Ultracompact X-ray binaries with He star companions

Ultracompact X-ray binaries (UCXBs) are low-mass X-ray binaries with hydrogen-deficient mass donors and ultrashort orbital periods. They have been suggested to be the potential Laser Interferometer Space Antenna (LISA) sources in the low-frequency region. Several channels for the formation of UCXBs have been proposed so far. In this paper, we carried out a systematic study on the He star donor channel, in which a neutron star (NS) accretes matter from a He main-sequence (MS) star through Roche lobe overflow, where the mass transfer is driven by the gravitational wave radiation. First, we followed the long-term evolution of the NS+He MS binaries by employing the stellar evolution code Modules for Experiments in Stellar Astrophysics (MESA ), and thereby obtained the initial parameter spaces for the production of UCXBs. We then used these results to perform a detailed binary population synthesis approach to obtain the Galactic rates of UCXBs through this channel. We estimate the Galactic rates of UCXBs appearing as LISA sources to be ${\sim} 3.1\!-\!11.9\, \rm Myr^{-1}$ through this channel, and the number of such UCXB-LISA sources in the Galaxy can reach about 1-26 calibrated by observations. This work indicates that the He star donor channel may contribute significantly to the Galactic UCXB formation rate. We found that the evolutionary tracks of UCXBs through this channel can account for the location of the five transient sources with relatively long orbital periods quite well. We also found that such UCXBs can be identified by their locations in the mass-transfer rate versus the orbital period diagram.