  A star enshrouded in a Dyson sphere with high covering fraction may manifest
itself as an optically subluminous object with a spectrophotometric distance
estimate significantly in excess of its parallax distance. Using this
criterion, the Gaia mission will in coming years allow for Dyson-sphere
searches that are complementary to searches based on waste-heat signatures at
infrared wavelengths. A limited search of this type is also possible at the
current time, by combining Gaia parallax distances with spectrophotometric
distances from ground-based surveys. Here, we discuss the merits and
shortcomings of this technique and carry out a limited search for Dyson-sphere
candidates in the sample of stars common to Gaia Data Release 1 and RAVE Data
Release 5. We find that a small fraction of stars indeed display distance
discrepancies of the type expected for nearly complete Dyson spheres. To shed
light on the properties of objects in this outlier population, we present
follow-up high-resolution spectroscopy for one of these stars, the late F-type
dwarf TYC 6111-1162-1. The spectrophotometric distance of this object is about
twice that derived from its Gaia parallax, and there is no detectable infrared
excess. While our analysis largely confirms the stellar parameters and the
spectrophotometric distance inferred by RAVE, a plausible explanation for the
discrepant distance estimates of this object is that the astrometric solution
has been compromised by an unseen binary companion, possibly a rather massive
white dwarf ($\approx 1\ M_\odot$). This scenario can be further tested through
upcoming Gaia data releases.
