Role of companion orbital energy in ejecting the inner envelope during common-envelope evolution

Determine whether and to what extent the companion’s orbital energy contributes to ejecting material from the inner envelope during common-envelope evolution that forms wide post-common-envelope binaries, and establish whether the envelope binding energy should be computed over the entire envelope (from the core to the photosphere) or only over the material exterior to the final orbital separation.

Background

Standard practice when applying the alpha-formalism computes the envelope binding energy by integrating from the core–envelope boundary to the photosphere. For wide post-common-envelope binaries, the companion does not spiral into the deep interior, raising the question of whether the companion’s orbital energy actually acts on the inner envelope.

The authors highlight that if only the outer envelope is relevant for ejection, integrating binding energies from the observed/final orbital separation outward could be more appropriate. This choice significantly affects the total energy budget and the predicted post-CEE separations in their MESA-based analyses.