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

The molecular ion H$_3^+$ is a potentially powerful tracer of the ionospheres and thermal structures of Jovian planets, but has never been detected in a planetary 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 powerful aurorae on brown dwarfs, will be between $10^2$ and $10^5\times$ more intense than that of Jupiter. If optimal conditions for the production of emission do exist, the emission may be detectable by current ground-based instruments or in the near future. We present the first search for H$_3^+$ line emission in brown dwarfs 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 brown dwarfs indicates that auroral generation of H$_3^+$ in these environments likely does not linearly scale from the processes found on Jupiter, plausibly due to deeper atmospheric penetration by precipitating auroral electrons. Detection of H$_3^+$ emission in brown dwarfs may be possible with the James Webb Space Telescope (JWST), or future thirty-meter class telescopes.