Population boundaries for compact white-dwarf binaries in LISA's amplitude-frequency domain

TL;DR

This paper refines population boundaries for white dwarf and neutron star-white dwarf binaries in LISA's amplitude-frequency domain by incorporating non-zero entropy donor models, affecting the predicted distribution and distinguishability of these systems.

Contribution

It introduces modified population boundaries using non-zero entropy donor models, expanding the understanding of DWD and NSWD system distributions in LISA's detection space.

Findings

Mass-transferring systems occupy larger regions in amplitude-frequency space.

Boundaries are smoothed, causing overlaps between DWD and NSWD trajectories.

Some systems may be undetectable due to sensitivity limits or background noise.

Abstract

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, {\it 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 non-zero entropy donor M-R relations of \cite{DB2003} 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 \cite{Deloyeetal2007}. 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 cut-off described in our earlier T=0 model. This will cause an overlap between a DWDs $&$ 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.