Cooling times, luminosity functions and progenitor masses of degenerate dwarfs.

Cooling models of degenerate dwarfs are obtained for a wide range of masses, luminosities, and envelope compositions. The method of determining cooling times is described, cooling characteristics of the models are discussed, and theoretically derived luminosity functions are compared with those derived from observations. Estimates of the progenitor masses of 22 degenerate dwarfs in clusters and three dwarfs of known mass in binary systems are obtained using recent scanner and four-color observations. The results show that: (1) weak turnover effects are present in the luminosity function, beginning at a bolometric magnitude of about 13.5 for at least 0.7 solar mass, due to Debye cooling and increased convective heat flow in the outer layers; (2) ages of cool dwarfs (maximum temperature of 10,000 K) are uncertain; (3) degenerate dwarfs have been born at a constant rate for at least the past 2 billion years; (4) the mean mass of degenerate dwarfs is likely to be close to 0.8 solar mass; and (5) mass loss of 1 to 2 solar masses or more is common in the pre-white-dwarf evolutionary phases.