Masses and envelope binding energies of primary stars at the onset of a common envelope

TL;DR

This paper analyzes the properties of primary stars at the start of common envelope phases in binaries, highlighting the variability of the envelope binding energy parameter and its impact on population-synthesis models.

Contribution

It provides a detailed study of the envelope binding energy and the variability of the lambda parameter, challenging the common assumption of its constancy in models.

Findings

Lambda varies significantly across systems.

Constant lambda assumptions lead to 20-50% errors.

Existing analytic fits can replace oversimplified assumptions.

Abstract

We present basic properties of primary stars that initiate a common envelope (CE) in a binary, while on the giant branch. We use the population-synthesis code described in Politano et al. (2010) and follow the evolution of a population of binary stars up to the point where the primary fills its Roche lobe and initiates a CE. We then collect the properties of each system, in particular the donor mass and the binding energy of the donor's envelope, which are important for the treatment of a CE. We find that for most CEs, the donor mass is sufficiently low to define the core-envelope boundary reasonably well. We compute the envelope-structure parameter {\lambda_\mathrm{env}} from the binding energy and compare its distribution to typical assumptions that are made in population-synthesis codes. We conclude that {\lambda_\mathrm{env}} varies appreciably and that the assumption of a constant value for this parameter results in typical errors of 20--50%. In addition, such an assumption may well result in the implicit assumption of unintended and/or unphysical values for the CE parameter {\alpha_\mathrm{CE}}. Finally, we discuss accurate existing analytic fits for the envelope binding energy, which make these oversimplified assumptions for {\lambda_\mathrm{env}}, and the use of {\lambda_\mathrm{env}} in general, unnecessary.