actually no, white dwarfs aren't ideal when looking for alien life
Looking for dying civilizations huddling around a cooling ember of a star isn't just a depressing idea, it's shortsighted science that dismisses life's ability to invent and innovate.
Astrophysicist and podcaster Paul Sutter has a very grim view of the future for Earthlings. In his mind, we'll never travel beyond the confines of our solar system due to the impossible energies and timespans involved. Instead, after our star dies, we'll huddle for warmth around the white dwarf and try to eke out an existence until it cools into a giant, dark diamond. This, he says, is a likely fate for most intelligent life and therefore, one promising place to look for alien beings we would define as intelligent is by looking for Dyson spheres around white dwarfs. But while this view is trying to be sober, it seems to be conservative to a fault and ignores numerous existing plans for covering vast distances in space and surviving the process.
Sutter's main argument is that any spaceship meant to reach another star will be a) painfully slow, b) require tremendous energies to get to its destination, and c) demand a lot of stuff to support a civilization on board. All these things are true. However, we have answers to these challenges in the works. We're creating and improving solar sails to greatly speed up our craft and achieve relativistic speeds. We're working on nuclear fusion while largely taming nuclear fission and have the capacity to power the giant lasers and engines we'd need for such trips. And finally, and most importantly, we've long had designs for comfortable generation ships in which 10,000 or more people would be expected to survive long journeys.
We should also note that we have some 8.5 billion years until the sun becomes a white dwarf, and in the meantime, it will destroy our planet as it expands a billion years before that, some 6.5 billion years after it rendered it completely uninhabitable. Humanity, if it survives that long, will be homeless for longer than Earth could support any life whatsoever at that point, and it's bizarre to assume that in all those billions of years we'd just hop between doomed worlds in our solar system will all the stuff necessary to support ourselves and never think to take our chances elsewhere. If we're looking at billions of years of planet hopping, trips to potentially habitable worlds Proxima Centauri, or Wolf 106, or Gliese 667C seem like no brainers.
It's true we have hundreds of millions of years left on our world, but at some point, it's doomed to first burn to a cinder, then be pulled apart by a red giant sun. If our species survives, it would be by learning how to build massive space arks and ships capable of easily traversing between significant distances in space with technology to speed up the trip. We ourselves will very likely be heavily modified through genetic engineering and technology to thrive on those arcs and the craft they'll host. It's absurd to think that we could accomplish all that, then look at the nearest stars and say "nope, too far and too scary, let's huddle here until we're extinct," and it's equally bizarre to assume other species capable of the same feats will think the same way.
It would be one thing if Earth would be habitable during the red giant phase, then move in close enough to benefit from the white dwarf's light. We could assume the laziest possible reaction from the remaining humans, shrug, and think the worst of our descendants billions of years from now. But we know that's not what's going to happen. Either humanity goes extinct as all life on the planet does between 500 million and a billion years from now, or it becomes capable of living in space for millennia and has fusion reactors, solar sails, antimatter manufacturing capacity, and augmentations that make them formidable and adaptable explorers. And judging by the history of our species, it would be most unwise to bet against our ingenuity.
