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Recent data on superflares on sun-like stars and radiocarbon data on solar activity in the past are both indicative of transient epochs of unusually high magnetic activity. We propose an explanation for the grand activity maxima in the framework of a solar dynamo model with fluctuating parameters. Solar-type dynamos are oscillatory because of the combination of the solar-type differential rotation with positive (in the Northern hemisphere) alpha-effect. An artificial reversal of the sign in the alpha-effect changes the dynamo to a steady regime with hundreds of times larger magnetic energy compared to the amplitude of the cyclic dynamo. Sufficiently large and durable fluctuations reversing the sign of the alpha-effect during the growth phase of a magnetic cycle can, therefore, cause a transient change to a steady dynamo with considerably increased magnetic energy. This qualitative scenario for grand activity maxima is supported by computations of the dynamo model with a fluctuating alpha-effect. The computed statistics of several thousand magnetic cycles gives examples of cycles with very high magnetic energy. Our preliminary estimations, however, suggest that the probability of solar superflares is extremely low., Comment: 8 pages, 8 figures, accepted by MNRAS

The magnetic activity of solar-type stars generally increases with stellar rotation rate. The increase, however, saturates for fast rotation. The Babcock-Leighton mechanism of stellar dynamos saturates as well when the mean tilt-angle of active regions approaches ninety degrees. Saturation of magnetic activity may be a consequence of this property of the Babcock-Leighton mechanism. Stellar dynamo models with a tilt-angle proportional to the rotation rate are constructed to probe this idea. Two versions of the model - treating the tilt-angles globally and using Joy's law for its latitude dependence - are considered. Both models show a saturation of dynamo-generated magnetic flux at high rotation rates. The model with latitude-dependent tilt-angles also shows a change in dynamo regime in the saturation region. The new regime combines a cyclic dynamo at low latitudes with an (almost) steady polar dynamo., Comment: 12 pages (one column), 7 figures, to appear in RAA

A solar-type dynamo model in a spherical shell is developed with allowance for random dependence of the poloidal field generation mechanism on time and latitude. The model shows repeatable epochs of strongly decreased amplitude of magnetic cycles similar to the Maunder minimum of solar activity. Random dependence of dynamo-parameters on latitude brakes the equatorial symmetry of generated fields. The model shows the correlation of the occurrence of grand minima with deviations in the dynamo-field from dipolar parity. An increased north-south asymmetry of magnetic activity can, therefore, be an indicator of transitions to grand minima. Qualitative interpretation of this correlation is suggested. Statistics of grand minima in the model are close to the Poisson random process indicating that the onset of a grand minimum is statistically independent of preceding minima., Comment: 8 pages, 9 figures, to apper in ApJ

Parameters of a special kind of \alpha-effect known in dynamo theory as the Babcock-Leighton mechanism are estimated using the data of sunspot catalogs. The estimates evidence the presence of the Babcock-Leighton \alpha-effect on the Sun. Fluctuations of the \alpha-effect are also estimated. The fluctuation amplitude appreciably exceeds the mean value, and the characteristic time for the fluctuations is comparable to the period of the solar rotation. Fluctuations with the parameters found are included in a numerical model for the solar dynamo. Computations show irregular changes in the amplitudes of the magnetic cycles on time scales of centuries and millennia. The calculated statistical characteristics of the grand solar minima and maxima agree with the data on solar activity over the Holocene., Comment: To appear in Astronomy Reports, 20 pages, 9 figures

Gyrochronology and recent theoretical findings are used to reduce the number of input parameters of differential rotation models. This eventually leads to a theoretical prediction for the surface differential rotation as a function of only two stellar parameters - surface temperature and rotation period - that can be defined observationally. An analytical approximation for this function is suggested. The tendency for the differential rotation to increase with temperature is confirmed. The increase is much steeper for late F-stars compared to G- and K-dwarfs. Slow and fast rotation regimes for internal stellar rotation are identified. A star attains its maximum differential rotation at rotation rates intermediate between these two regimes. The amplitude of the meridional flow increases with surface temperature and rotation rate. The structure of the flow changes considerably between cases of slow and fast rotation. The flow in rapid rotators is concentrated in the boundary layers near the top and bottom of the convection zone with very weak circulation in between., Comment: 8 pages,8 figures, 1 table, submitted to MNRAS

