Modeling High Mass X-ray Binaries to Double Neutron Stars through Common Envelope Evolution

We present detailed evolutionary simulations of wide binary systems with high-mass ($8-20\,M_{\odot}$) donor stars and a $1.4\,M_{\odot}$ neutron star. Mass transfer in such binaries is dynamically unstable and common envelope (CE) evolution is followed. We use a recently developed prescription to deal with CE evolution and consider various CE ejection efficiencies varying in the range of $0.1-3.0$. We focus on the evolutionary consequences of the binaries survived CE evolution. We demonstrate that it is possible for the binaries to enter a CE decoupling phase (CEDP) when the donor stars are partially stripped leaving a hydrogen envelope of $\lesssim1.0-4.0\,M_\odot$ after CE evolution. This phase is expected to last $\sim 10^4-10^5\,\rm yr$, during which mass transfer occurs stably via Roche lobe overflow with super-Eddington rates. Identification of some X-ray binaries in a CEDP is important for the understanding of the physics of CE evolution itself, the origin of ultraluminous X-ray sources, and the recycling process of accreting pulsars. Also, we discuss the formation of double neutron stars and the occurrence of ultra-stripped supernovae according to the results from our simulations. On the whole, the properties of post-CE binaries are sensitive to the options of CE ejection efficiencies.