Cooling of low-mass carbon-oxygen dwarfs from the planetary nucleus stage through the crystallization stage

Abstract

The evolution of an electron-degenerate dwarf of 0.6 solar mass is traced, beginning with its early life as the bright central star of a young planetary nebula, and continuing through to the stage of crystallization after about 10 billion yr of cooling. The luminosity-time relationship is discussed in terms of balances between the dominant physical processes occurring at various phases. It is concluded that the remarkable similarity of a modern cooling curve to the one predicted by the classical model of Mestel (1952) is the consequence of a series of accidents. It is shown that once the interior has completely crystallized and the interior temperature has dropped considerably below the Debye temperature, the time scale for cooling is about one year times the optical depth of the surface layer.