Supermodulation of the Sun's magnetic activity: the effects of symmetry changes

Abstract

In this paper we argue that the solar activity record, as revealed by telescopic observations and proxy data from the abundances of cosmogenic isotopes, is consistent with the action of a deterministic nonlinear chaotic dynamo. In particular we claim that the long timescale 'super-modulation' apparent in the isotopic record can be ascribed to switching of the dynamo between two different modulational patterns. The first (which is currently in operation) involves deep grand minima and occasional changes in symmetry triggered by these minima. The second, which exhibits only weak modulation and no grand minima, arises as a consequence of symmetry breaking. These processes are demonstrated for highly idealized simple models of the nonlinear dynamo equations.

Convective dynamo action in a spherical shell: symmetries and modulation

“…For example, in the shaded regions, the solution undergoes changes in symmetry with no deep minima (Type 1 modulation), while between t ≈ 6 and t ≈ 9 clusters of grand minima are found. From a mathematical perspective, it is no surprise that a chaotic nonlinear dynamo solution exhibits such behaviour which has indeed been predicted (Weiss & Tobias 2016).…”

“…This clearly shows the solution exhibiting both types of modulation; Type 1 modulation where there are no minima in activity but energy transfer between the modes of different symmetries and Type 2 modulation where the antisymmetric solution regularly visits grand minima in activity through interactions with the zonal wind. The transition between these two types of modulation has been termed supermodulation and is believed to be prominent in solar activity records (Weiss & Tobias 2016). The time series corresponding to the trajectories in figure 3 are shown in figure 4.…”

“…In the second (imaginatively termed Type 2 modulation) a magnetic mode with a given symmetry undergoes modulation via interaction with a large-scale velocity field; here changes in the amplitude of the basic cycle occur with no significant changes in the symmetry of solutions. Recently, Weiss & Tobias (2016) have argued from analysis of cosmogenic isotope records that both of these modulational mechanisms have been at play in the solar dynamo, leading to 'supermodulation' on long time scales. The precise modulational effects important in the system are sometimes model-dependent.…”

On the Synchronizability of Tayler–Spruit and Babcock–Leighton Type Dynamos

“…For intervening bands, and for larger values of τ , synchronization still occurs, but the 22.14 years oscillation is then replaced by a 11.07 years pulsation. Whether these pulsations are irrelevant for the sun, or whether they could be linked to the behaviour during grand minima (Weiss and Tobias, 2016;Moss and Sokoloff, 2017), remains to be clarified in higher-dimensional models. Remarkably, at any rate, is the phase coherence when passing from oscillations to pulsations, and back, as evidenced in Figure 3.…”

Magnetism, dynamo action and the solar-stellar connection

“…We can gain insights by turning to nonlinear mean field dynamo studies such as those of Tobias (1997), Moss and Brooke (2000), Bushby (2006). These mean field dynamo models take into account the retroaction by the large-scale Lorentz force (also known as the Malkus-Proctor effect) and have shown that low magnetic Prandtl dynamo models (Pm < 0.025) yields interesting intermittent/chaotic states akin to grand minima period (see also recent work by Weiss and Tobias (2016)). This is due to the various magnetic, velocity and diffusive time scales that leads to a highly time dependent behavior when there are far apart as it is the case for low Pm number.…”