Ibrahim Semiz & Salim Ogur, a pair of researchers in Turkey, have posed the possibility of extraterrestrial civilizations building Dyson Spheres around white dwarfs. It’s an astroengineering option for the long-lived civilization that wants a fixer-upper or is looking to renovate their own system after the sun has gone Red Giant.
Consider a white dwarf that has chilled to 1/2500th of the Sun’s luminosity. It’s habitable zone is at 0.02 AU, but to sustain a clement environment, the Shell has to be a bit further out at 0.04 AU, at the desirable thermal equilibrium temperature of ~280 K. More or less. That’s a radius of 6 million kilometres and a surface gravity of 3.75 m/s2 for a 1 solar mass white-dwarf. The habitable surface is on the outside. The habitat’s total area would be ~887,000 Earths, so it’s a substantial piece of real estate. To sustain a breathable atmosphere at 1 bar pressure a gas mass of 1.2E+25 kg is required – the mass of Neptune, though in the right mix of gases. While oxygen and carbon are fairly easy to source, the nitrogen might be more difficult, thus a heliox mixture might be required. Some nitrogen is still needed to make protein, but most of the atmosphere would be helium for fire suppression and reduction of oxygen toxicity risk.
Due to the intense gravity of a 1 solar mass white-dwarf star, mass falling onto would release ~27 TJ/kg from gravitational energy alone. By trickling mass on the star, very carefully, its luminosity could be sustained at 0.0004 solar for aeons before it ran into the Chandrasekhar Limit at 1.44 solar masses. Exactly how close one could get to that Limit, without triggering a C/O fusion conflagration and a Type Ia Supernova, is an important bit of astrophysics to learn before building the Sphere.
Such an object would “glow” in the infrared at ~280 K, 9 times the physical size of the Sun, and have a mostly helium spectrum. It’d look like a very odd infrared protostar from afar, compact and opaque to other frequencies.