Origin and Distributions of White Dwarfs

Abstract

Today there is no doubt that white dwarfs represent the most common final stage of stellar evolution. Considerable progress has been made during the last decade in our understanding of their origin and distributions. This is reflected by the fact that it is now possible to predict -from basic theory of stellar evolution and stellar atmospheres -the existence of cooling degenerate stars with nearly the observed properties, i.e. a sequence of white dwarfs which fill in their majority a narrow strip in both two-color and colormagnitude diagrams. With other words: the empirically determined surface gravity and radius distributions -which correspond via the mass-radius relation to mass distributions -can now be basically understood within the currently adopted general scheme of stellar evolution with mass loss.For the first time this opens the possibility of a synthetic approach which I shall adopt in the following. Crude as it may be it nevertheless sets the stage on which we then may post our more detailed questions and judge in which way we may try to answer them.We therefore assume that stars are born on the main sequence in numbers determined by a time-independent initial mass function (IMF) in a global rate which depends in a defined way on the time in the past, within a specified age of the Galaxy. We let these stars evolve according to currently accepted theory for single stars, through central hydrogen-, shell-, central helium-and double-shell-burning phases until the nuclear evolution is terminated either by fuel exhaustion in a growing degenerate C/O-core with envelope mass loss or by gravitational collapse and supernova explosion. If we assume the course of this evolution to depend on the initial mass only we arrive at a defined relation between initial and final masses, J~\^.(Mi). The main sequence birth rate then determines -delayed by the total time of nuclear evolution, and projected by the Mf. -%M; relation -the white dwarf (and supernova) birth rate at any chosen epoque of galactic evolution, as well as their mass distribution. This qualitative picture, so far, has been known and accepted for some time, and was first incorporated into a quantitative study of galactic evolution by Ostriker and coworkers (Thuan et al., 1975). During the last years, however, it has become evident that mass loss plays a much more important role than anticipated, both steady and unsteady, in stellar winds and/or planetary nebulae (see Reimers,1975, -206-https://www.cambridge.org/core/terms. https://doi