Since there are several ways planets can survive the giant phase of the host star, we examine the habitability and detection of planets orbiting white dwarfs. As a white dwarf cools from 6000 K to 4000 K, a planet orbiting at 0.01 AU would remain in the Continuous Habitable Zone (CHZ) for ~8 Gyr. We show that photosynthetic processes can be sustained on such planets. The DNA-weighted UV radiation dose for an Earth-like planet in the CHZ is less than the maxima encountered on Earth, hence non-magnetic white dwarfs are compatible with the persistence of complex life. Polarisation due to a terrestrial planet in the CHZ of a cool white dwarf is 10^2 (10^4) times larger than it would be in the habitable zone of a typical M-dwarf (Sun-like star). Polarimetry is thus a viable way to detect close-in rocky planets around white dwarfs. Multi-band polarimetry would also allow reveal the presence of a planet atmosphere, providing a first characterisation. Planets in the CHZ of a 0.6 M_sun white dwarf will be distorted by Roche geometry, and a Kepler-11d analogue would overfill its Roche lobe. With current facilities a Super-Earth-sized atmosphereless planet is detectable with polarimetry around the brightest known cool white dwarf. Planned future facilities render smaller planets detectable, in particular by increasing the instrumental sensitivity in the blue.
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