The Phase Diagram of High Density Binary Mixtures and the Luminosity Function of Single White Dwarfs

Abstract

For the last two decades, plasma physics developments have led to a better understanding of physical conditions in white dwarfs interiors. Following the pioneering work of Mestel (1952), the problem of white dwarf cooling has been a subject of continuous interest until the present time. In the early sixties, Kirzhnits (1960), Abrikosov (1960), and Salpeter (1961) recognised the importance of Coulomb interactions in the dense plasma which forms the white dwarf interior. A first-order transition from liquid to solid phase was predicted and the resultant release of latent heat was shown to somewhat affect the cooling rate (Mestel and Ruderman, 1967). Subsequently, improved theoretical luminosity functions (number of white dwarfs per pc9 and per magnitude interval as a function of luminosity) taking into account not only Coulomb interactions but also neutrino losses, and using detailed atmosphere models (Van Horn, 1968; Koester, 1972; Lamb and Van Horn, 1975; Shaviv and Kovets, 1976; Sweeney, 1976). Recently, Iben and Tutukov (1984) have discussed the evolution of a 0.6 M⊙ carbon-oxygen white dwarf from its nuclear burning stages to complete crystallization. Their luminosity function agrees reasonably well with observations in the range −4 ≤ log(L/L⊙) ≤ 4 but it predicts an excess of white dwarfs at low luminosities. Indeed, the luminosity function derived from observations grows monotonically until log(L/L⊙) ≃ −4.5 (Mv ≤ 16) and then makes an abrupt shortfall (Liebert, Dahn and Monet, 1988). The agreement between theory and observations is so good in the aforementioned range luminosity that we can wonder as to whether it is possible not only to test the theory of white dwarf cooling but also to obtain information on the galactic structure and evolution. One example of that is the use of the cutoff in the white distribution to determine the age of the galactic disk (Schmidt, 1959). Using this method, Winget et al. (1987) have found that the galactic disk age could be of the order of 9 Gyr old, in agreement with some predictions from nucleocosmochronology (Fowler et al. 1987).