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 Hz and 10^-1 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.