The relationship between flux emergence and subsurface toroidal magnetic flux

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
e-mail: cameron@mps.mpg.de
² School of Space and Environment, Beihang University, Beijing 100083, PR China

Received: 13 December 2018
Accepted: 8 September 2019

Abstract

Aims. The 1D mean-field equation describing the evolution of the subsurface toroidal field can be used with the observed surface radial field to model the subsurface toroidal flux density. Our aim is to test this model and determine the relationship between the observationally inferred surface toroidal field (as a proxy for flux emergence), and the modelled subsurface toroidal flux density.

Methods. We used a combination of sunspot area observations and the surface toroidal field inferred from Wilcox Solar Observatory (WSO) line-of-sight magnetic field observations. We then compared them with the results of a 1D mean-field evolution equation for the subsurface toroidal field, driven by the observed radial field from the National Solar Observatory/Kitt Peak and SOLIS observations.

Results. We derive calibration curves relating the subsurface toroidal flux density to the observed surface toroidal field strengths and sunspot areas. The calibration curves are for two regimes, one corresponding to ephemeral region emergence outside of the butterfly wings, the other to active region emergence in the butterfly wings. We discuss this in terms of the size and vertical velocity associated with the two types of flux emergence.