Loss of toroidal magnetic flux by emergence of bipolar magnetic regions

R H Cameron,M Schüssler

doi:10.1051/0004-6361/201937281

R H Cameron, M Schüssler

Open Access

https://doi.org/10.1051/0004-6361/201937281

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Abstract

The polarity of the toroidal magnetic field in the solar convection zone periodically reverses in the course of the 11/22-year solar cycle. Among the various processes that contribute to the removal of “old-polarity” toroidal magnetic flux is the emergence of flux loops forming bipolar regions at the solar surface. We quantify the loss of subsurface net toroidal flux by this process. To this end, we determine the contribution of an individual emerging bipolar loop and show that it is unaffected by surface flux transport after emergence. Together with the linearity of the diffusion process this means that the total flux loss can be obtained by adding the contributions of all emerging bipolar magnetic regions. The resulting total loss rate of net toroidal flux amounts to 1.3 × 1015 Mx s−1 during activity maxima and 6.1 × 1014 Mx s−1 during activity minima, to which ephemeral regions contribute about 90 and 97%, respectively. This rate is consistent with the observationally inferred loss rate of toroidal flux into interplanetary space and corresponds to a decay time of the subsurface toroidal flux of about 12 years, also consistent with a simple estimate based on turbulent diffusivity. Consequently, toroidal flux loss by flux emergence is a relevant contribution to the budget of net toroidal flux in the solar convection zone. The consistency between the toroidal flux loss rate due to flux emergence and what is expected from turbulent diffusion, and the similarity between the corresponding decay time and the length of the solar cycle are important constraints for understanding the solar cycle and the Sun’s internal dynamics.

Highlights

The solar dynamo consists of poloidal magnetic field being wound up to generate toroidal magnetic field, while a process involving the Coriolis force creates poloidal field from the toroidal field
Various processes can in principle affect the subsequent evolution of the emerged flux contained in the corresponding bipolar magnetic region (BMR): (1) transport by horizontal convective flows, which can be described as turbulent diffusion; (2) latitudinal differential rotation acting on tilted BMRs; (3) meridional flow; and (4) longitudinal drift of the two polarities in opposite directions caused by magnetic tension in the subsurface part of the loop
Our results show that the loss of net toroidal flux from the solar interior due to flux emergence can be faithfully estimated by adding the time-independent contributions of the individual bipolar regions to the reduction of the longitudinally averaged azimuthal field

Summary

Introduction

The solar dynamo consists of poloidal magnetic field being wound up to generate toroidal magnetic field, while a process involving the Coriolis force creates poloidal field from the toroidal field (see reviews by, e.g. Ossendrijver 2003; Charbonneau 2010, 2014; Cameron et al 2017; Brun & Browning 2017). The first two possibilities are discussed in Wang & Sheeley (1991), as is the fourth possibility which they discount for the same reasons as put forward by Parker (1984) and by Vainshtein & Rosner (1991) These latter authors pointed out that (nearly) perfect flux freezing implies a necessity to detach the magnetic field lines from their mass load in order to be able to escape from the solar interior. Flux emergence in the form of loops could provide a path to such escape through a wellorganised sequence of reconnection events between adjacent (“sea-serpent”) loops Such a situation is considered to be rather artificial and is not supported by observations. We consider the net toroidal flux integrated over a hemispheric meridional section, Bφ(r, θ) dS , where Bφ is the azimuthally averaged magnetic field (Cameron & Schüssler 2015).

Evolution of the net toroidal flux

Findings

Conclusions