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Project Hephaistos I. Upper limits on partial Dyson spheres in the Milky Way

Dyson spheres are hypothetical megastructures built by advanced extraterrestrial civilizations to harvest radiation energy from stars. Here, we combine optical data from Gaia DR2 with mid-infrared data from AllWISE to set the strongest upper limits to date on the prevalence of partial Dyson spheres within the Milky Way, based on their expected waste-heat signatures. Conservative upper limits are presented on the fraction of stars at G $\leq$ 21 that may potentially host non-reflective Dyson spheres that absorb 1 - 90$\%$ of the bolometric luminosity of their host stars and emit thermal waste-heat in the 100 - 1000 K range. Based on a sample of $\approx$ $2.7\mathrm{e}\,5$ stars within 100 pc, we find that a fraction less than $\approx$ $2\mathrm{e}\,-5$ could potentially host $\sim$300 K Dyson spheres at 90$\%$ completion. These limits become progressively weaker for less complete Dyson spheres due to increased confusion with naturally occurring sources of strong mid-infrared radiation, and also at larger distances, due to the detection limits of WISE. For the $\sim2.9\mathrm{e}\,8$ stars within 5 kpc in our Milky Way sample, the corresponding upper limit on the fraction of stars that could potentially be $\sim$300 K Dyson spheres at 90$\%$ completion is $\leq$ $8\mathrm{e}\,-4$.