Can Stochastic Resonance Explain Recurrence of Grand Minima?

Carlo Albert,Simone Ulzega,Antonio Ferriz-Mas,Filippo Gaia

doi:10.3847/2041-8213/ac0fd6

Abstract

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.

Highlights

It is well known that the Sun’s magnetic activity has a period of almost 11 yr with polarity reversals around the maximum of each solar cycle
We have demonstrated that a zero-dimensional dynamo model with delay and an upper threshold for the α-effect exhibits two fundamentally different stable oscillatory modes, which can co-exist for suitable parameter values
A similar observation has recently been made by Tripathi et al (2021). We believe that this is a generic feature that generalizes to more refined dynamo models of that type, which we plan to study in the future

Summary

Introduction

It is well known that the Sun’s magnetic activity has a period of almost 11 yr (the Schwabe cycle) with polarity reversals around the maximum of each solar cycle. The resulting system of delay ordinary differential equations (ODEs) shows interesting dynamic phenomena, which completely disappear if the time delay is set to zero We show that it exhibits two fundamentally different modes of stable oscillation, which can co-exist for certain ranges of parameter values. It is remarkable that many of the long-period cycles that we find in proxies of solar activity can be found in time-series of the torque exerted by the planets on the Sun (Abreu et al 2012) This has motivated us to study, by means of a simple dynamo model, whether a tiny (external) modulation can imprint its periodicities onto the modeswitching of the dynamo, whereby they are greatly amplified by Stochastic Resonance.

Stochastic Resonance in BL-type Dynamos

Discussion and Conclusions