  Recent observations have demonstrated that very-low mass stars and brown
dwarfs are capable of sustaining strong magnetic fields despite their cool and
neutral atmospheres. These kG field strengths are inferred based on strong
highly circularly polarized GHz radio emission, a consequence of the electron
cyclotron maser instability. Crucially, these observations imply the existence
of energetic non-thermal electron populations, associated with strong current
systems, as are found in the auroral regions of the magnetized planets of the
Solar System. Intense auroral electron precipitation will lead to electron
collisions with the H$_{2}$ gas that should ultimately generate the ion
H$_{3}^{+}$. With this motivation, we targeted a sample of ultracool dwarfs,
known to exhibit signatures associated with aurorae, in search of the K-band
emission features of H$_{3}^{+}$ using the Keck telescopes on Mauna Kea. From
our sample of 9 objects, we found no clear indication of H$_{3}^{+}$ emission
features in our low-medium resolution spectra (R$\sim$3600). We also modeled
the impact of an auroral electron beam on a brown dwarf atmosphere, determining
the depth at which energetic beams deposit their energy and drive particle
impact ionization. We find that the H$_{3}^{+}$ non-detections can be explained
by electron beams of typical energies $\gtrsim$2-10~keV, which penetrate deeply
enough that any H$_{3}^{+}$ produced is chemically destroyed before radiating
energy through its infrared transitions. Strong electron beams could further
explain the lack of UV detections, and suggest that most or nearly all of the
precipitating auroral energy must ultimately emerge as thermal emissions deep
in brown dwarf atmospheres.
