Stringent Limits on H$_3^+$ Emission from the Hot Jupiters WASP-80b and WASP-69b

Observations of auroras on exoplanets would provide numerous insights into planet-star systems, including potential detections of the planetary magnetic fields, constraints on host-star wind properties, and information on the thermal structures of planets. However, there have not yet been any discoveries of auroras on exoplanets. In this paper, we focus on the search for infrared auroral emission from the molecular ion H$_3^+$, which is common in the atmospheres of solar system planets Jupiter, Saturn, and Uranus. Using Keck/NIRSPEC high-resolution spectroscopy, we search for H$_3^+$ emission from two hot Jupiters, WASP-80b and WASP-69b. We do not see any evidence of emission in the observed spectra when cross-correlating with an H$_3^+$ spectral model or when using an auto-correlation approach to search for any significant features. We therefore place upper limits on the total emission of $5.32 \times 10^{18}$ W for WASP-80b and $1.64 \times 10^{19}$ W for WASP-69b. These upper limits represent the most stringent limits to date and approach the regime of emission suspected from theoretical models.