Electron conduction opacities at the transition between moderate and strong degeneracy: Uncertainties and impacts on stellar models

Abstract

Electron conduction opacities are one of the main physics inputs for the calculation of low- and intermediate-mass stellar models. A critical question considers how to devise a bridge when calculating both moderate and strong degeneracy, which are necessarily performed adopting different methods. The density-temperature regime at the boundary between moderate and strong degeneracy is, in fact, crucial for modelling the helium cores of red giant branch stars and the hydrogen-helium envelopes of white dwarfs. Prompted by newly published, improved calculations of electron thermal conductivities and opacities for moderate degeneracy, we study different, physically motivated prescriptions to bridge these new computations with well-established results in the regime of strong degeneracy. We find that these varied prescriptions have a sizable impact on the predicted He-core masses at the He-flash (up to 0.01 M⊙ for initial total masses far from the transition to non-degenerate He-cores and up to ∼0.04 M⊙ for masses around the transition), the tip of the red giant branch (up to ∼0.1 mag), and the zero-age horizontal branch luminosities (up to 0.03 dex for masses far from the transition and up to ∼0.2 dex around the transition), and white dwarf cooling times (up to 40–45% at high luminosities, and up to ∼25% at low luminosities). Current empirical constraints on the tip of the red giant branch and the zero age horizontal branch absolute magnitudes do not yet allow for the definitive exclusion of any of these alternative options for the conductive opacities. Tests against observations of slowly-cooling faint WDs in old stellar populations will need to be performed to see whether they are capable of setting some more stringent constraints on bridging calculations of conductive opacities for moderate and strong degeneracy.