The dynamics of Wolf numbers based on nonlinear dynamo with magnetic helicity: comparisons with observations

TL;DR

This paper models solar activity dynamics using a nonlinear dynamo approach incorporating magnetic helicity, successfully reproducing observed Wolf number variations and cycle characteristics with high correlation to historical data.

Contribution

It introduces a novel nonlinear dynamo model with magnetic helicity effects and a new evolution equation for Wolf numbers, aligning simulations closely with observations.

Findings

70% correlation between simulations and 270-year observational data

Dependence of Wolf number maximum on cycle period

Cycle asymmetry correlates with cycle amplitude

Abstract

We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution of Wolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behavior of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 years ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 % correlation over all intervals of observation (about 270 years). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependencies are in good agreement with observations.