Gravitational-wave background of neutron star-white dwarf binaries

We discuss the stochastic background of gravitational waves from ultra-compact neutron star-white dwarf (NS-WD) binaries at cosmological distances. Under the assumption that accreting neutron stars and donor white dwarf stars form most of the low-mass X-ray binaries (LMXBs), our calculation makes use of recent results related to the luminosity function determined from X-ray observations. Even after accounting for detached NS-WD binaries not captured in X-ray data, the NS-WD background is at least an order of magnitude below that due to extragalactic white dwarf-white dwarf binaries and below the detectability level of the Laser Interferometer Space Antenna (LISA) at frequencies between 10(-5) and 10(-1) Hz. While the extragalactic background is unlikely to be detected, we suggest that around one to 10 galactic NS-WD binaries may be resolved with LISA such that their positions are determined to an accuracy of several degrees on the sky.