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The molecular ion H$_3^+$ is a potentially powerful tracer of the ionospheresand thermal structures of Jovian planets, but has never been detected in aplanetary mass object outside of the solar system. Models predict that H$_3^+$emission driven by EUV flux and solar wind on hot Jupiters, or by powerfulaurorae on brown dwarfs, will be between $10^2$ and $10^5\times$ more intensethan that of Jupiter. If optimal conditions for the production of emission doexist, the emission may be detectable by current ground-based instruments or inthe near future. We present the first search for H$_3^+$ line emission in browndwarfs with Keck/NIRSPEC $L^\prime$ high-resolution spectroscopy. Additionally,we survey stars hosting giant planets at semi-major axes near $0.1-0.2$ au,which models suggest may be the best planetary targets. No candidate H$_3^+$emission is found. The limits we place on the emission of H$_3^+$ from browndwarfs indicates that auroral generation of H$_3^+$ in these environmentslikely does not linearly scale from the processes found on Jupiter, plausiblydue to deeper atmospheric penetration by precipitating auroral electrons.Detection of H$_3^+$ emission in brown dwarfs may be possible with the JamesWebb Space Telescope (JWST), or future thirty-meter class telescopes.

Limits on the Auroral Generation of H$_3^+$ in Brown Dwarf and Extrasolar Giant Planet Atmospheres with Keck/NIRSPEC