Search

Context. The large-scale magnetic field in the Sun varies with a period of approximately 22 years, although the amplitude of the cycle is subject to long-term modulation with recurrent phases of significantly reduced magnetic activity. It is believed that a hydromagnetic dynamo is responsible for producing this large-scale field, although this dynamo process is not well understood. Aims. Within the framework of mean-field dynamo theory, our aim is to investigate how competing mechanisms for poloidal field regeneration (namely a time-delayed Babcock-Leighton surface α-effect and an interface-type α-effect), can lead to the modulation of magnetic activity in a deep-seated solar dynamo model. Methods. We solve the standard αΩ dynamo equations in one spatial dimension, including source terms corresponding to both of the competing α-effects in the evolution equation for the poloidal field. This system is solved using two different methods. In addition to solving the one-dimensional partial differential equations directly, using numerical techniques, we also use a local approximation to reduce the governing equations to a set of coupled ordinary differential equations (ODEs), which are studied using a combination of analytical and numerical methods. Results. In the ODE model, it is straightforward to find parameters such that a series of bifurcations can be identified as the time delay is increased, with the dynamo transitioning from periodic states to chaotic states via multiply periodic solutions. Similar transitions can be observed in the full model, with the chaotically modulated solutions exhibiting solar-like behaviour. Conclusions. Competing α-effects could explain the observed modulation in the solar cycle. [ABSTRACT FROM AUTHOR]

Aims. The Sun shows strong variability in its magnetic activity, from Grand minima to Grand maxima, but the nature of the variability is not fully understood, mostly because of the insufficient length of the directly observed solar activity records and of uncertainties related to long-term reconstructions. Here we present a new adjustment-free reconstruction of solar activity over three millennia and study its different modes. Methods. We present a new adjustment-free, physical reconstruction of solar activity over the past three millennia, using the latest verified carbon cycle, 14C production, and archeomagnetic field models. This great improvement allowed us to study different modes of solar activity at an unprecedented level of details. Results. The distribution of solar activity is clearly bi-modal, implying the existence of distinct modes of activity. The main regular activity mode corresponds to moderate activity that varies in a relatively narrow band between sunspot numbers 20 and 67. The existence of a separate Grand minimum mode with reduced solar activity, which cannot be explained by random fluctuations of the regular mode, is confirmed at a high confidence level. The possible existence of a separate Grand maximum mode is also suggested, but the statistics is too low to reach a confident conclusion. Conclusions. The Sun is shown to operate in distinct modes - a main general mode, a Grand minimum mode corresponding to an inactive Sun, and a possible Grand maximum mode corresponding to an unusually active Sun. These results provide important constraints for both dynamo models of Sun-like stars and investigations of possible solar influence on Earth's climate. [ABSTRACT FROM AUTHOR]