  The search for signs of extraterrestrial technology, or technosignatures,
includes the search for objects which collect starlight for some technological
use, such as those composing a Dyson sphere. These searches typically account
for a star's light and some blackbody temperature for the surrounding
structure. However, such a structure inevitably returns some light back to the
surface of its star, either from direct reflection or thermal re-emission. In
this work, we explore how this feedback may affect the structure and evolution
of stars, and when such feedback may affect observations. We find that in
general this returned light can cause stars to expand and cool. Our MESA models
show that this energy is only transported toward a star's core effectively by
convection, so low mass stars are strongly affected, while higher mass stars
with radiative exteriors are not. Ultimately, the effect only has significant
observational consequences for spheres with very high temperatures (much higher
than the often assumed ~300 K) and/or high specular reflectivity. Lastly, we
produce color-magnitude diagrams of combined star-Dyson sphere systems for a
wide array of possible configurations.
