Effect of toroidal fields on baroclinic instability in the solar tachocline

Using an MHD generalization of a two-layer hydrostatic but non-geostrophic model, we show that a toroidal field tends to stabilize baroclinically unstable modes in the solar tachocline. In the hydrodynamic (HD) case, baroclinic instability occurs at almost all latitudes in both the radiative and overshoot tachoclines. The toroidal field creates stable bands of latitude near where the vertical rotation gradient changes sign, as well as near the equator and pole, which widen with increasing field until, by ∼2.25 kG, all latitudes are stable. The stable bands center on where the local latitudinal entropy gradient is smallest. This result is independent of how subadiabatic the local stratification is, provided it is not so subadiabatic that baroclinic instability is absent in the HD case. Growth rates and most unstable longitudinal wavenumbers remain close to their HD values until the toroidal field gets within ∼20% of the value that totally suppresses the instability. The results are similar to those found in the 1960s from an MHD geostrophic model, but apply to a much wider range of latitudes and subadiabatic stratifications. Where tachocline toroidal fields are weak enough to allow baroclinic instability, magnetic patterns in longitude should be produced that could be transmitted through the convection zone to be seen in the photosphere. The results also show it should be possible to construct a baroclinic wave dynamo for the solar tachocline.