The Chemical Composition of White Dwarfs as a Test of Convective Efficiency during Core Helium Burning

Abstract

Pulsating white dwarfs provide constraints to the evolution of progenitor stars. We revise He-burning stellar models, with particular attention to core convection and to its connection with the nuclear reactions powering energy generation and chemical evolution. Theoretical results are compared to the available measurements for the variable white dwarf GD 358, which indicate a rather large abundance of central oxygen (Metcalfe and coworkers). We show that the attempt to constrain the relevant nuclear reaction rate by means of the white dwarf composition is faced with a large degree of uncertainty related to evaluating the efficiency of convection-induced mixing. By combining the uncertainty of the convection theory with the error on the relevant reaction rate, we derive that the present theoretical prediction for the central oxygen mass fraction in white dwarfs varies between 0.3 and 0.9. Unlike previous claims, we find that models taking into account semiconvection and a moderate C-12(alpha,gamma)O-16 reaction rate are able to account for a high central oxygen abundance. The rate of the C-12(alpha,gamma)O-16 used in these models agrees with the one recently obtained in laboratory experiments by Kunz and coworkers. On the other hand, when semiconvection is inhibited, as in the case of classical models (bare Schwarzschild criterion) or in models with mechanical overshoot, an extremely high rate of the C-12(alpha,gamma)O-16 reaction is needed to account for a large oxygen production. Finally, we show that the apparent discrepancy between our result and those reported in previous studies depends on the method used to avoid the convective runaways (the so-called breathing pulses) that are usually encountered in modeling late stage of core He-burning phase

Can pulsating PG 1159 stars place constraints on the occurrence of core overshooting?

“…We begin by examining typical for situations in which extra mixing episodes beyond the fully convective core during central helium burning are allowed (Straniero et al 2003). In particular, the sharp variation around M r ≈ 0.56 M * induced by mechanical overshoot could be a potential source of mode trapping in the core region.…”

Evolutionary and pulsational properties of white dwarf stars

“…Because of the larger temperatures in the helium burning shell, the oxygen abundance decreases in the outer regions of the carbon-oxygen core. Possible extra-mixing episodes during core He burninglike overshooting and semiconvection (Straniero et al 2003) -and the existing uncertainties in the 12 C(α, γ) 16 O reaction rate turn the carbon-oxygen composition of the core into one of the main sources of uncertainty weighting upon the determination of white dwarf cooling times. The core chemical composition depends also on the initial stellar mass of the progenitor star.…”

The formation and evolution of hydrogen-deficient post-AGB white dwarfs: The emerging chemical profile and the expectations for the PG 1159-DB-DQ evolutionary connection

“…The occurrence of such mixing episodes, particularly core overshooting and/or semiconvection, is suggested by both theoretical and observational evidence. Recently, Straniero et al (2003) have presented an assessment of the inner chemical abundances in a 3 M model star resulting from different mixing processes occurring during the late stage of core helium burning phase. In particular, they conclude that models which incorporate semiconvection or a moderate overshoot (related to the inertia of the moving fluid elements) applied to core and convective shells predict a sharp variation of the chemical composition in the carbon-oxygen core.…”