  A number of ultra-cool dwarfs emit circularly polarised radio waves generated
by the electron cyclotron maser instability. In the solar system such radio is
emitted from regions of strong auroral magnetic field-aligned currents. We thus
apply ideas developed for Jupiter's magnetosphere, being a well-studied
rotationally-dominated analogue in our solar system, to the case of
fast-rotating UCDs. We explain the properties of the radio emission from UCDs
by showing that it would arise from the electric currents resulting from an
angular velocity shear in the fast-rotating magnetic field and plasma, i.e. by
an extremely powerful analogue of the process which causes Jupiter's auroras.
Such a velocity gradient indicates that these bodies interact significantly
with their space environment, resulting in intense auroral emissions. These
results strongly suggest that auroras occur on bodies outside our solar system.
