2009ApJ...697.2089K

In an earlier investigation, we proposed population boundaries for both inspiralling and mass-transferring double white dwarf (DWD) systems in the distance independent "absolute" amplitude-frequency domain of the proposed space-based gravitational-wave (GW) detector, Laser Interferometer Space Antenna (LISA). The degenerate zero-temperature mass-radius (M - R) relationship of individual white dwarf stars that we assumed, 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 use the nonzero entropy donor M - R relations of Deloye & Bildsten to modify these boundaries for both DWD and **neutron star-white dwarf (NSWD) binary systems. We find that the mass-transferring systems occupy a larger fraction of space in "absolute" amplitude-frequency domain compared to the simpler T = 0 donor model. We also discuss how these boundaries are modified with the new evolutionary phases found by Deloye et al.. In the initial contact phase, we find that the contact boundaries, which are the result of end of inspiral evolution, would have some width, as opposed to an abrupt cutoff described in our earlier T = 0 model. This will cause an overlap between a DWDs and NSWDs evolutionary trajectories, making them indistinguishable with only LISA observations within this region. In the cooling phase of the donor, which follows after the adiabatic donor evolution, the radius contracts, mass-transfer rate drops and slows down the orbital period evolution. Depending upon the entropy of the donor, these systems may then lie inside the fully degenerate T = 0 boundaries, but LISA may be unable to detect these systems as they might be below the sensitivity limit or within the unresolved DWD background noise. We assess the limits and applicability of our theoretical population boundaries with respect to observations and find that a measurement of by LISA at high frequencies (log [f] ≥ 2) would likely distinguish between DWD/NSWD binary. For low-frequency sources, GW observations alone would unlikely tell us about the binary components, without the help of electromagnetic observations.