Compact intermediate-mass black hole X-ray binaries: potential LISA sources?

The scientific aim of the space gravitational wave (GW) detector Laser Interferometer Space Antenna (LISA) that was scheduled to launch in the early 2030s is to detect the low-frequency GW signals in the Galaxy. Its main candidate GW sources are compact binaries of white dwarfs and neutron stars. In this work, we examine whether compact intermediate-mass black hole (IMBH) X-ray binaries could be potential LISA sources. Our simulations indicate that IMBH binary with a 1000 $M_{\odot}$ IMBH and a 3 $M_{\odot}$ donor star in an orbit of initial orbital period near the so-called bifurcation period of 0.77 d could evolve into an ultra-compact X-ray binary, which will emit GW signals with maximum frequency of 2.5 mHz. According to the evolutionary tracks of characteristic strain, IMBH X-ray binaries with the initial donor-star masses of $1-3~M_{\odot}$ and the initial orbital periods slightly less than the bifurcation periods will be detectable by the LISA in a distance of 15 kpc. Assuming each of 60 Galactic globular clusters hosts a 1000 $M_{\odot}$ IMBH, the maximum number of compact IMBH X-ray binaries that LISA will detect in the Galaxy should be less than ten. Therefore, the detectability of compact IMBH X-ray binaries by the LISA is not optimistic.