The contribution of the Babcock-Leighton mechanism to the generation of the Sun's poloidal magnetic field is estimated from sunspot data for three solar cycles. Comparison of the derived quantities with the A-index of the large-scale magnetic field suggests a positive answer to the question posed in the title of this paper., Comment: 5 pages, 2 figures, to apper in Astronomy Letters

A combination of diamagnetic pumping and a nonlocal alpha-effect of the Babcock-Leighton type in a solar dynamo model helps to reproduce observations of solar magnetic activity. The period of the solar cycle can be reproduced without reducing magnetic diffusivity in the bulk of the convection zone below the standard mixing-length value of $10^{13}$ cm$^2$s$^{-1}$. The simulated global fields are antisymmetric about the equator and the toroidal-to-poloidal field ratio is about a thousand. The time-latitude diagrams of magnetic fields in the model without meridional flow, however, differ from observations. Only when the meridional flow is included and the alpha-effect profile peaking at mid latitudes is applied, can the observational butterfly diagrams be reproduced., Comment: 17 pages, 10 figures, to appear in Solar Physics

The first results of the solar dynamo model that allows for the diamagnetic effect of inhomogeneous turbulence and the nonlocal alpha-effect due to the rise of magnetic loops are discussed. The nonlocal alpha-effect is not subject to the catastrophic quenching related to the conservation of magnetic helicity. Given the diamagnetic pumping, the magnetic fields are concentrated near the base of the convection zone, although the distributed-type model covers the entire thickness of the convection zone. The magnetic cycle period, the equatorial symmetry of the field, its meridional drift, and the polar-to-toroidal field ratio obtained in the model are in agreement with observations. There is also some disagreement with observations pointing the ways of improving the model., Comment: To appear in Astronomy Letters, 10 pages, 5 figures

The nonlocal alpha-effect of Babcock-Leighton type is not prone to the catastrophic quenching due to conservation of magnetic helicity. This is shown with a dynamo model, which jointly applies the nonlocal alpha-effect, the diamagnetic pumping, and dynamical equation for the magnetic alpha-effect. The same model shows catastrophic quenching when the alpha-effect is changed to its local formulation. The nonlocal model shows the preferred excitation of magnetic fields of dipolar symmetry, which oscillate with a period of about ten years and have a toroidal-to-polar fields ratio of about a thousand., Comment: 6 pages, 6 figures, submitted to Astronomische Nachrichten

A new version of a numerical model of stellar differential rotation based on mean-field hydrodynamics is presented and tested by computing the differential rotation of the Sun. The model is then applied to four individual stars including two moderate and two fast rotators to reproduce their observed differential rotation quite closely. A series of models for rapidly rotating ($P_{rot} = 1$ day) stars of different masses and compositions is generated. The effective temperature is found convenient to parameterize the differential rotation: variations with metallicity, that are quite pronounced when the differential rotation is considered as a function of the stellar mass, almost disappear in the dependence of differential rotation on temperature. The differential rotation increases steadily with surface temperature to exceed the largest differential rotation observed to date for the hottest F-stars we considered. This strong differential rotation is, however, found not to be efficient for dynamos when the efficiency is estimated with the standard $C_\Omega$-parameter of dynamo models. On the contrary, the small differential rotation of M-stars is the most dynamo-efficient. The meridional flow near the bottom of the convection zone is not small compared to the flow at the top in all our computations. The flow is distributed over the entire convection zone in slow rotators but retreats to the convection zone boundaries with increasing rotation rate, to consist of two near-boundary jets in rapid rotators. The implications of the change of the flow structure for stellar dynamos are briefly discussed., Comment: 9 pages, 11 figures, submitted to MNRAS