Alien 'Star Engine' Detectable in Exoplanet Data?

In 1948, astronomer Fred Zwicky, the esteemed co-discoverer of dark matter, speculated that “fusion jets” could be used by a future civilization to navigate our sun and solar system planets through the galaxy. He suggested that pellets of fuel could be fired into the sun to produce explosions that would push the sun along like firecrackers exploding in a tin can. But where to go?

Zwicky thought that the entire solar system could reach Alpha Centauri in a few thousand years.
Forty years later, physicist Leonid Shkadov proposed that far advanced extraterrestrial civilizations might harness the energy output of their sun for interstellar migration. They would use a “stellar engine” — no need for fusion motors here. Simply construct an immense spherical mirror that reflects some of the star’s radiation back onto its surface.

This radiation pressure on the star creates an imbalance where a net force pushes the star in the opposite direction. This is simply Newtonian physics, though Sir Isaac would have never imagined such an application.
To work, such a stellar engine would have to be a megastructure, millions of miles across (shown above). The bad news is that a planet might have to be dismantled to make such a monstrosity. The good news is that such megastructures — if they exist — should be detectable with today’s telescope technology.

Duncan Forgan, of the University of Edinburgh, proposes that such a mega-mirror might obstruct part of the disk of a star during our observations that look for planets passing across the face of a star, an event call a transit. More Here