Theory of Passive Magnetic Field Transport

Abstract

In recent years, our knowledge of photospheric magnetic fields went through a thorough transformation—nearly unnoticed by dynamo theorists. It is now practically certain that the overwhelming majority of the unsigned magnetic flux crossing the solar surface is in turbulent form (intranetwork and hidden fields). Furthermore, there are now observational indications (supported by theoretical arguments discussed in this paper) that the net polarity imbalance of the turbulent field may give a significant or even dominant contribution to the weak large-scale background magnetic fields outside unipolar network areas. This turbulent magnetic field consists of flux tubes with magnetic fluxes below 10¹⁰ Wb (10¹⁸ Mx). The motion of these thin tubes is dominated by the drag of the surrounding flows, so the transport of this component of the solar magnetic field must fully be determined by the kinematics of the turbulence (i.e. it is “passive”), and it can be described by a one-fluid model like mean-field theory (MFT). The recent advance in the direct and indirect observation of turbulent fields is therefore of great importance for MFT as these are the first-ever observations on the Sun of a field to which MFT may be applied. However, in order to utilize the observations of turbulent fields and their large-scale patterns as a possible diagnostic of MFT dynamo models, the transport mechanisms linking the surface field to the dynamo layer must be thoroughly understood.

This paper reviews the theory of passive magnetic field transport using mostly first (and occasionally higher) order smoothing formalism; the most important transport effects are however also independently derived using Lagrangian analysis for a simple two-component flow model. Solar applications of the theory are also presented. Among some other novel findings/propositions it is shown that the observed unsigned magnetic flux density in the photosphere requires a small-scale dynamo effect operating in the convective zone and it is proposed that the net polarity imbalance in turbulent (and, in particular, hidden) fields may give a major contribution to the weak large-scale background magnetic fields on the Sun.