Solar Grand Minima and random fluctuations in dynamo parameters

TL;DR

This paper investigates whether random fluctuations in solar dynamo parameters can explain Grand Minima, finding that while models produce Poisson-like distributions, actual data shows deviations, suggesting more complex dynamics or data limitations.

Contribution

The study demonstrates that fluctuations in the alpha-coefficient can mimic Grand Minima features, but cannot fully reproduce the non-Poissonian statistics observed in solar activity data.

Findings

Models produce exponential waiting time distributions.

Observed data shows significant deviations from Poisson statistics.

Discrepancies may be due to limited observational data.

Abstract

We consider to what extent the long-term dynamics of cyclic solar activity in the form of Grand Minima can be associated with random fluctuations of the parameters governing the solar dynamo. We consider fluctuations of the alpha-coefficient in the conventional Parker migratory dynamo, and also in slightly more sophisticated dynamo models, and demonstrate that they can mimic the gross features of the phenomenon of the occurrence of Grand Minima over a suitable parameter range. The temporal distribution of these Grand Minima appears chaotic, with a more or less exponential waiting time distribution, typical of Poisson processes. In contrast however, the available reconstruction of Grand Minima statistics based on cosmogenic isotope data demonstrates substantial deviations from this exponential law. We were unable to reproduce the non-Poissonic tail of the waiting time distribution either in the framework of a simple alpha-quenched Parker model, or in its straightforward generalization, nor in simple models with feedback on the differential rotation. We suggest that the disagreement may only be apparent and is plausibly related to the limited observational data, and that the observations and results of numerical modeling can be consistent and represent physically similar dynamo regimes.