Double core evolution. VII. The infall of a neutron star through the envelope of its massive star companion

Binary systems with properties similar to those of high-mass X-ray binaries are evolved through the common envelope phase. Three-dimensional simulations show that the timescale of the infall phase of the neutron star depends upon the evolutionary state of its massive companion. We find that tidal torques more effectively accelerate common envelope evolution for companions in their late core helium-burning stage and that the infall phase is rapid (∼several initial orbital periods). For less evolved companions the decay of the orbit is longer; however, once the neutron star is deeply embedded within the companion's envelope the timescale for orbital decay decreases rapidly. As the neutron star encounters the high-density region surrounding the helium core of its massive companion, the rate of energy loss from the orbit increases dramatically leading to either partial or nearly total envelope ejection. The outcome of the common envelope phase depends upon the structure of the evolved companion. In particular, it is found that the entire common envelope can be ejected by the interaction of the neutron star with a red supergiant companion in binaries with orbital periods similar to those of long-period Be X-ray binaries. For orbital periods ≳ 0.8-2 yr (for companions of mass 12-24 M_⊙) it is likely that a binary will survive the common envelope phase. For these systems, the structure of the progenitor star is characterized by a steep density gradient above the helium core, and the common envelope phase ends with a spin up of the envelope to within 50%-60% of corotation and with a slow mass outflow. The efficiency of mass ejection is found to be ∼30%-40%. For less evolved companions, there is insufficient energy in the orbit to unbind the common envelope and only a fraction of it is ejected. Since the timescale for orbital decay is always shorter than the mass-loss timescale from the common envelope, the two cores will likely merge to form a Thorne-Zytkow object. Implications for the origin of Cyg X-3, an X-ray source consisting of a Wolf-Rayet star and a compact companion, and for the fate of the remnant binary consisting of a helium star and a neutron star are briefly discussed.