Solar torsional oscillations as due to the magnetic quenchingof

The solar torsional oscillations are considered as the response of the Reynolds stress to the time-dependent dynamo-induced magnetic eld. This picture is opposite to the so far accepted idea that it is the large-scale Lorentz force which directly drives the temporal variations of the surface rotation proole. Here, the \magnetic quenching" of the components of the Reynolds stress { viscosity tensor and-eeect { is the basic reason for the cyclic rotation law. In order to produce the suppressing magnetic eld it was necessary to construct a turbulent dynamo. Its site is the overshoot region, with the-eeect existing only in an equatorial domain. The produced butterry diagram is shown in Fig. 5. Mainly the toroidal eld quenches the turbulent Reynolds stress deep in the convection zone. For a simpliied model we nd indeed that an observable ow pattern of 1{2 m/s appears with the correct frequency at the solar surface. The pattern can be interpreted as a wave originating at 30 o and vanishing at the equator. The phase relation with respect to the magnetic eld does, however, not meet the observations. A more complete model of the solar overshoot dynamo works with turbulence intensities of 20 m/s and turnover times from mixing length theory. The complete Reynolds tensor is applied. The magnetic diiusivity below the overshoot domain is put to 10 10 cm 2 /s. Then the surface value of thètorsional oscillation' increases to values up to 3 m/s and the phase relation between magnetic cycle and torsional oscillations is correct. The amplitude of the oscillations proves to depend strongly on the magnetic Prandtl number. The results indicate that the value of the turbulent viscosity should not be smaller than 10 12 cm 2 =s. It is shown in foregoing papers that the Reynolds stress theory of diierential rotation well complies with the angular velocity pattern derived from helioseismology (Kitchatinov & R udiger 1993; K uker et al. 1993). Neglecting the innuence of meridional ow the correct pole-equator diierence of the angular velocity at the surface is provided, the rather smooth behaviour of beneath the equator and the strong inwards increase of the angular velocity along the polar axis. The only free parameter is the MLT of mixing-length theory. Inclusion of the meridional ow and an internal magnetic eld also reproduces the \observed" behaviour of the angular velocity below the bottom of the convection zone (R udiger & Kitchatinov 1995). …