Two Earth-Sized Bodies With Oxygen-Rich Atmospheres
tugfoigel writes "Astrophysicists at the University of Warwick and Kiel University have discovered two bodies the size of earth with oxygen-rich atmospheres — however, there is a disappointing snag for anyone looking for a potential home for alien life, or even a future home for ourselves. These are not planets, but are actually two unusual white dwarf stars." The objects, 220 and 400 light-years distant, are believed to be remnants of stars between 7 and 10 solar masses. Such stars, the largest that evolve to white dwarves, have been sought for years. If the stars were a little more massive they would collapse to neutron stars, or so the theory goes. Here is the paper on the arXiv.
Not quite so small, as the Schwarzschild radius of the sun is about 3 km.
Actually, it's believed that type 1A supernovae do not reach gravitational collapse, they explode in a runaway carbon fusion before reaching the Chandrasekar limit. It's type II supernovae that explode the way you mention.