This so-called Dyson sphere is legendary and there have even been searches for the signature of such artifacts in astronomical infrared databases. The problem is that a star enshrouded in dust would look pretty much like a Dyson sphere.
The image above from NASA's Wide-field Infrared Survey Explorer is an example. The red object at upper left is an aging star shrouded in dust. Nevertheless, in a survey of 250,000 infrared sky sources cataloged in the 1970s, 17 "quasi-plausible" Dyson sphere signatures came up, according to Richard Carrigan of Fermilab.
It's imaginable that a super-civilization would begin a wave of colonization that spread out to neighboring solar type stars from its home base. Each offshoot would "astro-form" the colonized planetary system by constructing a Dyson sphere around the host star.
Carrigan envisions seeing "Dyson bubbles" in nearby galaxies. These would be clusters of Dyson spheres that enclosed a grouping of stars colonized by a Type II Kardashev civilization. The logic is that after you've built a backyard fence you can start to conceptualize building the Great Wall of China and still hope to gain perspective on the process, Carrigan writes.
These would be detected as anomalous dark voids in a galaxy's disk. When these voids were observed in infrared light they would glow brightly with the heat radiation from the surfaces of Dyson spheres. This would show that they are not that simply voids where solar-type stars are conspicuously missing.
NASA's Hubble Space Telescope is conducting a multi-year survey across a swath of the neighboring Andromeda galaxy (M31). The images are filled with so many resolved stars that they resemble at grains of sand on a beach. This could make an excellent citizen science project, to scour the Andromeda fields for anomalous-looking regions.
The magnificent face-on Whirlpool galaxy, M51, is also an ideal place to go looking for Dyson bubbles. Hubble has photographed the entire galaxy down to a resolution of roughly 15 light-years across. Present Hubble and Spitzer Space Telescope infrared photos of the Whirlpool reveal the typical intricate cobweb tracing in dusty filaments.
However, a rough qualitative estimate by Carrigan suggests that there are no unexplained bubbles or voids in M51. This analysis is complicated by the fact that the infrared light skeletal dust pattern of a spiral galaxy pattern itself is shaped by voids.