Population boundaries and gravitational-wave templates for evolving white dwarf binaries

We present results from our analysis of double white dwarf (DWD) binary star systems in the inspiraling and mass-transfer stages of their evolution. Theoretical constraints on the properties of the white dwarf stars allow us to map out the DWD trajectories in the gravitational-wave amplitude-frequency domain and to identify population boundaries that define distinct sub-domains where inspiraling and/or mass-transferring systems will and will not be found. We identify for what subset of these populations it should be possible to measure frequency changes and, hence, directly follow orbit evolutions given the anticipated operational time of the proposed space-based gravitational-wave detector, LISA. We show how such measurements should permit the determination of binary system parameters, such as luminosity distances and chirp masses, for mass-transferring as well as inspiraling systems. We also present results from our efforts to generate gravitational-wave templates for a subset of mass-transferring DWD systems that fall into one of the above mentioned sub-domains. Realizing that the templates from a point-mass approximation prove to be inadequate when the radii of the stars are comparable to the binary separation, we build an evolutionary model that includes finite-size effects such as the spin of the stars and tidal and rotational distortions. In two cases, we compare our model evolution with three-dimensional hydrodynamical models of mass-transferring binaries to demonstrate the accuracy of our results. We conclude that the match is good, except during the final phase of the evolution when the mass transfer rate is rapidly increasing and the mass donating star is severely distorted