Black Hole Ultracompact X-Ray Binaries as Galactic Low-frequency Gravitational Wave Sources: the He Star Channel

Black hole (BH) ultracompact X-ray binaries (UCXBs) are potential Galactic low-frequency gravitational wave (GW) sources. As an alternative channel, BH UCXBs can evolve from BH+He star binaries. In this work, we perform a detailed stellar evolution model for the formation and evolution of BH UCXBs evolving from the He star channel to diagnose their detectability as low-frequency GW sources. Our calculations found that some nascent BH+He star binaries after the common-envelope (CE) phase could evolve into UCXB-LISA sources with a maximum GW frequency of $\sim5~\rm mHz$, which can be detected in a distance of 10 kpc (or 100 kpc). Once BH+He star systems become UCXBs through mass transfer, they would emit X-ray luminosities of $\sim10^{38}~\rm erg\, s^{-1}$, making them ideal multimessenger objects. If the initial He-star masses are $\geq 0.7 M_{\odot}$, those systems are likely to experience two Roche lobe overflows, and the X-ray luminosity can reach a maximum of $3.5\times 10^{39}~\rm erg\, s^{-1}$ in the second mass-transfer stage. The initial He-star masses and initial orbital periods of progenitors of Galactic BH UCXB-LISA sources are in the range of 0.32-2.9 $M_{\odot}$ and 0.02-0.19 days, respectively. Nearly all BH+He star binaries in the above parameter space can evolve into GW sources whose chirp masses can be accurately measured. Employing a population synthesis simulation, we predict the birthrate and detection number of Galactic BH UCXB-LISA source evolving from the He star channel are $R=2.2\times10^{-6}~\rm yr^{-1}$ and 33 for an optimistic CE parameter, respectively.