In a preprint science paper published on October 26, 2021, astronomers review the impact a Dyson sphere might have on its central star and conclude that modern astronomical instruments should be able to identify these changes. From the abstract:
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.
A plain-language description of the paper can be found here, which summarizes this work as follows:
This study shows that Dyson spheres can result in measurable changes to stellar properties. Megastructures have long been confined to science fiction, imagination and certain video games. However, if there are indeed Dyson spheres out there waiting to be found, we could soon be in a position to find them.