Detectability of Ultra-compact X-Ray Binaries as LISA Sources

Ultra-compact X-ray binaries (UCXBs) are low-mass X-ray binaries with ultra-short orbital periods (usually less than 1 hr) and hydrogen-poor donor stars, which are proposed to be potential Laser Interferometer Space Antenna (LISA) sources. In this work, we first employ the Modules for Experiments in Stellar Astrophysics code to examine the parameter space of the progenitors of UCXBs that LISA will detect. Our simulations indicate that the initial binaries with a neutron star and a $0.4\mbox{--}3.5\,{M}_{\odot }$ companion star, in an orbit of initial orbital period smaller than the bifurcation period, could evolve into UCXBs, some of which will emit gravitational wave signals that can be detectable by LISA. However, the initial orbital periods of the binaries that will evolve into UCXB-LISA sources in a distance of 10 kpc are located in a very narrow range, i.e., the formation of these LISA source requires an extreme fine-tuning of initial parameter. According to the characteristic strains and the derived maximum detectable distances, four sources among eight UCXBs with the observed distances are expected to be detected by LISA. Based on the parameter space given by the detailed binary evolution models and the rapid binary star evolution code, the birthrate of UCXBs appearing as LISA sources in the Galaxy is estimated to be $(2\mbox{--}2.6)\times {10}^{-6}\,{\mathrm{yr}}^{-1}$. Considering the contribution of UCXBs in globular clusters, the number of UCXB-LISA sources can reach 240–320. Although the formation condition is severe, the detectability of UCXBs by LISA is still significant because it provides an opportunity to pursue full multi-messenger investigations.