Bounds on the magnetic fields in the radiative zone of the Sun

We discuss bounds on the strength of the magnetic fields that could be buried in the radiative zone of the Sun. The field profiles and decay times are computed for all axisymmetric toroidal ohmic decay eigenmodes with lifetimes exceeding the age of the Sun. The measurements of the solar oblateness yield a bound of ≲7 MG on the strength of the field. A comparable bound is expected to come from the analysis of the splitting of the solar oscillation frequencies. The theoretical analysis of the double diffusive instability also yields a similar bound. The oblateness measurements at their present level of sensitivity are therefore not expected to measure a toroidal field contribution.