The helium absorption line at 10830 {AA}, originating from the metastable triplet state 2$^3$S, has been suggested as an excellent probe for the extended atmospheres of hot Jupiters and their hydrodynamic escape processes, and has recently been detected in the transmission spectra of a handful of planets. The isotropic re-emission will lead to helium airglow that may be observable at other orbital phases. The goal of this paper is to investigate the detectability of He I emission at 10830 {AA} in the atmospheres of exoplanets using high-resolution spectroscopy, providing insights into the properties of the upper atmospheres of close-in gas giants. We estimated the expected strength of He I emission in hot Jupiters based on their transmission signal. We searched for the He I 10830 {AA} emission feature in tau Boo b in three nights of high-resolution spectra taken by CARMENES at the 3.5m Calar Alto telescope. The spectra from each night were corrected for telluric absorption, sky emission lines, and stellar features, and were shifted to the planetary rest frame to search for the emission. The He I emission is not detected in tau Boo b, reaching a 5 sigma contrast limit of 4$times$10$^{-4}$ for emission line widths above 20 km/s. This is roughly a factor of 8 above the expected level of emission (assuming a typical He I transit absorption of 1% for hot Jupiters). This suggests that targeting the He I emission with well-designed observations using upcoming instruments such as VLT/CRIRES+ and E-ELT/HIRES is possible.
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