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

Abstract

The key elements of the Babcock-Leighton dynamos are the generation of poloidal field through decay and dispersal of tilted bipolar active regions and the generation of toroidal field through the observed differential rotation. These models are traditionally known as flux transport dynamo models as the equatorward propagations of the butterfly wings in these models are produced due to an equatorward flow at the bottom of the convection zone. Here we investigate the role of downward magnetic pumping near the surface using a kinematic Babcock-Leighton model. We find that the pumping causes the poloidal field to become predominately radial in the near-surface shear layer, which allows the negative radial shear to effectively act on the radial field to produce a toroidal field. We observe a clear equatorward migration of the toroidal field at low latitudes as a consequence of the dynamo wave even when there is no meridional flow in the deep convection zone. Both the dynamo wave and the flux transport type solutions are thus able to reproduce some of the observed features of the solar cycle, including the 11-year periodicity. The main difference between the two types of solutions is the strength of the Babcock-Leighton source required to produce the dynamo action. A second consequence of the magnetic pumping is that it suppresses the diffusion of fields through the surface, which helps to allow an 11-year cycle at (moderately) larger values of magnetic diffusivity than have previously been used.

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

“…The cycle period then becomes unrealistically short; see Run B2 in Table 1. Karak & Cameron (2016) have shown that a downward pumping near the surface reduces the diffusion of the flux across the surface and helps to achieve a dynamo at a higher value of η t than hitherto. However, even with a reasonable amount of surface pumping, we tend to get decaying solutions unless we increase the observed flux distribution by a small value; see Runs B3-B4.…”

“…As discussed in Karak & Cameron (2016), the pumping is efficient near the surface (mainly caused by the topological asymmetry of the convective flow), while the deeper convection is weaker and less stratified (Spruit 1997). The pumping helps to boost the efficiency of the dynamo by suppressing the diffusion of toroidal flux through the surface.…”

“…Comparing Runs B2, B6, and B10, we notice that the cycle period increases with the increase of surface pumping γ S . This is expected from the study of Karak & Cameron (2016) that the pumping makes the dynamo efficient and thus allows us to use a smaller value of Φ 0 . This makes the period longer by regulating the strength of the BL α effect.…”

“…For the meridional circulation, we use the profile given in many previous publications, particularly in Karak & Cameron (2016) (Equation 5) which closely resembles the surface observations. Hence, without repeating the mathematical equations of this flow we just make a few comments: near the surface it is poleward with a maximum speed of 20 m s −1 , near the base of the CZ it is equatorward with a speed of about 2 m s −1 , and it smoothly goes to zero at the lower boundary (0.69R); see dashed line in Figure 1 (a).…”

“…In most of the simulations, we include a downward magnetic pumping motivated by the study of Karak & Cameron (2016). Thus we write γ = γ r (r)r, where…”