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surely one of the side-effects of a Dyson sphere, for instance, would be to render the star almost undetectable to our telescopes.

No. A Dyson sphere would just emit a lot less radiation in the region that we happen to perceive as "visible". This is a special case of "Stealth is (close to) impossible in Space"

http://www.projectrho.com/rocket/spacewardetect.php

http://scienceblogs.com/builtonfacts/2010/03/while_doing_som...

http://scienceblogs.com/builtonfacts/2010/03/stealth_in_spac...

http://tvtropes.org/pmwiki/pmwiki.php/Main/StealthInSpace



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