Population Boundaries for Galactic White Dwarf Binaries in LISA ’s Amplitude‐Frequency Domain

Abstract

Detached, inspiraling and semi-detached, mass-transferring double white dwarf (DWD) binary systems are both expected to be important sources for the proposed space-based gravitational-wave detector, LISA. The mass-radius relationship of individual white dwarf stars in combination with the constraints imposed by Roche geometries permit us to identify population boundaries for DWD systems in LISA's ``absolute'' amplitude-frequency diagram. With five key population boundaries in place, we are able to identify four principal population sub-domains, including one sub-domain that identifies where progenitors of Type Ia supernovae will reside. Given one full year of uninterrupted operation, LISA should be able to measure the rate at which the gravitational-wave frequency $f$ and, hence, the orbital period is changing in the highest frequency subpopulation of our Galaxy's DWD systems. We provide a formula by which the distance to each DWD system in this subpopulation can be determined; in addition, we show how the masses of the individual white dwarf stars in mass-transferring systems may be calculated.