Evolution of White Dwarfs: Starting from Planetary Nebulae

Abstract

The ultimate aim in the study of White Dwarf (WD) evolution is to understand properly the observed Luminosity Function (LF) of WDs, that is the number of WDs observed per unit magnitude interval. The complicated route to the interpretation of this scarne quantity (12 fiducial points in the recent update of Liebert et al. 1988) is schematically summarized in figure 1. Clearly, the main input to the LF are the evolutionary (cooling) times, but it is necessary to consider their non trivial dependence on galactic evolutionary inputs, namely the initial mass function of disk stars, their age distribution with time (ultimately: the disk age), and their evolutionary properties. Stellar evolution enters in the problem of cooling by two main routes: first, by determining the mass of the WD as a function of the inital stellar mass and chemistry, second by fixing the internal constitution of the WD remnant for each given mass, and the initial physical conditions at the start of WD evolution (mainly the temperature distribution, which is important for the first phases of evolution). Of course, there is no need of good evolutionary inputs to study “theoretical” WDs. In fact, historically, the first approach in the study of “cooling” (Mestel 1952, Schwarzschild 1958)) has been directly related to the stimulating physical properties of these objects, in which neutrino losses at the beginning (Vila 1966, Savedoff et al. 1969) and, in late stages, liquification and crystallization of the plasma (Brush,Sahlin and Teller 1966, Hansen 1973) long recognized to be dominated by coulomb interactions, (Kirzhnits 1960, Abrikosov 1960, Salpeter 1961), are the main features to be investigated (Mestel and Ruderman 1967, Van Horn 1968, Kovetz and Shaviv 1970).