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A friend of mine was telling me that if there is an alien structure out there, we could detect it by the energy it would be producing or sending out. Im aware of hubble’s mission (RIP) and how we could make calculations base on transit, but never heard of such a thing... is it true? Thanks in advance!

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Freeman Dyson originally suggested the structure that now bears his name (he prefers Stapledon sphere) in a 1960 paper in Science because it (1) may be a likely end-state of civilisations using their local resources, and (2) it would be detectable from infrared emissions.

If the foregoing argument is accepted, then the search for extraterrestrial intelligent beings should not be confined to the neighborhood of visible stars. The most likely habitat for such beings would be a dark object, having a size comparable with the Earth's orbit, and a surface temperature of 200 deg. to 300 deg. K. Such a dark object would be radiating as copiously as the star which is hidden inside it, but the radiation would be in the far infrared, around 10 microns wavelength.

A sphere of radius $R$ that receives the luminosity $L$ of the star will radiate like a blackbody with temperature $$T=\left[\frac{L}{4\pi R^2 \sigma}\right ]^{1/4}.$$ The "standard" assumptions are like in Dyson's paper that it is about 1 AU and at "room temperature". From an energy collecting efficiency perspective this is likely not optimal, and one might have to look for other temperature objects. They still would look like IR point sources, possibly with a bit of normal starlight mixed in if there are small gaps between the orbiting collector.

Looking for transiting artificial objects is a different issue; here the light curve would look odd but the spectrum is unchanged.

People have done searches for Dyson sphere-like sources, with so far no luck.