A Babcock-Leighton dynamo model of the Sun incorporating toroidal flux loss and the helioseismically inferred meridional flow

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
e-mail: cloutier@mps.mpg.de
² Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany

Received: 26 May 2023
Accepted: 28 September 2023

Abstract

Context. Key elements of the Babcock-Leighton model for the solar dynamo are increasingly constrained by observations.

Aims. We investigate whether the Babcock-Leighton flux-transport dynamo model remains in agreement with observations if the meridional flow profile is taken from helioseismic inversions. Additionally, we investigate the effect of the loss of toroidal flux through the solar surface.

Methods. We employ the two-dimensional flux-transport Babcock-Leighton dynamo framework. We use the helioseismically inferred meridional flow profile, and include toroidal flux loss in a way that is consistent with the amount of poloidal flux generated by Joy’s law. Our model does not impose a preference for emergences at low latitudes; however, we do require that the model produces such a preference.

Results. We can find solutions that are in general agreement with observations, including the latitudinal migration of the butterfly wings and the 11 year period of the cycle. The most important free parameters in the model are the depth to which the radial turbulent pumping extends and the turbulent diffusivity in the lower half of the convection zone. We find that the pumping needs to extend to depths of about 0.80 R_⊙ and that the bulk turbulent diffusivity needs to be around 10 km² s⁻¹ or less. We find that the emergences are restricted to low latitudes without the need to impose such a preference.

Conclusions. The flux-transport Babcock-Leighton model, incorporating the helioseismically inferred meridional flow and toroidal field loss term, is compatible with the properties of the observed butterfly diagram and with the observed toroidal loss rate. Reasonably tight constraints are placed on the remaining free parameters. The pumping needs to be just below the depth corresponding to the location where the meridional flow changes direction, and where numerical simulations suggest the convection zone becomes marginally subadiabatic. However, our linear model does not reproduce the observed ‘rush to the poles’ of the diffuse surface radial field resulting from the decay of sunspots; reproducing this might require the imposition of a preference for flux to emerge near the equator.