Study of bi-orthogonal modes in magnetic butterflies

We present a bi-orthogonal decomposition of the temporal and latitudinal distribution of solar magnetic fields from synoptic magnetograms. Results are compared with a similar decomposition of the distribution of sunspots since 1874. We show that the butterfly diagrams can be interpreted as the result of approximately constant amplitudes and phases of two oscillations with periods close to 22 years. A clear periodicity of 7 years can also be identified in the most energetic modes of both spatio-temporal series. These results can be used to obtain relevant information concerning the physics of the solar dynamo.