The turbulent diffusion of toroidal magnetic flux as inferred from properties of the sunspot butterfly diagram

Abstract

Context. In order to match observed properties of the solar cycle, flux-transport dynamo models require the toroidal magnetic flux to be stored in a region of low magnetic diffusivity, typically located at or below the bottom of the convection zone. Aims. We infer the turbulent magnetic diffusivity affecting the toroidal field on the basis of empirical data. Methods. We considered the time evolution of mean latitude and width of the activity belts of solar cycles 12-23 and their dependence on cycle strength. We interpreted the decline phase of the cycles as a diffusion process. Results. The activity level of a given cycle begins to decline when the centers of its equatorward propagating activity belts come within their (full) width (at half maximum) from the equator. This happens earlier for stronger cycles because their activity belts are wider. From that moment on, the activity and the belt width decrease in the same manner for all cycles, independent of their maximum activity level. In terms of diffusive cancellation of opposite-polarity toroidal flux across the equator, we infer the turbulent diffusivity experienced by the toroidal field, wherever it is located, to be in the range 150-450 km 2 s −1 . Strong diffusive latitudinal spreading of the toroidal flux underneath the activity belts can be inhibited by an inflow toward the toroidal field bands in the convection zone with a magnitude of several meters per second. Conclusions. The inferred value of the turbulent magnetic diffusivity affecting the toroidal field agrees, to order of magnitude, with estimates based on mixing-length models for the solar convection zone. This is at variance with the requirement of flux-transport dynamo models. The inflows required to keep the toroidal field bands together before they approach the equator are similar to the inflows toward the activity belts observed with local helioseismology.

Babcock–leighton Solar Dynamo: The Role of Downward Pumping and the Equatorward Propagation of Activity

“…We could obtain dynamo solutions with the correct period and equatorial propagation at a diffusivity of 10 12 cm 2 s −1 using a simplified version of the differential rotation, which gives an indication of our sensitivity to the differential rotation, pumping and choice of diffusivity profile. While this is still an order of magnitude less than expected from mixing length arguments, it is close to the values suggested from the study of Cameron & Schüssler (2016). All previous flux transport dynamo models were constructed with a diffusivity much weaker than 10 12 cm 2 s −1 (Muñoz-Jaramillo et al 2011;Miesch & Teweldebirhan 2016).…”

“…Such field strengths are not plausible. Another possibility for weaker diffusion is that changes in the mean flows (e.g., the inflow observed around active regions) could play a role (Cameron & Schüssler 2016). In any case, exploring the range of values of η for which the Babcock-Leighton dynamos have equatorial propagation and the 11-year period is a useful exercise.…”

Solar Cycle Variability Induced by Tilt Angle Scatter in a Babcock–Leighton Solar Dynamo Model

“…We do not have a reliable estimate of η t in the deep CZ. The mixing length theory and other theoretical studies suggest that the value of η t in the mid convection zone is of the order of 10 12 cm 2 s −1 (Parker 1979;Miesch et al 2012;Cameron & Schüssler 2016;Simard et al 2016). Near the surface, at least, it is fairly constrained by observations as well as by the surface flux transport model (e.g., Komm et al 1995;Lemerle et al 2015) and it is about a few times 10 12 cm 2 s −1 .…”

Loss of toroidal magnetic flux by emergence of bipolar magnetic regions

“…Warnecke et al 2018), or inferred from observations (e.g. Cameron & Schüssler 2016). Near-surface values of η t are typically around 10 12 cm 2 s −1 .…”

“…1. 'Unwinding' by the action of differential rotation on the new (reversed) poloidal field, 2. cancellation of opposite-polarity magnetic flux at the equatorial plane due to latitudinal transport of toroidal flux by meridional flow, turbulent diffusion/pumping, or dynamo wave propagation (e.g., Cameron & Schüssler 2016), 3. O-type neutral point dissipation along the dipole axis, 4. loss through the surface due to flux emergence.…”