  Context: Observations of auroral emissions are powerful means to remotely
sense the space plasma environment around planetary bodies and ultracool
dwarfs. Therefore successful searches and characterization of aurorae outside
the Solar System will open new avenues in the area of extrasolar space physics.
Aims: We aim to demonstrate that brown dwarfs are ideal objects to search for
UV aurora outside the Solar System. We specifically search for UV aurora on the
late-type T6.5 brown dwarf 2MASS J12373919+6526148 (in the following 2MASS
J1237+6526). Methods: Introducing a parameter referred to as auroral power
potential, we derive scaling models for auroral powers for rotationally driven
aurora applicable to a broad range of wavelengths. We also analyze Hubble Space
Telescope observations obtained with the STIS camera at near-UV, far-UV, and
Ly-$\alpha$ wavelengths of 2MASS J1237+6526. Results: We show that brown
dwarfs, due to their typically strong surface magnetic fields and fast
rotation, can produce auroral UV powers on the order of 10$^{19}$ watt or more.
Considering their negligible thermal UV emission, their potentially powerful
auroral emissions make brown dwarfs ideal candidates for detecting extrasolar
aurorae. We find possible emission from 2MASS J1237+6526, but cannot
conclusively attribute it to the brown dwarf due to low signal-to-noise values
in combination with nonsystematic trends in the background fluxes. The
observations provide upper limits for the emission at various UV wavelength
bands. The upper limits for the emission correspond to a UV luminosity of
$\sim$1 $\times$ 10$^{19}$ watt, which lies in the range of the theoretically
expected values. Conclusions: The possible auroral emission from the dwarf
could be produced by a close-in companion and/or magnetospheric transport
processes.
