymbol{B}}}$ . Conventionally, the α effect is thought to be the main dynamo effect converting kinetic energy into magnetic energy and transferring it to the large-scale regime. In contrast, β effect has been thought to diffuse magnetic energy. However, these conclusions are not based on the exact definition of α and β . In this paper, instead of the analytic definition of α and β , we derive a semi-analytic equation and apply it to the simulation data. The half analytic and numerical result shows that the averaged α effect is not so important in amplifying the $\overline{{\boldsymbol{B}}}$ field. Rather, it is the negative β effect combined with the Laplacian (∇ ^2 → − k ^2 ) that plays a key role in the dynamo process. Further, the negative magnetic diffusivity accounts for the attenuation of the plasma kinetic energy ${\overline{E}}_{V}$ in large scales. We discuss this process using the theoretical method and the intuitive field structure model.

The importance of the quiet-Sun magnetism is that it is always there to a greater or lesser extent, being a constant provider of energy, independently of the solar cycle phase. The open questions about the quiet-Sun magnetism include those related to its origin. Most people claim that the local dynamo action is the mechanism that causes it. This fact would imply that the quiet-Sun magnetism is nearly the same at any location over the solar surface and at any time. Many works claim that the quiet Sun does not have any variation at all, although a few of them raise doubt on this claim and find mild evidence of a cyclic variation in the the quiet-Sun magnetism. In this work, we detect clear variations in the internetwork magnetism both with latitude and solar cycle. In terms of latitude, we find an increase in the averaged magnetic fields toward the solar poles. We also find long-term variations in the averaged magnetic field at the disk center and solar poles, and both variations are almost anticorrelated. These findings do not support the idea that the local dynamo action is the unique factory of the quiet-Sun magnetism.

In this paper, we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamo action, is third order and has cubic nonlinearities while the second has only quadratic nonlinearities and describes the interaction of convection and an aperiodically reversing magnetic field. We show how DSS can be used to solve for the statistics of these systems of equations both in the presence and the absence of stochastic terms, by truncating the cumulant hierarchy at either second or third order. We compare two different techniques for solving for the statistics: timestepping, which is able to locate only stable solutions of the equations for the statistics, and direct detection of the fixed points. We develop a complete methodology and symbolic package in Python for deriving the statistical equations governing the low-order dynamic systems in cumulant expansions. We demonstrate that although direct detection of the fixed points is efficient and accurate for DSS truncated at second order, the addition of higher order terms leads to the inclusion of many unstable fixed points that may be found by direct detection of the fixed point by iterative methods. In those cases, timestepping is a more robust protocol for finding meaningful solutions to DSS. [ABSTRACT FROM AUTHOR]

The sunspot cycle is quite variable in duration and amplitude, yet in the long term, it seems to return to solar minimum on schedule, as if guided by a clock with an average period of close to 11.05 years for the sunspot number cycle and 22.1 years for the magnetic cycle. This paper provides a brief review of the sunspot number cycle since 1750, discusses some of the processes controlling the solar dynamo, and provides clues that may add to our understanding of what controls the cadence of the solar clock. [ABSTRACT FROM AUTHOR]

The profile of the differential rotation together with the sign of the alpha-effect determine the dynamo wave direction. In early models of the solar dynamo the dynamo wave often leads to a poleward migration of the activity belts. Flux transport by the meridional flow or the effect of the surface shear layer are possible solutions. In a model including the corona, we show that various migrations can be obtained by varying the properties of the corona. A new dynamo of Babcock-Leighton type also leads to the correct equatorward migration by the non-linear relation between flux density and rise time of the flux. [ABSTRACT FROM AUTHOR]

The dynamic activity of the Sun—sustained by a magnetohydrodynamic dynamo mechanism working in its interior—modulates the electromagnetic, particulate, and radiative environment in space. While solar activity variations on short timescale create space weather, slow long-term modulation forms the basis of space climate. Space weather impacts diverse space-reliant technologies while space climate influences planetary atmospheres and climate. Having prior knowledge of the Sun's activity is important in these contexts. However, forecasting solar-stellar magnetic activity has remained an outstanding challenge. In this review, predictions for Sunspot Cycle 24 and the upcoming Solar Cycle 25 are summarized, and critically assessed. The analysis demonstrates that while predictions based on diverse techniques disagree across Solar Cycles 24–25, physics-based predictions for Solar Cycle 25 have converged and indicates a weak to moderate–weak sunspot cycle. I argue that this convergence in physics-based predictions is indicative of progress in the fundamental understanding of solar cycle predictability. Based on this understanding, resolutions to several outstanding questions related to solar cycle predictions are discussed; these questions include: is it possible to predict the solar cycle, what is the best proxy for predictions, how early can we predict the solar cycle and how many cycles into the future can we predict relying on our current understanding? Based on our analysis, we also suggest a rigorous pathway towards generating and disseminating a "consensus forecast" by any solar cycle prediction panels tasked with such a challenge. [ABSTRACT FROM AUTHOR]

A review of solar cycle prediction methods and their performance is given, including early forecasts for Cycle 25. The review focuses on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is further restricted to the issue of predicting the amplitude (and optionally the epoch) of an upcoming solar maximum no later than right after the start of the given cycle. Prediction methods form three main groups. Precursor methods rely on the value of some measure of solar activity or magnetism at a specified time to predict the amplitude of the following solar maximum. The choice of a good precursor often implies considerable physical insight: indeed, it has become increasingly clear that the transition from purely empirical precursors to model-based methods is continuous. Model-based approaches can be further divided into two groups: predictions based on surface flux transport models and on consistent dynamo models. The implicit assumption of precursor methods is that each numbered solar cycle is a consistent unit in itself, while solar activity seems to consist of a series of much less tightly intercorrelated individual cycles. Extrapolation methods, in contrast, are based on the premise that the physical process giving rise to the sunspot number record is statistically homogeneous, i.e., the mathematical regularities underlying its variations are the same at any point of time, and therefore it lends itself to analysis and forecasting by time series methods. In their overall performance during the course of the last few solar cycles, precursor methods have clearly been superior to extrapolation methods. One method that has yielded predictions consistently in the right range during the past few solar cycles is the polar field precursor. Nevertheless, some extrapolation methods may still be worth further study. Model based forecasts are quickly coming into their own, and, despite not having a long proven record, their predictions are received with increasing confidence by the community. [ABSTRACT FROM AUTHOR]

We present a non-kinematic axisymetric α2Ω mean-field dynamo model in which the complete α-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-kinematic αΩ models using a scalar α-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. [ABSTRACT FROM AUTHOR]