The decay of the large-scale solar magnetic field

Abstract

In the absence of new bipolar sources of flux, the large-scale magnetic field at the solar photosphere decays due to differential rotation, meridional flow, and supergranular diffusion. The rotational shear quickly winds up the nonaxisymmetric components of the field, increasing their latitudinal gradients and thus the rates of diffusive mixing of their flux. This process is particularly effective at mid latitudes, where the rotational shear is largest, so that eventually low- and high-latitude remnants of the initial, nonaxisymmetric field pattern survive. In this paper I solve analytically the transport equation describing the evolution of the large-scale photospheric field, to study its time-asymptotic behavior. The solutions are rigidly rotating, uniformly decaying distributions of flux, wound up by differential rotation and localized near either the equator or the poles. A balance between azimuthal transport of flux by the rotational shear and meridional transport by the diffusion gives rise to the rigidly rotating field patterns. The time-scale on which this balance is achieved, and also on which the nonaxisymmetric flux decays away, is the geometric mean of the short time-scale for shearing by differential rotation and the long time-scale for dispersal by supergranular diffusion. A poleward meridional flow alters this balance on its own, intermediate time-scale, accelerating the decay of the nonaxisymmetric flux at low latitudes. Such a flow also hastens the relaxation of the axisymmetric field to a modified dipolar configuration.