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.
Highlights
The most visible manifestations of the solar dynamo are sunspots
Sunspots appear as part of the flux emergence process, where a magnetic field rises through the photosphere from below in bipolar active regions
In this paper we investigated the relationship between the surface toroidal field as a function of the subsurface toroidal field as predicted by the surface radial field measurements applied to the 1D mean-field evolution equation for the subsurface toroidal flux density with a poloidal field derived from the surface radial magnetic field observations
Summary
The most visible manifestations of the solar dynamo are sunspots. These appear at latitudes of about ±30◦ at the beginning of a solar activity cycle, and progressively closer to the equator as the solar cycle progresses to latitudes of about ±8◦ (Spoerer 1889) 11 years later (Schwabe 1849). The solar dynamo is thought to be an alpha-omega dynamo This means the subsurface toroidal magnetic field is mainly generated by differential rotation acting on the poloidal magnetic field. The ability of this 1D equation to describe the evolution of the toroidal field can be tested in conjunction with a few additional assumptions These assumptions are that the poloidal field corresponds to the radial field at the surface, and that the rate at which systematically east-west oriented flux emerges is related to the amount of subsurface toroidal field. These latter assumptions are part of the Babcock–Leighton model (some variants of which fall within the mean-field formalism)
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