Population boundaries for Neutron star-White Dwarf binaries in LISA’s amplitude-frequency domain

In an earlier investigation, we proposed population boundaries for both inspiralling and masstransferring double white dwarf (DWD) systems in the distance independent “absolute” amplitudefrequency domain of the proposed space-based gravitational-wave (GW) detector, LISA. The massradius relationship of individual white dwarf stars, in combination with the constraints imposed by Roche geometries, permits us to identify five key population boundaries for DWD systems in various phases of evolution. Here we extend these boundaries to both inspiralling and mass-transferring neutron star-white dwarf (NSWD) binary systems, which occupy distinct sub-domains than DWDs, in the “absolute” amplitude-frequency space. Assuming that the currently known ultra-compact xray binaries (UCXBs) are NSWD systems in conservative mass transfer (CMT) phase, we assess the limits and applicability of our theoretical population boundaries with respect to observations. The fairly known issue of the apparent clustering of UCXBs in the orbital period range of 40 ∼ 50 minutes can also be explained through our population boundaries, noting that the evolutionary time-scale for these systems is approaching the hubble time, hence more systems accumulate at longer orbital periods. We suggest that if LISA measures just the GW amplitude h and frequency f and if by independent means we know the (DWD or NSWD) binary system is undergoing conservative mass transfer, then the population boundaries proposed here can be used to set limits on the distance to these binaries. Subject headings: accretion, accretion disks – binaries: close — gravitational waves — stars: white dwarfs, neutron stars