Formation of Recycled Pulsars in Common Envelope Binaries

We present a systematic study of the evolution of low- and intermediate-mass X-ray binaries (L/IMXBs) consisting of a $1.4\,M_{\odot}$ neutron star (NS) and a donor star of mass $1-8\,M_{\odot}$. Using grids of detailed MESA simulations, we show that for donor masses of $2-8\,M_{\odot}$, mass transfer may be dynamically unstable, leading to a common envelope (CE) phase. By adopting CE ejection efficiencies in the range $α_{\rm CE} = 0.3-3.0$, we find that post-CE binaries frequently experience a CE decoupling phase (CEDP), which plays a critical role in determining their final orbital and compositional properties. Systems with initial donor masses $\gtrsim 3.5\,M_{\odot}$ predominantly evolve into NS binaries with carbon-oxygen or oxygen-neon white dwarfs (WDs) with masses between $0.5\,M_{\odot}$ and $1.4\,M_{\odot}$. Comparison with the observed population of binary pulsars with a WD companion shows better agreement with higher CE ejection efficiencies ($α_{\rm CE} = 3.0$). Furthermore, we demonstrate that NSs can accrete a sufficient amount of matter ($\gtrsim 0.01\,M_{\odot}$) during the CEDP and subsequent Case BA/BB/BC mass transfer phases to be effectively recycled into millisecond pulsars. We identify two distinct evolutionary channels capable of reproducing the observed characteristics of the millisecond pulsar PSR J1928+1815 with a helium-star companion. Our results highlight the importance of the CEDP in the formation of recycled pulsars and provide constraints on the CE ejection efficiency during binary evolution.