Abstract:
With reasonable assumptions and approximations, we solve analytically the full set of Chandrasekhar's (1956) MHD equations in the convective envelope, for steady part of rotation and toroidal component of the magnetic field which may vary on diffusion time scales. Depending upon the two assumptions made about the boundary condition at the lower boundary, viz., base of the convection zone, we have the following two solutions. In the first solution, we assumed that the Sun may be rotating uniformly at base of the convection zone. Except in the magnitudes of rotational velocities near the polar regions, the first solution yields similar rotational isocontours as that of helioseismology. Near the poles, the resulting solution yields faster rotation rates compared with that of the rotation rates inferred by helioseismology. Moreover, the chi-square fit of the resulting rotational results with the helio-seismologically inferred rotational results is also not so good. These results lead to the second solution in which we made the assumption that the Sun may be rotating differentially at base of the convection zone. Compared with the helioseismic inferred results, the second solution yields almost similar rotational isocontours everywhere in the convective envelope. The chi-square fit improved significantly in this solution. This result suggests that, at base of the convection zone, differential rotation is more likely than uniform rotation. Correspondingly, it was necessary to solve the toroidal component of the magnetic field. Except near base of the convection zone, both the solutions yield similar field structure for the steady component of the toroidal magnetic field. This consists of a two-zone like field structure of intensity ~ 1G near the surface and a four-zone like field structure of intensity ~ 104 G near base of the convection zone. However, near base of the convective envelope, compared to the field structure obtained from the first solution, the resulting field structure from the second solution is closer to the sites of sunspot formation. Implications of these results in the context of lithium depletion and solar activity phenomena are briefly discussed.
