Electron-capture supernovae in NS+He star systems and the double neutron star systems

Electron-capture supernovae (EC-SNe) provide an alternative channel for producing neutron stars (NSs). They play an important role in the formation of double NS (DNS) systems and the chemical evolution of galaxies, and contribute to the NS mass distribution in observations. It is generally believed that EC-SNe originate from $e$-captures on $\rm^{24}Mg$ and $\rm^{20}Ne$ in the massive degenerate oxygen-neon (ONe) cores with masses close to the Chandrasekhar limit ($M_{\rm Ch}$). However, the origin of EC-SNe is still uncertain. In this paper, we systematically studied the EC-SNe in NS+He star systems by considering the explosive oxygen burning that may occur in the near-$M_{\rm Ch}$ ONe core. We provided the initial parameter spaces for producing EC-SNe in the initial orbital period $-$ initial He star mass (log$P_{\rm orb}^{\rm i}-M_{\rm He}^{\rm i}$) diagram, and found that both $M_{\rm He}^{\rm i}$ and minimum $P_{\rm orb}^{\rm i}$ for EC-SNe increase with metallicity. Then, by considering NS kicks added to the newborn NS, we investigated the properties of the formed DNS systems after the He star companions collapse into NSs, such as the orbital periods, eccentricities and spin periods of recycle pulsars ($P_{\rm spin}$), etc. The results show that most of the observed DNS systems can be produced by NS kicks of $\lesssim50\rm\,km\,s^{-1}$. In addition, we found that NSs could accrete more material if the residual H envelope on the He star companions is considered, which can form the mildly recycled pulsars ($P_{\rm spin}\sim20\,$ms) in DNS systems.