The gravitational wave signal from diverse populations of double white dwarf binaries in the Galaxy

Context. The gravitational wave (GW) background in the range 0.01-30 mHz has been assumed to be dominated by unresolved radiation from double white dwarf binaries (DWDs). Recent investigations indicate that, at short periods, a number of DWDs should be resolvable sources of GW. Aims. We characterize the GW signal which would be detected by LISA from DWDs in the Galaxy. Methods. We have constructed a Galactic model in which we consider distinct contributions from the bulge, thin disc, thick disc, and halo, and subsequently executed a population synthesis approach to determine the birth rates, numbers, and period distributions of DWDs within each component. Results. In the Galaxy as a whole, our model predicts the current birth rate of DWDs to be 3.21 x 10(-2) yr(-1), the local density to be 2.2 x 10(-4) pc(-3) and the total number to be 2.76 x 10(8). Assuming SNIa are formed from the merger of two CO white dwarfs, the SNIa rate should be 0.0013 yr(-1). The frequency spectra of DWD strain amplitude and number distribution are presented as a function of galactic component, DWD type, formation channel, and metallicity. Conclusions. We confirm that CO+He and He+He white dwarf (WD) pairs should dominate the GW signal at very high frequencies (log f Hz(-1) > -2.3), while CO+CO and ONeMg WD pairs have a dominant contribution at log f Hz(-1) <= -2.3. Formation channels involving two common-envelope (CE) phases or a stable Roche lobe overflow phase followed by a CE phase dominate the production of DWDs detectable by LISA at log f Hz(-1) > -4.5. DWDs with the shortest orbital periods will come from the CE+CE channel. The Exposed Core plus CE channel is a minor channel. A number of resolved DWDs would be detected, making up 0.012% of the total number of DWDs in the Galaxy. The majority of these would be CO+He and He+He pairs formed through the CE+CE channel.