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 Hz and 10 Hz. While the extragalactic background is unlikely to be detected, we suggest that around one to ten galactic NS-WD binaries may be resolved with LISA such that their positions are determined to an accuracy of several degrees on the sky.