A STUDY OF METAL ABUNDANCE PATTERNS IN COOL WHITE-DWARFS .1. TIME-DEPENDENT CALCULATIONS OF GRAVITATIONAL SETTLING

As a first step toward understanding the presence of traces of metals in a minority of cool white dwarfs, we investigate in detail the settling of Mg, Si, Ca, and Fe in models of these stars. We use powerful numerical tools based on finite-element techniques to study the evolution of the abundance distribution of a given metal over 25 orders of magnitude. A state of diffusive equilibrium is nearly reached by the time a star has cooled to T(eff) = 5000 K. However, the surface abundances have long reached vanishingly low levels by then. We show that the behavior of the surface abundance of a given metal follows very closely an exponential law e(-t/theta), where the time constant theta is equal to the local diffusion time scale. at least in the initial phases which are of interest from an observational point of view. The behavior of the abundance at a given radiative shell below the superficial convection zone is, however, quite different from an exponential law. We confirm that primordial heavy elements can only leave negligible traces in the surface layers of a white dwarf, and that there is a need for an extrinsic source of metals in cool white dwarfs. We also find that settling of heavy elements freezes over the inner 99%-99.9% of the mass of a white dwarf, which may have significant impact on the computations of cooling time scales.