A Two-stage Formalism for Common-envelope Phases of Massive Stars

We propose a new simple formalism to predict the orbital separations after common-envelope phases with massive star donors. focus on fact that red supergiants tend have sizeable radiative layer between dense helium core and convective envelope. Our treats phase in two stages: dynamical in-spiral through outer envelope thermal timescale mass transfer from intershell. With fiducial choices of parameters, typically predicts much wider compared classical energy formalism. Moreover, our final strongly depend donor evolutionary stage companion mass. provides physically-motivated alternative option for population synthesis studies treat evolution. This treatment will impact predictions massive-star binaries, including gravitational-wave sources, X-ray binaries stripped-envelope supernovae.