DB white dwarf evolution in the frame of the full spectrum turbulence theory

Abstract

We present an analysis of the evolution of carbon-oxygen DB white dwarfs (helium­ rich envelope) for a wide range of effective temperatures and luminosities. To this end, we employ a full stellar evolution code, in which we include a new equation of state for helium plasmas recently developed by Saumon, Chabrier & Van Hom and new OPAL radiative opacities. The most important feature of our models is that the transport of energy by convection is described by the full spectrum turbulence theory. In particular, we have adopted two versions of this theory for stellar convection: the Canuto & Mazzitelli theory and the more recent, self-consistent theory developed by Canuto, Goldman & Mazzitelli. Both theories, which have no free parameters and account for the whole spectrum of turbulent eddies, represent a great improvement compared to the mixing-length theory approach used thus far in almost all white dwarf studies. Neutrino energy losses as well as crystallization were taken into account. In order to explore the sensitivity of our results to various input model parameters, we vary the model mass from 0.5 to 1.0 Mo in intervals of 0.1 Mo, and the helium layer mass in the interval of 10-6 ~ MHe/M* ~ 10- 2 • The emphasis is put mainly on the behaviour of the evolving outer convection zone. In particular, we analyse the dependence of the location of the theoretical blue edge of the instability strip on the various input parameters. We find that the new ingredients we have incorporated in this study - mostly the new formulations for stellar convection -lead to theoretical blue edges in agreement with observations of pulsating DB white dwarfs. In this context, the Canuto, Goldman & Mazzitelli self­ consistent theory yields theoretical blue edges somewhat hotter than those given by the Canuto & Mazzitelli theory, which is more consistent with a recent determination of the effective temperature of the hot DBV GD 358. Contrary to previous results, we find that, according to the new theories for convection, non­ variable DB white dwarfs falling within the instability strip cannot be low-mass configurations. In order to compare with previous computations, we include in our calculations the most common parametrizations of the mixing-length theory usually employed in almost all previous white dwarf studies. In this context, we find that the ML2 parametrization provides a reasonable agreement with the observed blue edge for the DB instability strip. However, the profile of the outer convective zone given by the mixing-length theory is markedly different from that given by both of the new convective formulations.