Merger by migration at the final phase of common envelope evolution

I find the common envelope (CE) energy formalism, the CE α-prescription, to be inadequate to predict the final orbital separation of the CE evolution in massive envelopes. I find that when the orbital separation decreases to ∼10 times the final orbital separation predicted by the CE α-prescription, the companion has not enough mass in its vicinity to carry away its angular momentum. The core-secondary binary system must get rid of its angular momentum by interacting with mass further out. The binary system interacts gravitationally with a rapidly-rotating flat envelope, in a situation that resembles planet-migration in protoplanetary disks. The envelope convection of the giant carries energy and angular momentum outward. The basic assumption of the CE α-prescription, that the binary system's gravitational energy goes to unbind the envelope, breaks down. Based on that, I claim that merger is a common outcome of the CE evolution of AGB and red super-giants stars with an envelope to secondary mass ratio of M _env/M ₂ ≳ 5. I discuss some other puzzling observations that might be explained by the migration and merger processes.