The rush to the poles and the role of magnetic buoyancy in the solar dynamo

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen, Germany
² Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany

^⋆ Corresponding author; cloutier@mps.mpg.de

Received: 3 June 2024
Accepted: 8 November 2024

Abstract

Context. The butterfly diagram of the solar cycle shows a poleward migration of the diffuse magnetic field resulting from the decay of trailing sunspots. It is one component of what is sometimes referred to as the ‘rush to the poles’ and is responsible for the reversal and buildup of the polar cap fields.

Aims. We investigated under which conditions the rush to the poles can be reproduced in flux-transport Babcock-Leighton dynamo models. We also considered other observational consequences of the different mechanisms that reproduce the rush to the poles.

Methods. We identified three main ways to achieve the rush to the poles: a flux emergence probability that decreases rapidly with latitude; a threshold for the sub-surface toroidal field strength below which the toroidal flux emerges only slowly and above which the emergence rate is high; and an emergence rate that depends on the mean magnetic field squared, mimicking magnetic buoyancy. We implemented these three mechanisms in a 2D Babcock-Leighton flux transport dynamo model that incorporates toroidal flux loss and deep downward turbulent pumping. Moreover, we directly compared the observational sunspot zone migration law with what our models predict.

Results. We find that all three mechanisms lead to solar-like butterfly diagrams, but with notable differences. The shape of the butterfly diagram is very sensitive to model parameters for the threshold prescription, while most models that incorporate magnetic buoyancy converge to very similar butterfly diagrams, with butterfly wing widths of ≲ ± 30°, in very good agreement with observations. With turbulent diffusivities above 35 km²/s but below about 40 km²/s, buoyancy models are strikingly solar-like. The threshold and magnetic buoyancy prescriptions make the models non-linear and as such they can saturate the dynamo through latitudinal quenching; during this process, emergences at higher latitudes are less efficient at transporting fields across the equator and hence less efficient in reversing the polar fields – although only the magnetic buoyancy prescription can saturate the dynamo when emergence loss is turned off. The period of the models that involve buoyancy is independent of the source term amplitude, but emergence loss increases it by ≃60%. The models with the right advection amplitude and turbulent diffusivity match the observational equatorward migration law very well.

Conclusions. For the rush to the poles to be visible, a mechanism suppressing (enhancing) emergences at high (low) latitudes must operate. It is not sufficient that the toroidal field be stored at low latitudes for emergences to be limited to low latitudes. Magnetic buoyancy appears to be the most promising non-linearity as models that incorporate it produce the most solar-like butterfly diagrams, with the exact width of the butterfly wings being roughly independent of model parameters. Dynamo saturation is achieved by a competition between latitudinal quenching and a quenching due to the tilt of the mean bipolar magnetic region. From these models we infer that the Sun is not in the advection-dominated regime, but nor is it in the diffusion-dominated regime. The cycle period is set through a balance between advection, diffusion, and flux emergence in accordance with the observational sunspot zone migration law. This accordance seems to imply that the toroidal field is indeed stored in the equatorial region of the lower convection zone.