Multifractal measure of the solar magnetic field

We analyze high-resolution, digital, photoelectric images of solar photospheric magnetic fields. The line-of-sight fields are found to scale in a self-similar way with resolution and thus can be expressed in the form of a signed multifractal measure. The scaling properties of the measure are used to extrapolate field integrals, such as moments of the magnetic field, below resolvable limits. The scaling of the field moments is characteristic of highly intermittent fields. We suggest that the quiet-Sun photospheric fields are generated by local dynamo action based on random convective motions at high magnetic Reynolds number. The properties of active region images are determined by the presence of fields generated by the global, mean field dynamo.