The idea of a habitable world orbiting a white dwarf--a stellar ember, what our Sol will become after it completes its burning of its hydrogen and other fuels--was raised a decade ago by a reader of this blog. Centauri Dreams has picked up on a paper exploring this theme.
Agol's paper, "Transit surveys for Earths in the habitable zones of white dwarfs", is available for reading here, abstract as follows.
An interesting paper from Eric Agol (University of Washington) takes a look at exoplanet possibilities around white dwarfs, and draws some surprising conclusions. We have, of course, searched for habitable planets primarily around stars that are much younger, assuming that a planetary system that had undergone the transformation of a red giant into a white dwarf would be unlikely to provide a suitable home for life. But Agol isn’t so sure.
Remember the process: Stars like the Sun eventually exhaust their nuclear fuel and at some point lose their outer envelope, leaving only the hot core behind. The core, now a hot white dwarf at temperatures exceeding 100,000 Kelvin, will begin a long process of cooling. A typical white dwarf might be half as massive as the Sun, but not much larger than the Earth in size, and as this NASA article points out, that means it’s extremely dense, perhaps 200,000 times as dense as the Earth itself. When it comes to matter, only neutron stars surpass that density.
Agol points out that the most common white dwarfs have surface temperatures in the range of 5000 K, which leads to his calculation that a planet would need to orbit no closer than about 0.01 AU to be at a temperature where liquid water could exist on the surface. What’s intriguing from the standpoint of finding such planets is that a potentially habitable world like this, Earth-sized or even smaller, would in principle be detectable because of the small size of the host star. The white dwarf, in fact, could be completely eclipsed by a habitable planet that orbits it.
But how does a planet survive the preceding red giant phase? One possibility is that new planets could form out of gases near the white dwarf, especially in binary systems where gravitational interactions could play a helpful role. We know of two neutron stars that have planets that conceivably formed from the disk created after a supernova event. Moreover, the pulsar 4U 0142+61 has been shown to have a circumstellar disk thought to have been formed from supernova debris. Planetary capture or migration can’t be ruled out, either.
Agol's paper, "Transit surveys for Earths in the habitable zones of white dwarfs", is available for reading here, abstract as follows.
To date the search for habitable Earth-like planets has primarily focused on nuclear burning stars. I propose that this search should be expanded to cool white dwarf stars that have expended their nuclear fuel. I define the continuously habitable zone of white dwarfs, and show that it extends from ~0.005 to 0.02 AU for white dwarfs with masses from 0.4-0.9 solar masses, temperatures less than 10,000 K, and habitable durations of at least 3 Gyr. As they are similar in size to Earth, white dwarfs may be completely eclipsed by terrestrial planets that orbit edge-on, which can easily be detected with ground-based telescopes. If planets can migrate inward or reform near white dwarfs, I show that a global robotic telescope network could carry out a transit survey of nearby white dwarfs placing interesting constraints on the presence of habitable Earths. If planets were detected, I show that the survey would favor detection of planets similar to Earth: similar size, temperature, rotation period, and host star temperatures similar to the Sun. The Large Synoptic Survey Telescope (LSST) could place even tighter constraints on the frequency of habitable Earths around white dwarfs. The confirmation and characterization of these planets might be carried out with large ground and space telescopes.