Resonances and Stellar Cycles: Observations and Modelling

TL;DR

The paper investigates whether planetary gravitational forcing can set or modulate solar/stellar magnetic activity cycles. It uses the Parker dynamo model with parametric modulation of the dynamo-number, $D(t)=D_0(1+0.1\\sin(\\Omega t))$, to explore resonance, growth-rate suppression, and beat phenomena. The results show that planetary forcing is unlikely to be the primary driver, but weak parametric effects can modulate oscillations and produce frequency splitting and beats near resonance. Observational data corroborate that orbital periods do not generally align with activity cycles, suggesting dynamo-driven cycles with limited planetary influence. The findings highlight non-classical dynamical responses in simplified dynamos and imply possible long-term modulation (roughly 100–200 years) if small period offsets exist, prompting more realistic modelling of stellar dynamos.

Abstract

In the paper we discuss the possibility of the influence of parametric excitation, in particular, planetary gravitational interaction, on the behavior of stellar magnetic activity cycles. Using the well-known Parker dynamo modeling, we demonstrate the doubtfulness of the fact that planetary rotation can be a determining factor in the formation of the cycle itself. However, we show that even a weak parametric influence can be sufficient to modulation of magnetic field oscillations, and, in particular, to the occurrence of beats. This result is discussed in the context of the influence of Jupiter on the occurrence of maxima and minima of the magnetic activity of our Sun.

Figures (1)

• Figure 1: Dependencies of the relative exponential growth rates $\gamma/\gamma_0$ (left panel) and the relative oscillation frequencies $\omega/\omega_0$ (right panel) on the relative parametric excitation frequency $\Omega/\omega_0$. Here we suppose ten percent excitation of the dynamo number: $D(t)=D_0(1+0.1\sin(\Omega t))$ and $D_0=750$.