"Steady" and "Fluctuating" Parts of the Sun's Internal Magnetic Field: Improved Model

Abstract

Using reasonable assumptions and approximations it is shown that the poloidal component part of the magnetic field in the Sun's radiative core (RC) and convection zone (CE) can be modeled as in an analytical solution of the equation for magnetic diffusion in an incompressible medium of constant diffusivity, which is subject to (1) continuity of the normal component across the RC-CE boundary and (2) merging with an asymptotically uniform field of finite strength at large distances, and whose field lines isorotate with the solar plasma. The last requirement enables determination of the values of the parameters in the first two eigenmodes of the diffusion equation. The resulting model does not have any singularity, separatrix, or closed loop, and yet it yields a much better fit with the helioseismologically determined isorotation contours than the fit given by the earlier model. (Gokhale & Hiremath 1993). The ratio of the range of the travel times of Alfven waves along the field lines in this model, to their mean value, is comparable to the relative range of the periods of the sunspot cycle. For example, it is 9.5-12.5 yr if Bo~0.02 G. The model enables us to estimate the "initial" (at zero-age main sequence) relative strengths of the two diffusion eigenmodes as 4:1. The characteristics diffusion timescales of these modes are estimated to be ~10.6 and ~2.7x109 yr, respectively. The model is consistent with (1) nonisorotation in the neighborhood of the RC-CE boundary which may lead to built-up of a strong (eg., ~1MG) toroidal field on timescales ~ 107-108 yr, and (2) the presence of a torsional MHD perturbation, with the dominant scale of latitudinal variation in CE and the scale of temporal variation, both comparable to the observed scales of the solar magnetic cycles