The interacting double white dwarf population with LISA: Stochastic foreground and resolved sources

Aims. We investigate the impact of tidal torques and mass transfer on the population of double white dwarfs that will be observed with LISA. Methods. Our Galactic distribution of double white dwarfs is based on the combination of a cosmological simulation and a binary population synthesis model. We used a semi-analytical model to evolve double white dwarf binaries considering ten different hypotheses for the efficiency of tidal coupling and three hypotheses for the birth spins of white dwarfs. We then estimated the stochastic foreground and the population of resolvable binaries for LISA for these different combinations. Results. Our predicted double white dwarf binary distribution can differ substantially from the distribution expected if only gravitational waves (GWs) are considered. If white dwarfs spin slowly, then we predict an excess of systems around a few due to binaries that outspiral after the onset of mass transfer. This excess of systems leads to differences in the confusion noise, which are most pronounced for strong tidal coupling. In that case, we find a significantly higher number of resolvable binaries than in the GW-only scenario. If instead white dwarfs spin rapidly and tidal coupling is weak, then we find no excess around a few mHz, and the confusion noise due to double white dwarfs is very low. In that scenario, we also predict a subpopulation of outspiralling binaries below 0.1 mHz. Using the Fisher matrix approximation, we estimate the uncertainty on the GW-frequency derivative of resolvable systems. We find that, even for non-accreting systems, the mismodelling error due to neglecting effects other than GWs is larger than the statistical uncertainty, and thus this neglect would lead to biased estimates for mass and distance. Conclusions. Our results suggest that the population of double white dwarfs is likely to be different from what is expected in the standard picture, which highlights the need for flexible tools in LISA data analysis. Because our semi-analytical model hinges upon a simplistic approach to determining the stability of mass accretion, it will be important to deepen our comprehension of stability in mass-transferring double white dwarf binaries.