Closing the solar dynamo loop: Poloidal field generated at the surface by plasma flows

¹ Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany
² Centre for Space Science and Technology, University of Newcastle, NSW, Australia
³ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁴ Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany

^⋆ Corresponding author: cameron@mps.mpg.de

Received: 21 January 2025
Accepted: 4 August 2025

Abstract

Context. The large-scale magnetic field of the Sun is produced by dynamo action due to convection and rotation. The toroidal magnetic field is maintained by the Sun’s differential rotation that winds up the azimuthally averaged radial and latitudinal (poloidal) magnetic field. The generation of the poloidal flux has long been considered to be due to an alpha effect acting on the toroidal magnetic field.

Aims. We investigated the observed flows associated with the longitudinal and latitudinal separation of the two magnetic polarities of an active region during and immediately after it has emerged. The observed separations are known to statistically obey Joy’s law, and this paper aims to identify the flows and transport mechanisms involved in producing Joy’s law.

Methods. We analyzed 182 isolated active region emergences observed using the Helioseismic and Magnetic Imager (HMI) from the Solar Dynamics Observatory (SDO) satellite that were previously reported in the literature. We investigated the different terms contributing to the separation in both longitude and latitude. We performed a similar analysis on the emergences in a dynamo simulation performed using the Anelastic Spherical Harmonics (ASH) code.

Results. While we do not exclude the possibility of an alpha effect operating in the convection zone, our results show that the poloidal field corresponding to Joy’s law, which reverses the polar fields and which is required to close the dynamo loop, is generated at the surface not from an alpha effect, but instead from the delta effect (also called the Rädler effect). The difference between the two is that the alpha effect generates a poloidal magnetic field from the presence of toroidal field, while the delta effect does so via the turbulent transport of toroidal field.