Fits for the Convective Envelope Mass in Massive Stars

We explore the evolution of massive stars (>8 M _⊙) with 1D models and present analytical fits to the masses and binding energies of the convective portions of their envelopes. These fits are given as functions of total mass, metallicity, and surface temperature (used as a proxy for evolutionary phase). They enable the application of the two-stage common envelope (CE) formalism in rapid binary population synthesis frameworks. We estimate that the degree of orbital hardening following CE ejection spans 6 orders of magnitude and is a very strong function of the accretor mass, and, to a lesser extent, donor evolutionary phase.