The probability distribution of binary pulsar coalescence rates. II. Neutron star-white dwarf binaries

We consider the statistics of pulsar binaries with white dwarf companions (NS-WD). Using the statistical analysis method developed by Kim and coworkers, we calculate the Galactic coalescence rate of NS-WD binaries due to gravitational wave emission. We find that the most likely values for the total Galactic coalescence rate (R_tot) of NS-WD binaries lie in the range 0.2-10 Myr^-1, depending on different assumed pulsar population models. For our reference model, we obtain R_tot = 4.1 _-2.56^+2.25 Myr^-1 at a 68% statistical confidence level. These rate estimates are not corrected for pulsar beaming, and as such they are found to be about a factor of 20 smaller than the Galactic coalescence rate estimates for double neutron star systems. Based on our rate estimates, we calculate the gravitational wave background due to coalescing NS-WD binaries out to extragalactic distances within the frequency band of the Laser Interferometer Space Antenna. We find the contribution from NS-WD binaries to the gravitational wave background to be negligibly.