If they're using any technology that we know to be feasible (and they haven't already been here for a century or more), their approach would involve a star-hot

If they're using any technology that we know to be feasible (and they haven't already been here for a century or more), their approach would involve a star-hot plume of nuclear flame that burns in the sky for weeks or months at least. Now, as Baybal said, if they've uncovered fundamental physics that we don't know about, all bets are off. Or they could have showed up centuries ago and been hanging around ever since, for all we know, recorded by history as a supernova or something. But if they arrived recently and use known physics, we most likely would have seen them.