Evolution of low-mass He stars and implications for electron-capture supernova formation in close binaries
The evolution of low-mass helium (He) stars ($\sim2.5$--$5\,M_\odot$) with neutron-star (NS) companions in close binaries has been extensively studied, but the combined effects of rotation and tidal interaction remain poorly understood. We investigate how rotation, mass transfer, and tidal interactions affect the evolution of low-mass He stars, the formation of electron-capture supernovae (ECSNe), and the properties of the resulting NSs. Using detailed stellar and binary evolution calculations that include mass loss, differential rotation, and tidal interactions, we systematically explore the initial binary parameter space leading to ECSNe. We find that rotation has only a modest effect on the evolution of low-mass He stars. ECSNe occur within a narrow initial He-star mass range of $2.42$--$2.67\,M_\odot$ at solar metallicity ($Z_\odot$) and $2.37$--$2.62\,M_\odot$ at $0.01\,Z_\odot$. The resulting NSs have spin periods of $7.7$--$83.8\,\mathrm{ms}$, magnetic fields of order $10^{12}\,\mathrm{G}$, and rotational energies of $2.6\times10^{48}$--$2.5\times10^{50}\,\mathrm{erg}$, although these values would be substantially reduced if efficient angular-momentum transport mechanisms, such as the Spruit--Tayler dynamo, were included. We further show that the evolutionary outcome is highly sensitive to the initial orbital period, with shorter-period systems undergoing Roche-lobe overflow at earlier evolutionary stages and experiencing stronger binary interactions. Finally, comparison with Galactic double NS systems indicates that most observed binaries can be reproduced in the eccentricity--orbital-period plane by adopting relatively large natal kick velocities.